diff --git a/lib/std/crypto.zig b/lib/std/crypto.zig index b9191585ec..522a545fcf 100644 --- a/lib/std/crypto.zig +++ b/lib/std/crypto.zig @@ -64,6 +64,7 @@ pub const ecc = struct { pub const P256 = @import("crypto/pcurves/p256.zig").P256; pub const P384 = @import("crypto/pcurves/p384.zig").P384; pub const Ristretto255 = @import("crypto/25519/ristretto255.zig").Ristretto255; + pub const Secp256k1 = @import("crypto/pcurves/secp256k1.zig").Secp256k1; }; /// Hash functions. @@ -205,6 +206,7 @@ test { _ = ecc.P256; _ = ecc.P384; _ = ecc.Ristretto255; + _ = ecc.Secp256k1; _ = hash.blake2; _ = hash.Blake3; diff --git a/lib/std/crypto/pcurves/common.zig b/lib/std/crypto/pcurves/common.zig index 1160334fe4..5abc6d348f 100644 --- a/lib/std/crypto/pcurves/common.zig +++ b/lib/std/crypto/pcurves/common.zig @@ -295,6 +295,17 @@ pub fn Field(comptime params: FieldParams) type { const x63 = x32.sqn(31).mul(x31); const x126 = x63.sqn(63).mul(x63); return x126.sqn(126).mul(x126).sqn(3).mul(t111).sqn(33).mul(x32).sqn(64).mul(x2).sqn(30); + } else if (field_order == 115792089237316195423570985008687907853269984665640564039457584007908834671663) { + const t11 = x2.mul(x2.sq()); + const t1111 = t11.mul(t11.sqn(2)); + const t11111 = x2.mul(t1111.sq()); + const t1111111 = t11.mul(t11111.sqn(2)); + const x11 = t1111111.sqn(4).mul(t1111); + const x22 = x11.sqn(11).mul(x11); + const x27 = x22.sqn(5).mul(t11111); + const x54 = x27.sqn(27).mul(x27); + const x108 = x54.sqn(54).mul(x54); + return x108.sqn(108).mul(x108).sqn(7).mul(t1111111).sqn(23).mul(x22).sqn(6).mul(t11).sqn(2); } else { return x2.pow(std.meta.Int(.unsigned, field_bits), (field_order + 1) / 4); } diff --git a/lib/std/crypto/pcurves/secp256k1.zig b/lib/std/crypto/pcurves/secp256k1.zig new file mode 100644 index 0000000000..79698bd7dd --- /dev/null +++ b/lib/std/crypto/pcurves/secp256k1.zig @@ -0,0 +1,556 @@ +const std = @import("std"); +const crypto = std.crypto; +const math = std.math; +const mem = std.mem; +const meta = std.meta; + +const EncodingError = crypto.errors.EncodingError; +const IdentityElementError = crypto.errors.IdentityElementError; +const NonCanonicalError = crypto.errors.NonCanonicalError; +const NotSquareError = crypto.errors.NotSquareError; + +/// Group operations over secp256k1. +pub const Secp256k1 = struct { + /// The underlying prime field. + pub const Fe = @import("secp256k1/field.zig").Fe; + /// Field arithmetic mod the order of the main subgroup. + pub const scalar = @import("secp256k1/scalar.zig"); + + x: Fe, + y: Fe, + z: Fe = Fe.one, + + is_base: bool = false, + + /// The secp256k1 base point. + pub const basePoint = Secp256k1{ + .x = Fe.fromInt(55066263022277343669578718895168534326250603453777594175500187360389116729240) catch unreachable, + .y = Fe.fromInt(32670510020758816978083085130507043184471273380659243275938904335757337482424) catch unreachable, + .z = Fe.one, + .is_base = true, + }; + + /// The secp256k1 neutral element. + pub const identityElement = Secp256k1{ .x = Fe.zero, .y = Fe.one, .z = Fe.zero }; + + pub const B = Fe.fromInt(7) catch unreachable; + + pub const Endormorphism = struct { + const lambda: u256 = 37718080363155996902926221483475020450927657555482586988616620542887997980018; + const beta: u256 = 55594575648329892869085402983802832744385952214688224221778511981742606582254; + + const lambda_s = s: { + var buf: [32]u8 = undefined; + mem.writeIntLittle(u256, &buf, Endormorphism.lambda); + break :s buf; + }; + + pub const SplitScalar = struct { + r1: [32]u8, + r2: [32]u8, + }; + + /// Compute r1 and r2 so that k = r1 + r2*lambda (mod L). + pub fn splitScalar(s: [32]u8, endian: std.builtin.Endian) SplitScalar { + const b1_neg_s = comptime s: { + var buf: [32]u8 = undefined; + mem.writeIntLittle(u256, &buf, 303414439467246543595250775667605759171); + break :s buf; + }; + const b2_neg_s = comptime s: { + var buf: [32]u8 = undefined; + mem.writeIntLittle(u256, &buf, scalar.field_order - 64502973549206556628585045361533709077); + break :s buf; + }; + const k = mem.readInt(u256, &s, endian); + + const t1 = math.mulWide(u256, k, 21949224512762693861512883645436906316123769664773102907882521278123970637873); + const t2 = math.mulWide(u256, k, 103246583619904461035481197785446227098457807945486720222659797044629401272177); + + const c1 = @truncate(u128, t1 >> 384) + @truncate(u1, t1 >> 383); + const c2 = @truncate(u128, t2 >> 384) + @truncate(u1, t2 >> 383); + + var buf: [32]u8 = undefined; + + mem.writeIntLittle(u256, &buf, c1); + const c1x = scalar.mul(buf, b1_neg_s, .Little) catch unreachable; + + mem.writeIntLittle(u256, &buf, c2); + const c2x = scalar.mul(buf, b2_neg_s, .Little) catch unreachable; + + const r2 = scalar.add(c1x, c2x, .Little) catch unreachable; + + var r1 = scalar.mul(r2, lambda_s, .Little) catch unreachable; + r1 = scalar.sub(s, r1, .Little) catch unreachable; + + return SplitScalar{ .r1 = r1, .r2 = r2 }; + } + }; + + /// Reject the neutral element. + pub fn rejectIdentity(p: Secp256k1) IdentityElementError!void { + if (p.x.isZero()) { + return error.IdentityElement; + } + } + + /// Create a point from affine coordinates after checking that they match the curve equation. + pub fn fromAffineCoordinates(p: AffineCoordinates) EncodingError!Secp256k1 { + const x = p.x; + const y = p.y; + const x3B = x.sq().mul(x).add(B); + const yy = y.sq(); + const on_curve = @boolToInt(x3B.equivalent(yy)); + const is_identity = @boolToInt(x.equivalent(AffineCoordinates.identityElement.x)) & @boolToInt(y.equivalent(AffineCoordinates.identityElement.y)); + if ((on_curve | is_identity) == 0) { + return error.InvalidEncoding; + } + var ret = Secp256k1{ .x = x, .y = y, .z = Fe.one }; + ret.z.cMov(Secp256k1.identityElement.z, is_identity); + return ret; + } + + /// Create a point from serialized affine coordinates. + pub fn fromSerializedAffineCoordinates(xs: [32]u8, ys: [32]u8, endian: std.builtin.Endian) (NonCanonicalError || EncodingError)!Secp256k1 { + const x = try Fe.fromBytes(xs, endian); + const y = try Fe.fromBytes(ys, endian); + return fromAffineCoordinates(.{ .x = x, .y = y }); + } + + /// Recover the Y coordinate from the X coordinate. + pub fn recoverY(x: Fe, is_odd: bool) NotSquareError!Fe { + const x3B = x.sq().mul(x).add(B); + var y = try x3B.sqrt(); + const yn = y.neg(); + y.cMov(yn, @boolToInt(is_odd) ^ @boolToInt(y.isOdd())); + return y; + } + + /// Deserialize a SEC1-encoded point. + pub fn fromSec1(s: []const u8) (EncodingError || NotSquareError || NonCanonicalError)!Secp256k1 { + if (s.len < 1) return error.InvalidEncoding; + const encoding_type = s[0]; + const encoded = s[1..]; + switch (encoding_type) { + 0 => { + if (encoded.len != 0) return error.InvalidEncoding; + return Secp256k1.identityElement; + }, + 2, 3 => { + if (encoded.len != 32) return error.InvalidEncoding; + const x = try Fe.fromBytes(encoded[0..32].*, .Big); + const y_is_odd = (encoding_type == 3); + const y = try recoverY(x, y_is_odd); + return Secp256k1{ .x = x, .y = y }; + }, + 4 => { + if (encoded.len != 64) return error.InvalidEncoding; + const x = try Fe.fromBytes(encoded[0..32].*, .Big); + const y = try Fe.fromBytes(encoded[32..64].*, .Big); + return Secp256k1.fromAffineCoordinates(.{ .x = x, .y = y }); + }, + else => return error.InvalidEncoding, + } + } + + /// Serialize a point using the compressed SEC-1 format. + pub fn toCompressedSec1(p: Secp256k1) [33]u8 { + var out: [33]u8 = undefined; + const xy = p.affineCoordinates(); + out[0] = if (xy.y.isOdd()) 3 else 2; + mem.copy(u8, out[1..], &xy.x.toBytes(.Big)); + return out; + } + + /// Serialize a point using the uncompressed SEC-1 format. + pub fn toUncompressedSec1(p: Secp256k1) [65]u8 { + var out: [65]u8 = undefined; + out[0] = 4; + const xy = p.affineCoordinates(); + mem.copy(u8, out[1..33], &xy.x.toBytes(.Big)); + mem.copy(u8, out[33..65], &xy.y.toBytes(.Big)); + return out; + } + + /// Return a random point. + pub fn random() Secp256k1 { + const n = scalar.random(.Little); + return basePoint.mul(n, .Little) catch unreachable; + } + + /// Flip the sign of the X coordinate. + pub fn neg(p: Secp256k1) Secp256k1 { + return .{ .x = p.x, .y = p.y.neg(), .z = p.z }; + } + + /// Double a secp256k1 point. + // Algorithm 9 from https://eprint.iacr.org/2015/1060.pdf + pub fn dbl(p: Secp256k1) Secp256k1 { + var t0 = p.y.sq(); + var Z3 = t0.dbl(); + Z3 = Z3.dbl(); + Z3 = Z3.dbl(); + var t1 = p.y.mul(p.z); + var t2 = p.z.sq(); + // b3 = (2^2)^2 + 2^2 + 1 + const t2_4 = t2.dbl().dbl(); + t2 = t2_4.dbl().dbl().add(t2_4).add(t2); + var X3 = t2.mul(Z3); + var Y3 = t0.add(t2); + Z3 = t1.mul(Z3); + t1 = t2.dbl(); + t2 = t1.add(t2); + t0 = t0.sub(t2); + Y3 = t0.mul(Y3); + Y3 = X3.add(Y3); + t1 = p.x.mul(p.y); + X3 = t0.mul(t1); + X3 = X3.dbl(); + return .{ + .x = X3, + .y = Y3, + .z = Z3, + }; + } + + /// Add secp256k1 points, the second being specified using affine coordinates. + // Algorithm 8 from https://eprint.iacr.org/2015/1060.pdf + pub fn addMixed(p: Secp256k1, q: AffineCoordinates) Secp256k1 { + var t0 = p.x.mul(q.x); + var t1 = p.y.mul(q.y); + var t3 = q.x.add(q.y); + var t4 = p.x.add(p.y1); + t3 = t3.mul(t4); + t4 = t0.add(t1); + t3 = t3.sub(t4); + t4 = q.y.mul(p.z); + t4 = t4.add(p.y); + var Y3 = q.x.mul(p.z); + Y3 = Y3.add(p.x); + var X3 = t0.dbl(); + t0 = X3.add(t0); + // b3 = (2^2)^2 + 2^2 + 1 + const t2_4 = p.z.dbl().dbl(); + var t2 = t2_4.dbl().dbl().add(t2_4).add(p.z); + var Z3 = t1.add(t2); + t1 = t1.sub(t2); + const Y3_4 = Y3.dbl().dbl(); + Y3 = Y3_4.dbl().dbl().add(Y3_4).add(Y3); + X3 = t4.mul(Y3); + t2 = t3.mul(t1); + X3 = t2.sub(X3); + Y3 = Y3.mul(t0); + t1 = t1.mul(Z3); + Y3 = t1.add(Y3); + t0 = t0.mul(t3); + Z3 = Z3.mul(t4); + Z3 = Z3.add(t0); + + var ret = Secp256k1{ + .x = X3, + .y = Y3, + .z = Z3, + }; + ret.cMov(p, @boolToInt(q.x.isZero())); + return ret; + } + + /// Add secp256k1 points. + // Algorithm 7 from https://eprint.iacr.org/2015/1060.pdf + pub fn add(p: Secp256k1, q: Secp256k1) Secp256k1 { + var t0 = p.x.mul(q.x); + var t1 = p.y.mul(q.y); + var t2 = p.z.mul(q.z); + var t3 = p.x.add(p.y); + var t4 = q.x.add(q.y); + t3 = t3.mul(t4); + t4 = t0.add(t1); + t3 = t3.sub(t4); + t4 = p.y.add(p.z); + var X3 = q.y.add(q.z); + t4 = t4.mul(X3); + X3 = t1.add(t2); + t4 = t4.sub(X3); + X3 = p.x.add(p.z); + var Y3 = q.x.add(q.z); + X3 = X3.mul(Y3); + Y3 = t0.add(t2); + Y3 = X3.sub(Y3); + X3 = t0.dbl(); + t0 = X3.add(t0); + // b3 = (2^2)^2 + 2^2 + 1 + const t2_4 = t2.dbl().dbl(); + t2 = t2_4.dbl().dbl().add(t2_4).add(t2); + var Z3 = t1.add(t2); + t1 = t1.sub(t2); + const Y3_4 = Y3.dbl().dbl(); + Y3 = Y3_4.dbl().dbl().add(Y3_4).add(Y3); + X3 = t4.mul(Y3); + t2 = t3.mul(t1); + X3 = t2.sub(X3); + Y3 = Y3.mul(t0); + t1 = t1.mul(Z3); + Y3 = t1.add(Y3); + t0 = t0.mul(t3); + Z3 = Z3.mul(t4); + Z3 = Z3.add(t0); + + return .{ + .x = X3, + .y = Y3, + .z = Z3, + }; + } + + /// Subtract secp256k1 points. + pub fn sub(p: Secp256k1, q: Secp256k1) Secp256k1 { + return p.add(q.neg()); + } + + /// Subtract secp256k1 points, the second being specified using affine coordinates. + pub fn subMixed(p: Secp256k1, q: AffineCoordinates) Secp256k1 { + return p.addMixed(q.neg()); + } + + /// Return affine coordinates. + pub fn affineCoordinates(p: Secp256k1) AffineCoordinates { + const zinv = p.z.invert(); + var ret = AffineCoordinates{ + .x = p.x.mul(zinv), + .y = p.y.mul(zinv), + }; + ret.cMov(AffineCoordinates.identityElement, @boolToInt(p.x.isZero())); + return ret; + } + + /// Return true if both coordinate sets represent the same point. + pub fn equivalent(a: Secp256k1, b: Secp256k1) bool { + if (a.sub(b).rejectIdentity()) { + return false; + } else |_| { + return true; + } + } + + fn cMov(p: *Secp256k1, a: Secp256k1, c: u1) void { + p.x.cMov(a.x, c); + p.y.cMov(a.y, c); + p.z.cMov(a.z, c); + } + + fn pcSelect(comptime n: usize, pc: *const [n]Secp256k1, b: u8) Secp256k1 { + var t = Secp256k1.identityElement; + comptime var i: u8 = 1; + inline while (i < pc.len) : (i += 1) { + t.cMov(pc[i], @truncate(u1, (@as(usize, b ^ i) -% 1) >> 8)); + } + return t; + } + + fn slide(s: [32]u8) [2 * 32 + 1]i8 { + var e: [2 * 32 + 1]i8 = undefined; + for (s) |x, i| { + e[i * 2 + 0] = @as(i8, @truncate(u4, x)); + e[i * 2 + 1] = @as(i8, @truncate(u4, x >> 4)); + } + // Now, e[0..63] is between 0 and 15, e[63] is between 0 and 7 + var carry: i8 = 0; + for (e[0..64]) |*x| { + x.* += carry; + carry = (x.* + 8) >> 4; + x.* -= carry * 16; + std.debug.assert(x.* >= -8 and x.* <= 8); + } + e[64] = carry; + // Now, e[*] is between -8 and 8, including e[64] + std.debug.assert(carry >= -8 and carry <= 8); + return e; + } + + fn pcMul(pc: *const [9]Secp256k1, s: [32]u8, comptime vartime: bool) IdentityElementError!Secp256k1 { + std.debug.assert(vartime); + const e = slide(s); + var q = Secp256k1.identityElement; + var pos = e.len - 1; + while (true) : (pos -= 1) { + const slot = e[pos]; + if (slot > 0) { + q = q.add(pc[@intCast(usize, slot)]); + } else if (slot < 0) { + q = q.sub(pc[@intCast(usize, -slot)]); + } + if (pos == 0) break; + q = q.dbl().dbl().dbl().dbl(); + } + try q.rejectIdentity(); + return q; + } + + fn pcMul16(pc: *const [16]Secp256k1, s: [32]u8, comptime vartime: bool) IdentityElementError!Secp256k1 { + var q = Secp256k1.identityElement; + var pos: usize = 252; + while (true) : (pos -= 4) { + const slot = @truncate(u4, (s[pos >> 3] >> @truncate(u3, pos))); + if (vartime) { + if (slot != 0) { + q = q.add(pc[slot]); + } + } else { + q = q.add(pcSelect(16, pc, slot)); + } + if (pos == 0) break; + q = q.dbl().dbl().dbl().dbl(); + } + try q.rejectIdentity(); + return q; + } + + fn precompute(p: Secp256k1, comptime count: usize) [1 + count]Secp256k1 { + var pc: [1 + count]Secp256k1 = undefined; + pc[0] = Secp256k1.identityElement; + pc[1] = p; + var i: usize = 2; + while (i <= count) : (i += 1) { + pc[i] = if (i % 2 == 0) pc[i / 2].dbl() else pc[i - 1].add(p); + } + return pc; + } + + const basePointPc = pc: { + @setEvalBranchQuota(50000); + break :pc precompute(Secp256k1.basePoint, 15); + }; + + /// Multiply an elliptic curve point by a scalar. + /// Return error.IdentityElement if the result is the identity element. + pub fn mul(p: Secp256k1, s_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 { + const s = if (endian == .Little) s_ else Fe.orderSwap(s_); + if (p.is_base) { + return pcMul16(&basePointPc, s, false); + } + try p.rejectIdentity(); + const pc = precompute(p, 15); + return pcMul16(&pc, s, false); + } + + /// Multiply an elliptic curve point by a *PUBLIC* scalar *IN VARIABLE TIME* + /// This can be used for signature verification. + pub fn mulPublic(p: Secp256k1, s_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 { + const s = if (endian == .Little) s_ else Fe.orderSwap(s_); + const zero = comptime scalar.Scalar.zero.toBytes(.Little); + if (mem.eql(u8, &zero, &s)) { + return error.IdentityElement; + } + const pc = precompute(p, 8); + var lambda_p = try pcMul(&pc, Endormorphism.lambda_s, true); + var split_scalar = Endormorphism.splitScalar(s, .Little); + var px = p; + + // If a key is negative, flip the sign to keep it half-sized, + // and flip the sign of the Y point coordinate to compensate. + if (split_scalar.r1[split_scalar.r1.len / 2] != 0) { + split_scalar.r1 = scalar.neg(split_scalar.r1, .Little) catch zero; + px = px.neg(); + } + if (split_scalar.r2[split_scalar.r2.len / 2] != 0) { + split_scalar.r2 = scalar.neg(split_scalar.r2, .Little) catch zero; + lambda_p = lambda_p.neg(); + } + return mulDoubleBasePublicEndo(px, split_scalar.r1, lambda_p, split_scalar.r2); + } + + // Half-size double-base public multiplication when using the curve endomorphism. + // Scalars must be in little-endian. + // The second point is unlikely to be the generator, so don't even try to use the comptime table for it. + fn mulDoubleBasePublicEndo(p1: Secp256k1, s1: [32]u8, p2: Secp256k1, s2: [32]u8) IdentityElementError!Secp256k1 { + var pc1_array: [9]Secp256k1 = undefined; + const pc1 = if (p1.is_base) basePointPc[0..9] else pc: { + pc1_array = precompute(p1, 8); + break :pc &pc1_array; + }; + const pc2 = precompute(p2, 8); + std.debug.assert(s1[s1.len / 2] == 0); + std.debug.assert(s2[s2.len / 2] == 0); + const e1 = slide(s1); + const e2 = slide(s2); + var q = Secp256k1.identityElement; + var pos: usize = 2 * 32 / 2; // second half is all zero + while (true) : (pos -= 1) { + const slot1 = e1[pos]; + if (slot1 > 0) { + q = q.add(pc1[@intCast(usize, slot1)]); + } else if (slot1 < 0) { + q = q.sub(pc1[@intCast(usize, -slot1)]); + } + const slot2 = e2[pos]; + if (slot2 > 0) { + q = q.add(pc2[@intCast(usize, slot2)]); + } else if (slot2 < 0) { + q = q.sub(pc2[@intCast(usize, -slot2)]); + } + if (pos == 0) break; + q = q.dbl().dbl().dbl().dbl(); + } + try q.rejectIdentity(); + return q; + } + + /// Double-base multiplication of public parameters - Compute (p1*s1)+(p2*s2) *IN VARIABLE TIME* + /// This can be used for signature verification. + pub fn mulDoubleBasePublic(p1: Secp256k1, s1_: [32]u8, p2: Secp256k1, s2_: [32]u8, endian: std.builtin.Endian) IdentityElementError!Secp256k1 { + const s1 = if (endian == .Little) s1_ else Fe.orderSwap(s1_); + const s2 = if (endian == .Little) s2_ else Fe.orderSwap(s2_); + try p1.rejectIdentity(); + var pc1_array: [9]Secp256k1 = undefined; + const pc1 = if (p1.is_base) basePointPc[0..9] else pc: { + pc1_array = precompute(p1, 8); + break :pc &pc1_array; + }; + try p2.rejectIdentity(); + var pc2_array: [9]Secp256k1 = undefined; + const pc2 = if (p2.is_base) basePointPc[0..9] else pc: { + pc2_array = precompute(p2, 8); + break :pc &pc2_array; + }; + const e1 = slide(s1); + const e2 = slide(s2); + var q = Secp256k1.identityElement; + var pos: usize = 2 * 32; + while (true) : (pos -= 1) { + const slot1 = e1[pos]; + if (slot1 > 0) { + q = q.add(pc1[@intCast(usize, slot1)]); + } else if (slot1 < 0) { + q = q.sub(pc1[@intCast(usize, -slot1)]); + } + const slot2 = e2[pos]; + if (slot2 > 0) { + q = q.add(pc2[@intCast(usize, slot2)]); + } else if (slot2 < 0) { + q = q.sub(pc2[@intCast(usize, -slot2)]); + } + if (pos == 0) break; + q = q.dbl().dbl().dbl().dbl(); + } + try q.rejectIdentity(); + return q; + } +}; + +/// A point in affine coordinates. +pub const AffineCoordinates = struct { + x: Secp256k1.Fe, + y: Secp256k1.Fe, + + /// Identity element in affine coordinates. + pub const identityElement = AffineCoordinates{ .x = Secp256k1.identityElement.x, .y = Secp256k1.identityElement.y }; + + fn cMov(p: *AffineCoordinates, a: AffineCoordinates, c: u1) void { + p.x.cMov(a.x, c); + p.y.cMov(a.y, c); + } +}; + +test "secp256k1" { + _ = @import("tests/secp256k1.zig"); +} diff --git a/lib/std/crypto/pcurves/secp256k1/field.zig b/lib/std/crypto/pcurves/secp256k1/field.zig new file mode 100644 index 0000000000..e8113196c6 --- /dev/null +++ b/lib/std/crypto/pcurves/secp256k1/field.zig @@ -0,0 +1,12 @@ +const std = @import("std"); +const common = @import("../common.zig"); + +const Field = common.Field; + +pub const Fe = Field(.{ + .fiat = @import("secp256k1_64.zig"), + .field_order = 115792089237316195423570985008687907853269984665640564039457584007908834671663, + .field_bits = 256, + .saturated_bits = 256, + .encoded_length = 32, +}); diff --git a/lib/std/crypto/pcurves/secp256k1/scalar.zig b/lib/std/crypto/pcurves/secp256k1/scalar.zig new file mode 100644 index 0000000000..2d91f8bc99 --- /dev/null +++ b/lib/std/crypto/pcurves/secp256k1/scalar.zig @@ -0,0 +1,227 @@ +const std = @import("std"); +const common = @import("../common.zig"); +const crypto = std.crypto; +const debug = std.debug; +const math = std.math; +const mem = std.mem; + +const Field = common.Field; + +const NonCanonicalError = std.crypto.errors.NonCanonicalError; +const NotSquareError = std.crypto.errors.NotSquareError; + +/// Number of bytes required to encode a scalar. +pub const encoded_length = 32; + +/// A compressed scalar, in canonical form. +pub const CompressedScalar = [encoded_length]u8; + +const Fe = Field(.{ + .fiat = @import("secp256k1_scalar_64.zig"), + .field_order = 115792089237316195423570985008687907852837564279074904382605163141518161494337, + .field_bits = 256, + .saturated_bits = 256, + .encoded_length = encoded_length, +}); + +/// The scalar field order. +pub const field_order = Fe.field_order; + +/// Reject a scalar whose encoding is not canonical. +pub fn rejectNonCanonical(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!void { + return Fe.rejectNonCanonical(s, endian); +} + +/// Reduce a 48-bytes scalar to the field size. +pub fn reduce48(s: [48]u8, endian: std.builtin.Endian) CompressedScalar { + return Scalar.fromBytes48(s, endian).toBytes(endian); +} + +/// Reduce a 64-bytes scalar to the field size. +pub fn reduce64(s: [64]u8, endian: std.builtin.Endian) CompressedScalar { + return ScalarDouble.fromBytes64(s, endian).toBytes(endian); +} + +/// Return a*b (mod L) +pub fn mul(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(a, endian)).mul(try Scalar.fromBytes(b, endian)).toBytes(endian); +} + +/// Return a*b+c (mod L) +pub fn mulAdd(a: CompressedScalar, b: CompressedScalar, c: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(a, endian)).mul(try Scalar.fromBytes(b, endian)).add(try Scalar.fromBytes(c, endian)).toBytes(endian); +} + +/// Return a+b (mod L) +pub fn add(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(a, endian)).add(try Scalar.fromBytes(b, endian)).toBytes(endian); +} + +/// Return -s (mod L) +pub fn neg(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(s, endian)).neg().toBytes(endian); +} + +/// Return (a-b) (mod L) +pub fn sub(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(a, endian)).sub(try Scalar.fromBytes(b, endian)).toBytes(endian); +} + +/// Return a random scalar +pub fn random(endian: std.builtin.Endian) CompressedScalar { + return Scalar.random().toBytes(endian); +} + +/// A scalar in unpacked representation. +pub const Scalar = struct { + fe: Fe, + + /// Zero. + pub const zero = Scalar{ .fe = Fe.zero }; + + /// One. + pub const one = Scalar{ .fe = Fe.one }; + + /// Unpack a serialized representation of a scalar. + pub fn fromBytes(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!Scalar { + return Scalar{ .fe = try Fe.fromBytes(s, endian) }; + } + + /// Reduce a 384 bit input to the field size. + pub fn fromBytes48(s: [48]u8, endian: std.builtin.Endian) Scalar { + const t = ScalarDouble.fromBytes(384, s, endian); + return t.reduce(384); + } + + /// Reduce a 512 bit input to the field size. + pub fn fromBytes64(s: [64]u8, endian: std.builtin.Endian) Scalar { + const t = ScalarDouble.fromBytes(512, s, endian); + return t.reduce(512); + } + + /// Pack a scalar into bytes. + pub fn toBytes(n: Scalar, endian: std.builtin.Endian) CompressedScalar { + return n.fe.toBytes(endian); + } + + /// Return true if the scalar is zero.. + pub fn isZero(n: Scalar) bool { + return n.fe.isZero(); + } + + /// Return true if a and b are equivalent. + pub fn equivalent(a: Scalar, b: Scalar) bool { + return a.fe.equivalent(b.fe); + } + + /// Compute x+y (mod L) + pub fn add(x: Scalar, y: Scalar) Scalar { + return Scalar{ .fe = x.fe.add(y.fe) }; + } + + /// Compute x-y (mod L) + pub fn sub(x: Scalar, y: Scalar) Scalar { + return Scalar{ .fe = x.fe.sub(y.fe) }; + } + + /// Compute 2n (mod L) + pub fn dbl(n: Scalar) Scalar { + return Scalar{ .fe = n.fe.dbl() }; + } + + /// Compute x*y (mod L) + pub fn mul(x: Scalar, y: Scalar) Scalar { + return Scalar{ .fe = x.fe.mul(y.fe) }; + } + + /// Compute x^2 (mod L) + pub fn sq(n: Scalar) Scalar { + return Scalar{ .fe = n.fe.sq() }; + } + + /// Compute x^n (mod L) + pub fn pow(a: Scalar, comptime T: type, comptime n: T) Scalar { + return Scalar{ .fe = a.fe.pow(n) }; + } + + /// Compute -x (mod L) + pub fn neg(n: Scalar) Scalar { + return Scalar{ .fe = n.fe.neg() }; + } + + /// Compute x^-1 (mod L) + pub fn invert(n: Scalar) Scalar { + return Scalar{ .fe = n.fe.invert() }; + } + + /// Return true if n is a quadratic residue mod L. + pub fn isSquare(n: Scalar) Scalar { + return n.fe.isSquare(); + } + + /// Return the square root of L, or NotSquare if there isn't any solutions. + pub fn sqrt(n: Scalar) NotSquareError!Scalar { + return Scalar{ .fe = try n.fe.sqrt() }; + } + + /// Return a random scalar < L. + pub fn random() Scalar { + var s: [48]u8 = undefined; + while (true) { + crypto.random.bytes(&s); + const n = Scalar.fromBytes48(s, .Little); + if (!n.isZero()) { + return n; + } + } + } +}; + +const ScalarDouble = struct { + x1: Fe, + x2: Fe, + x3: Fe, + + fn fromBytes(comptime bits: usize, s_: [bits / 8]u8, endian: std.builtin.Endian) ScalarDouble { + debug.assert(bits > 0 and bits <= 512 and bits >= Fe.saturated_bits and bits <= Fe.saturated_bits * 3); + + var s = s_; + if (endian == .Big) { + for (s_) |x, i| s[s.len - 1 - i] = x; + } + var t = ScalarDouble{ .x1 = undefined, .x2 = Fe.zero, .x3 = Fe.zero }; + { + var b = [_]u8{0} ** encoded_length; + const len = math.min(s.len, 24); + mem.copy(u8, b[0..len], s[0..len]); + t.x1 = Fe.fromBytes(b, .Little) catch unreachable; + } + if (s_.len >= 24) { + var b = [_]u8{0} ** encoded_length; + const len = math.min(s.len - 24, 24); + mem.copy(u8, b[0..len], s[24..][0..len]); + t.x2 = Fe.fromBytes(b, .Little) catch unreachable; + } + if (s_.len >= 48) { + var b = [_]u8{0} ** encoded_length; + const len = s.len - 48; + mem.copy(u8, b[0..len], s[48..][0..len]); + t.x3 = Fe.fromBytes(b, .Little) catch unreachable; + } + return t; + } + + fn reduce(expanded: ScalarDouble, comptime bits: usize) Scalar { + debug.assert(bits > 0 and bits <= Fe.saturated_bits * 3 and bits <= 512); + var fe = expanded.x1; + if (bits >= 192) { + const st1 = Fe.fromInt(1 << 192) catch unreachable; + fe = fe.add(expanded.x2.mul(st1)); + if (bits >= 384) { + const st2 = st1.sq(); + fe = fe.add(expanded.x3.mul(st2)); + } + } + return Scalar{ .fe = fe }; + } +}; diff --git a/lib/std/crypto/pcurves/secp256k1/secp256k1_64.zig b/lib/std/crypto/pcurves/secp256k1/secp256k1_64.zig new file mode 100644 index 0000000000..2309b48ac9 --- /dev/null +++ b/lib/std/crypto/pcurves/secp256k1/secp256k1_64.zig @@ -0,0 +1,1964 @@ +// Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase --public-type-case UpperCamelCase --private-type-case UpperCamelCase --no-prefix-fiat --package-name secp256k1 '' 64 '2^256 - 2^32 - 977' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp +// curve description (via package name): secp256k1 +// machine_wordsize = 64 (from "64") +// requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp +// m = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f (from "2^256 - 2^32 - 977") +// +// NOTE: In addition to the bounds specified above each function, all +// functions synthesized for this Montgomery arithmetic require the +// input to be strictly less than the prime modulus (m), and also +// require the input to be in the unique saturated representation. +// All functions also ensure that these two properties are true of +// return values. +// +// Computed values: +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +const std = @import("std"); +const mode = @import("builtin").mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels + +// The type MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const MontgomeryDomainFieldElement = [4]u64; + +// The type NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const NonMontgomeryDomainFieldElement = [4]u64; + +/// The function addcarryxU64 is an addition with carry. +/// +/// Postconditions: +/// out1 = (arg1 + arg2 + arg3) mod 2^64 +/// out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +inline fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @addWithOverflow(u64, arg2, arg3, &t); + const carry2 = @addWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function subborrowxU64 is a subtraction with borrow. +/// +/// Postconditions: +/// out1 = (-arg1 + arg2 + -arg3) mod 2^64 +/// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +inline fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @subWithOverflow(u64, arg2, arg3, &t); + const carry2 = @subWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function mulxU64 is a multiplication, returning the full double-width result. +/// +/// Postconditions: +/// out1 = (arg1 * arg2) mod 2^64 +/// out2 = ⌊arg1 * arg2 / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0xffffffffffffffff] +inline fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x = @as(u128, arg1) * @as(u128, arg2); + out1.* = @truncate(u64, x); + out2.* = @truncate(u64, x >> 64); +} + +/// The function cmovznzU64 is a single-word conditional move. +/// +/// Postconditions: +/// out1 = (if arg1 = 0 then arg2 else arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +inline fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + const mask = 0 -% @as(u64, arg1); + out1.* = (mask & arg3) | ((~mask) & arg2); +} + +/// The function mul multiplies two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn mul(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg2[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg2[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg2[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg2[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (@as(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0xd838091dd2253531); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffffffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xffffffffffffffff); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xfffffffefffffc2f); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (@as(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg2[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg2[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg2[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg2[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (@as(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, @as(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0xd838091dd2253531); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffffffffffff); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xffffffffffffffff); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xffffffffffffffff); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xfffffffefffffc2f); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (@as(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (@as(u64, x98) + @as(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg2[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg2[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg2[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg2[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (@as(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0xd838091dd2253531); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffffffffffff); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xffffffffffffffff); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xffffffffffffffff); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xfffffffefffffc2f); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (@as(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (@as(u64, x151) + @as(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg2[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg2[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg2[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg2[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (@as(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0xd838091dd2253531); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffffffffffff); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xffffffffffffffff); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xffffffffffffffff); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xfffffffefffffc2f); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (@as(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (@as(u64, x204) + @as(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xfffffffefffffc2f); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xffffffffffffffff); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xffffffffffffffff); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffffffffffff); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, 0x0); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function square squares a field element in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn square(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg1[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg1[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg1[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg1[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (@as(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0xd838091dd2253531); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffffffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xffffffffffffffff); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xfffffffefffffc2f); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (@as(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg1[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg1[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg1[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg1[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (@as(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, @as(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0xd838091dd2253531); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffffffffffff); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xffffffffffffffff); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xffffffffffffffff); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xfffffffefffffc2f); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (@as(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (@as(u64, x98) + @as(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg1[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg1[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg1[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg1[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (@as(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0xd838091dd2253531); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffffffffffff); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xffffffffffffffff); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xffffffffffffffff); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xfffffffefffffc2f); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (@as(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (@as(u64, x151) + @as(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg1[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg1[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg1[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg1[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (@as(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0xd838091dd2253531); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffffffffffff); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xffffffffffffffff); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xffffffffffffffff); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xfffffffefffffc2f); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (@as(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (@as(u64, x204) + @as(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xfffffffefffffc2f); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xffffffffffffffff); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xffffffffffffffff); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffffffffffff); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, 0x0); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function add adds two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn add(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + addcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + addcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + addcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + var x10: u1 = undefined; + subborrowxU64(&x9, &x10, 0x0, x1, 0xfffffffefffffc2f); + var x11: u64 = undefined; + var x12: u1 = undefined; + subborrowxU64(&x11, &x12, x10, x3, 0xffffffffffffffff); + var x13: u64 = undefined; + var x14: u1 = undefined; + subborrowxU64(&x13, &x14, x12, x5, 0xffffffffffffffff); + var x15: u64 = undefined; + var x16: u1 = undefined; + subborrowxU64(&x15, &x16, x14, x7, 0xffffffffffffffff); + var x17: u64 = undefined; + var x18: u1 = undefined; + subborrowxU64(&x17, &x18, x16, @as(u64, x8), 0x0); + var x19: u64 = undefined; + cmovznzU64(&x19, x18, x9, x1); + var x20: u64 = undefined; + cmovznzU64(&x20, x18, x11, x3); + var x21: u64 = undefined; + cmovznzU64(&x21, x18, x13, x5); + var x22: u64 = undefined; + cmovznzU64(&x22, x18, x15, x7); + out1[0] = x19; + out1[1] = x20; + out1[2] = x21; + out1[3] = x22; +} + +/// The function sub subtracts two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn sub(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, 0x0, 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xfffffffefffffc2f)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, x9); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, x9); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x9); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function opp negates a field element in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m +/// 0 ≤ eval out1 < m +/// +pub fn opp(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, 0x0, (arg1[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, 0x0, (arg1[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, 0x0, (arg1[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, 0x0, (arg1[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, 0x0, 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xfffffffefffffc2f)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, x9); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, x9); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x9); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function fromMontgomery translates a field element out of the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m +/// 0 ≤ eval out1 < m +/// +pub fn fromMontgomery(out1: *NonMontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[0]); + var x2: u64 = undefined; + var x3: u64 = undefined; + mulxU64(&x2, &x3, x1, 0xd838091dd2253531); + var x4: u64 = undefined; + var x5: u64 = undefined; + mulxU64(&x4, &x5, x2, 0xffffffffffffffff); + var x6: u64 = undefined; + var x7: u64 = undefined; + mulxU64(&x6, &x7, x2, 0xffffffffffffffff); + var x8: u64 = undefined; + var x9: u64 = undefined; + mulxU64(&x8, &x9, x2, 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u64 = undefined; + mulxU64(&x10, &x11, x2, 0xfffffffefffffc2f); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, x11, x8); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x9, x6); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x4); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, 0x0, x1, x10); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, 0x0, x12); + var x22: u64 = undefined; + var x23: u1 = undefined; + addcarryxU64(&x22, &x23, x21, 0x0, x14); + var x24: u64 = undefined; + var x25: u1 = undefined; + addcarryxU64(&x24, &x25, x23, 0x0, x16); + var x26: u64 = undefined; + var x27: u1 = undefined; + addcarryxU64(&x26, &x27, x25, 0x0, (@as(u64, x17) + x5)); + var x28: u64 = undefined; + var x29: u1 = undefined; + addcarryxU64(&x28, &x29, 0x0, x20, (arg1[1])); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, x29, x22, 0x0); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x24, 0x0); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x26, 0x0); + var x36: u64 = undefined; + var x37: u64 = undefined; + mulxU64(&x36, &x37, x28, 0xd838091dd2253531); + var x38: u64 = undefined; + var x39: u64 = undefined; + mulxU64(&x38, &x39, x36, 0xffffffffffffffff); + var x40: u64 = undefined; + var x41: u64 = undefined; + mulxU64(&x40, &x41, x36, 0xffffffffffffffff); + var x42: u64 = undefined; + var x43: u64 = undefined; + mulxU64(&x42, &x43, x36, 0xffffffffffffffff); + var x44: u64 = undefined; + var x45: u64 = undefined; + mulxU64(&x44, &x45, x36, 0xfffffffefffffc2f); + var x46: u64 = undefined; + var x47: u1 = undefined; + addcarryxU64(&x46, &x47, 0x0, x45, x42); + var x48: u64 = undefined; + var x49: u1 = undefined; + addcarryxU64(&x48, &x49, x47, x43, x40); + var x50: u64 = undefined; + var x51: u1 = undefined; + addcarryxU64(&x50, &x51, x49, x41, x38); + var x52: u64 = undefined; + var x53: u1 = undefined; + addcarryxU64(&x52, &x53, 0x0, x28, x44); + var x54: u64 = undefined; + var x55: u1 = undefined; + addcarryxU64(&x54, &x55, x53, x30, x46); + var x56: u64 = undefined; + var x57: u1 = undefined; + addcarryxU64(&x56, &x57, x55, x32, x48); + var x58: u64 = undefined; + var x59: u1 = undefined; + addcarryxU64(&x58, &x59, x57, x34, x50); + var x60: u64 = undefined; + var x61: u1 = undefined; + addcarryxU64(&x60, &x61, x59, (@as(u64, x35) + @as(u64, x27)), (@as(u64, x51) + x39)); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x54, (arg1[2])); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x56, 0x0); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x58, 0x0); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x60, 0x0); + var x70: u64 = undefined; + var x71: u64 = undefined; + mulxU64(&x70, &x71, x62, 0xd838091dd2253531); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x70, 0xffffffffffffffff); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x70, 0xffffffffffffffff); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x70, 0xffffffffffffffff); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x70, 0xfffffffefffffc2f); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, 0x0, x79, x76); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x77, x74); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x75, x72); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, 0x0, x62, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x64, x80); + var x90: u64 = undefined; + var x91: u1 = undefined; + addcarryxU64(&x90, &x91, x89, x66, x82); + var x92: u64 = undefined; + var x93: u1 = undefined; + addcarryxU64(&x92, &x93, x91, x68, x84); + var x94: u64 = undefined; + var x95: u1 = undefined; + addcarryxU64(&x94, &x95, x93, (@as(u64, x69) + @as(u64, x61)), (@as(u64, x85) + x73)); + var x96: u64 = undefined; + var x97: u1 = undefined; + addcarryxU64(&x96, &x97, 0x0, x88, (arg1[3])); + var x98: u64 = undefined; + var x99: u1 = undefined; + addcarryxU64(&x98, &x99, x97, x90, 0x0); + var x100: u64 = undefined; + var x101: u1 = undefined; + addcarryxU64(&x100, &x101, x99, x92, 0x0); + var x102: u64 = undefined; + var x103: u1 = undefined; + addcarryxU64(&x102, &x103, x101, x94, 0x0); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x96, 0xd838091dd2253531); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x104, 0xffffffffffffffff); + var x108: u64 = undefined; + var x109: u64 = undefined; + mulxU64(&x108, &x109, x104, 0xffffffffffffffff); + var x110: u64 = undefined; + var x111: u64 = undefined; + mulxU64(&x110, &x111, x104, 0xffffffffffffffff); + var x112: u64 = undefined; + var x113: u64 = undefined; + mulxU64(&x112, &x113, x104, 0xfffffffefffffc2f); + var x114: u64 = undefined; + var x115: u1 = undefined; + addcarryxU64(&x114, &x115, 0x0, x113, x110); + var x116: u64 = undefined; + var x117: u1 = undefined; + addcarryxU64(&x116, &x117, x115, x111, x108); + var x118: u64 = undefined; + var x119: u1 = undefined; + addcarryxU64(&x118, &x119, x117, x109, x106); + var x120: u64 = undefined; + var x121: u1 = undefined; + addcarryxU64(&x120, &x121, 0x0, x96, x112); + var x122: u64 = undefined; + var x123: u1 = undefined; + addcarryxU64(&x122, &x123, x121, x98, x114); + var x124: u64 = undefined; + var x125: u1 = undefined; + addcarryxU64(&x124, &x125, x123, x100, x116); + var x126: u64 = undefined; + var x127: u1 = undefined; + addcarryxU64(&x126, &x127, x125, x102, x118); + var x128: u64 = undefined; + var x129: u1 = undefined; + addcarryxU64(&x128, &x129, x127, (@as(u64, x103) + @as(u64, x95)), (@as(u64, x119) + x107)); + var x130: u64 = undefined; + var x131: u1 = undefined; + subborrowxU64(&x130, &x131, 0x0, x122, 0xfffffffefffffc2f); + var x132: u64 = undefined; + var x133: u1 = undefined; + subborrowxU64(&x132, &x133, x131, x124, 0xffffffffffffffff); + var x134: u64 = undefined; + var x135: u1 = undefined; + subborrowxU64(&x134, &x135, x133, x126, 0xffffffffffffffff); + var x136: u64 = undefined; + var x137: u1 = undefined; + subborrowxU64(&x136, &x137, x135, x128, 0xffffffffffffffff); + var x138: u64 = undefined; + var x139: u1 = undefined; + subborrowxU64(&x138, &x139, x137, @as(u64, x129), 0x0); + var x140: u64 = undefined; + cmovznzU64(&x140, x139, x130, x122); + var x141: u64 = undefined; + cmovznzU64(&x141, x139, x132, x124); + var x142: u64 = undefined; + cmovznzU64(&x142, x139, x134, x126); + var x143: u64 = undefined; + cmovznzU64(&x143, x139, x136, x128); + out1[0] = x140; + out1[1] = x141; + out1[2] = x142; + out1[3] = x143; +} + +/// The function toMontgomery translates a field element into the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +pub fn toMontgomery(out1: *MontgomeryDomainFieldElement, arg1: NonMontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, 0x7a2000e90a1); + var x7: u64 = undefined; + var x8: u1 = undefined; + addcarryxU64(&x7, &x8, 0x0, x6, x4); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x5, 0xd838091dd2253531); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x9, 0xffffffffffffffff); + var x13: u64 = undefined; + var x14: u64 = undefined; + mulxU64(&x13, &x14, x9, 0xffffffffffffffff); + var x15: u64 = undefined; + var x16: u64 = undefined; + mulxU64(&x15, &x16, x9, 0xffffffffffffffff); + var x17: u64 = undefined; + var x18: u64 = undefined; + mulxU64(&x17, &x18, x9, 0xfffffffefffffc2f); + var x19: u64 = undefined; + var x20: u1 = undefined; + addcarryxU64(&x19, &x20, 0x0, x18, x15); + var x21: u64 = undefined; + var x22: u1 = undefined; + addcarryxU64(&x21, &x22, x20, x16, x13); + var x23: u64 = undefined; + var x24: u1 = undefined; + addcarryxU64(&x23, &x24, x22, x14, x11); + var x25: u64 = undefined; + var x26: u1 = undefined; + addcarryxU64(&x25, &x26, 0x0, x5, x17); + var x27: u64 = undefined; + var x28: u1 = undefined; + addcarryxU64(&x27, &x28, x26, x7, x19); + var x29: u64 = undefined; + var x30: u1 = undefined; + addcarryxU64(&x29, &x30, x28, @as(u64, x8), x21); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, x30, 0x0, x23); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, 0x0, (@as(u64, x24) + x12)); + var x35: u64 = undefined; + var x36: u64 = undefined; + mulxU64(&x35, &x36, x1, 0x7a2000e90a1); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x36, x1); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, 0x0, x27, x35); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x29, x37); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x31, @as(u64, x38)); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x33, 0x0); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x39, 0xd838091dd2253531); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x47, 0xffffffffffffffff); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x47, 0xffffffffffffffff); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x47, 0xffffffffffffffff); + var x55: u64 = undefined; + var x56: u64 = undefined; + mulxU64(&x55, &x56, x47, 0xfffffffefffffc2f); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, 0x0, x56, x53); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x54, x51); + var x61: u64 = undefined; + var x62: u1 = undefined; + addcarryxU64(&x61, &x62, x60, x52, x49); + var x63: u64 = undefined; + var x64: u1 = undefined; + addcarryxU64(&x63, &x64, 0x0, x39, x55); + var x65: u64 = undefined; + var x66: u1 = undefined; + addcarryxU64(&x65, &x66, x64, x41, x57); + var x67: u64 = undefined; + var x68: u1 = undefined; + addcarryxU64(&x67, &x68, x66, x43, x59); + var x69: u64 = undefined; + var x70: u1 = undefined; + addcarryxU64(&x69, &x70, x68, x45, x61); + var x71: u64 = undefined; + var x72: u1 = undefined; + addcarryxU64(&x71, &x72, x70, (@as(u64, x46) + @as(u64, x34)), (@as(u64, x62) + x50)); + var x73: u64 = undefined; + var x74: u64 = undefined; + mulxU64(&x73, &x74, x2, 0x7a2000e90a1); + var x75: u64 = undefined; + var x76: u1 = undefined; + addcarryxU64(&x75, &x76, 0x0, x74, x2); + var x77: u64 = undefined; + var x78: u1 = undefined; + addcarryxU64(&x77, &x78, 0x0, x65, x73); + var x79: u64 = undefined; + var x80: u1 = undefined; + addcarryxU64(&x79, &x80, x78, x67, x75); + var x81: u64 = undefined; + var x82: u1 = undefined; + addcarryxU64(&x81, &x82, x80, x69, @as(u64, x76)); + var x83: u64 = undefined; + var x84: u1 = undefined; + addcarryxU64(&x83, &x84, x82, x71, 0x0); + var x85: u64 = undefined; + var x86: u64 = undefined; + mulxU64(&x85, &x86, x77, 0xd838091dd2253531); + var x87: u64 = undefined; + var x88: u64 = undefined; + mulxU64(&x87, &x88, x85, 0xffffffffffffffff); + var x89: u64 = undefined; + var x90: u64 = undefined; + mulxU64(&x89, &x90, x85, 0xffffffffffffffff); + var x91: u64 = undefined; + var x92: u64 = undefined; + mulxU64(&x91, &x92, x85, 0xffffffffffffffff); + var x93: u64 = undefined; + var x94: u64 = undefined; + mulxU64(&x93, &x94, x85, 0xfffffffefffffc2f); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, 0x0, x94, x91); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x92, x89); + var x99: u64 = undefined; + var x100: u1 = undefined; + addcarryxU64(&x99, &x100, x98, x90, x87); + var x101: u64 = undefined; + var x102: u1 = undefined; + addcarryxU64(&x101, &x102, 0x0, x77, x93); + var x103: u64 = undefined; + var x104: u1 = undefined; + addcarryxU64(&x103, &x104, x102, x79, x95); + var x105: u64 = undefined; + var x106: u1 = undefined; + addcarryxU64(&x105, &x106, x104, x81, x97); + var x107: u64 = undefined; + var x108: u1 = undefined; + addcarryxU64(&x107, &x108, x106, x83, x99); + var x109: u64 = undefined; + var x110: u1 = undefined; + addcarryxU64(&x109, &x110, x108, (@as(u64, x84) + @as(u64, x72)), (@as(u64, x100) + x88)); + var x111: u64 = undefined; + var x112: u64 = undefined; + mulxU64(&x111, &x112, x3, 0x7a2000e90a1); + var x113: u64 = undefined; + var x114: u1 = undefined; + addcarryxU64(&x113, &x114, 0x0, x112, x3); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x103, x111); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x105, x113); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x107, @as(u64, x114)); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x109, 0x0); + var x123: u64 = undefined; + var x124: u64 = undefined; + mulxU64(&x123, &x124, x115, 0xd838091dd2253531); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x123, 0xffffffffffffffff); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x123, 0xffffffffffffffff); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x123, 0xffffffffffffffff); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x123, 0xfffffffefffffc2f); + var x133: u64 = undefined; + var x134: u1 = undefined; + addcarryxU64(&x133, &x134, 0x0, x132, x129); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, x134, x130, x127); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x128, x125); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, 0x0, x115, x131); + var x141: u64 = undefined; + var x142: u1 = undefined; + addcarryxU64(&x141, &x142, x140, x117, x133); + var x143: u64 = undefined; + var x144: u1 = undefined; + addcarryxU64(&x143, &x144, x142, x119, x135); + var x145: u64 = undefined; + var x146: u1 = undefined; + addcarryxU64(&x145, &x146, x144, x121, x137); + var x147: u64 = undefined; + var x148: u1 = undefined; + addcarryxU64(&x147, &x148, x146, (@as(u64, x122) + @as(u64, x110)), (@as(u64, x138) + x126)); + var x149: u64 = undefined; + var x150: u1 = undefined; + subborrowxU64(&x149, &x150, 0x0, x141, 0xfffffffefffffc2f); + var x151: u64 = undefined; + var x152: u1 = undefined; + subborrowxU64(&x151, &x152, x150, x143, 0xffffffffffffffff); + var x153: u64 = undefined; + var x154: u1 = undefined; + subborrowxU64(&x153, &x154, x152, x145, 0xffffffffffffffff); + var x155: u64 = undefined; + var x156: u1 = undefined; + subborrowxU64(&x155, &x156, x154, x147, 0xffffffffffffffff); + var x157: u64 = undefined; + var x158: u1 = undefined; + subborrowxU64(&x157, &x158, x156, @as(u64, x148), 0x0); + var x159: u64 = undefined; + cmovznzU64(&x159, x158, x149, x141); + var x160: u64 = undefined; + cmovznzU64(&x160, x158, x151, x143); + var x161: u64 = undefined; + cmovznzU64(&x161, x158, x153, x145); + var x162: u64 = undefined; + cmovznzU64(&x162, x158, x155, x147); + out1[0] = x159; + out1[1] = x160; + out1[2] = x161; + out1[3] = x162; +} + +/// The function nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +pub fn nonzero(out1: *u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); + out1.* = x1; +} + +/// The function selectznz is a multi-limb conditional select. +/// +/// Postconditions: +/// out1 = (if arg1 = 0 then arg2 else arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn selectznz(out1: *[4]u64, arg1: u1, arg2: [4]u64, arg3: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + cmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); + var x2: u64 = undefined; + cmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); + var x3: u64 = undefined; + cmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); + var x4: u64 = undefined; + cmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); + out1[0] = x1; + out1[1] = x2; + out1[2] = x3; + out1[3] = x4; +} + +/// The function toBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31] +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +pub fn toBytes(out1: *[32]u8, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[3]); + const x2 = (arg1[2]); + const x3 = (arg1[1]); + const x4 = (arg1[0]); + const x5 = @truncate(u8, (x4 & 0xff)); + const x6 = (x4 >> 8); + const x7 = @truncate(u8, (x6 & 0xff)); + const x8 = (x6 >> 8); + const x9 = @truncate(u8, (x8 & 0xff)); + const x10 = (x8 >> 8); + const x11 = @truncate(u8, (x10 & 0xff)); + const x12 = (x10 >> 8); + const x13 = @truncate(u8, (x12 & 0xff)); + const x14 = (x12 >> 8); + const x15 = @truncate(u8, (x14 & 0xff)); + const x16 = (x14 >> 8); + const x17 = @truncate(u8, (x16 & 0xff)); + const x18 = @truncate(u8, (x16 >> 8)); + const x19 = @truncate(u8, (x3 & 0xff)); + const x20 = (x3 >> 8); + const x21 = @truncate(u8, (x20 & 0xff)); + const x22 = (x20 >> 8); + const x23 = @truncate(u8, (x22 & 0xff)); + const x24 = (x22 >> 8); + const x25 = @truncate(u8, (x24 & 0xff)); + const x26 = (x24 >> 8); + const x27 = @truncate(u8, (x26 & 0xff)); + const x28 = (x26 >> 8); + const x29 = @truncate(u8, (x28 & 0xff)); + const x30 = (x28 >> 8); + const x31 = @truncate(u8, (x30 & 0xff)); + const x32 = @truncate(u8, (x30 >> 8)); + const x33 = @truncate(u8, (x2 & 0xff)); + const x34 = (x2 >> 8); + const x35 = @truncate(u8, (x34 & 0xff)); + const x36 = (x34 >> 8); + const x37 = @truncate(u8, (x36 & 0xff)); + const x38 = (x36 >> 8); + const x39 = @truncate(u8, (x38 & 0xff)); + const x40 = (x38 >> 8); + const x41 = @truncate(u8, (x40 & 0xff)); + const x42 = (x40 >> 8); + const x43 = @truncate(u8, (x42 & 0xff)); + const x44 = (x42 >> 8); + const x45 = @truncate(u8, (x44 & 0xff)); + const x46 = @truncate(u8, (x44 >> 8)); + const x47 = @truncate(u8, (x1 & 0xff)); + const x48 = (x1 >> 8); + const x49 = @truncate(u8, (x48 & 0xff)); + const x50 = (x48 >> 8); + const x51 = @truncate(u8, (x50 & 0xff)); + const x52 = (x50 >> 8); + const x53 = @truncate(u8, (x52 & 0xff)); + const x54 = (x52 >> 8); + const x55 = @truncate(u8, (x54 & 0xff)); + const x56 = (x54 >> 8); + const x57 = @truncate(u8, (x56 & 0xff)); + const x58 = (x56 >> 8); + const x59 = @truncate(u8, (x58 & 0xff)); + const x60 = @truncate(u8, (x58 >> 8)); + out1[0] = x5; + out1[1] = x7; + out1[2] = x9; + out1[3] = x11; + out1[4] = x13; + out1[5] = x15; + out1[6] = x17; + out1[7] = x18; + out1[8] = x19; + out1[9] = x21; + out1[10] = x23; + out1[11] = x25; + out1[12] = x27; + out1[13] = x29; + out1[14] = x31; + out1[15] = x32; + out1[16] = x33; + out1[17] = x35; + out1[18] = x37; + out1[19] = x39; + out1[20] = x41; + out1[21] = x43; + out1[22] = x45; + out1[23] = x46; + out1[24] = x47; + out1[25] = x49; + out1[26] = x51; + out1[27] = x53; + out1[28] = x55; + out1[29] = x57; + out1[30] = x59; + out1[31] = x60; +} + +/// The function fromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +/// +/// Preconditions: +/// 0 ≤ bytes_eval arg1 < m +/// Postconditions: +/// eval out1 mod m = bytes_eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn fromBytes(out1: *[4]u64, arg1: [32]u8) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (@as(u64, (arg1[31])) << 56); + const x2 = (@as(u64, (arg1[30])) << 48); + const x3 = (@as(u64, (arg1[29])) << 40); + const x4 = (@as(u64, (arg1[28])) << 32); + const x5 = (@as(u64, (arg1[27])) << 24); + const x6 = (@as(u64, (arg1[26])) << 16); + const x7 = (@as(u64, (arg1[25])) << 8); + const x8 = (arg1[24]); + const x9 = (@as(u64, (arg1[23])) << 56); + const x10 = (@as(u64, (arg1[22])) << 48); + const x11 = (@as(u64, (arg1[21])) << 40); + const x12 = (@as(u64, (arg1[20])) << 32); + const x13 = (@as(u64, (arg1[19])) << 24); + const x14 = (@as(u64, (arg1[18])) << 16); + const x15 = (@as(u64, (arg1[17])) << 8); + const x16 = (arg1[16]); + const x17 = (@as(u64, (arg1[15])) << 56); + const x18 = (@as(u64, (arg1[14])) << 48); + const x19 = (@as(u64, (arg1[13])) << 40); + const x20 = (@as(u64, (arg1[12])) << 32); + const x21 = (@as(u64, (arg1[11])) << 24); + const x22 = (@as(u64, (arg1[10])) << 16); + const x23 = (@as(u64, (arg1[9])) << 8); + const x24 = (arg1[8]); + const x25 = (@as(u64, (arg1[7])) << 56); + const x26 = (@as(u64, (arg1[6])) << 48); + const x27 = (@as(u64, (arg1[5])) << 40); + const x28 = (@as(u64, (arg1[4])) << 32); + const x29 = (@as(u64, (arg1[3])) << 24); + const x30 = (@as(u64, (arg1[2])) << 16); + const x31 = (@as(u64, (arg1[1])) << 8); + const x32 = (arg1[0]); + const x33 = (x31 + @as(u64, x32)); + const x34 = (x30 + x33); + const x35 = (x29 + x34); + const x36 = (x28 + x35); + const x37 = (x27 + x36); + const x38 = (x26 + x37); + const x39 = (x25 + x38); + const x40 = (x23 + @as(u64, x24)); + const x41 = (x22 + x40); + const x42 = (x21 + x41); + const x43 = (x20 + x42); + const x44 = (x19 + x43); + const x45 = (x18 + x44); + const x46 = (x17 + x45); + const x47 = (x15 + @as(u64, x16)); + const x48 = (x14 + x47); + const x49 = (x13 + x48); + const x50 = (x12 + x49); + const x51 = (x11 + x50); + const x52 = (x10 + x51); + const x53 = (x9 + x52); + const x54 = (x7 + @as(u64, x8)); + const x55 = (x6 + x54); + const x56 = (x5 + x55); + const x57 = (x4 + x56); + const x58 = (x3 + x57); + const x59 = (x2 + x58); + const x60 = (x1 + x59); + out1[0] = x39; + out1[1] = x46; + out1[2] = x53; + out1[3] = x60; +} + +/// The function setOne returns the field element one in the Montgomery domain. +/// +/// Postconditions: +/// eval (from_montgomery out1) mod m = 1 mod m +/// 0 ≤ eval out1 < m +/// +pub fn setOne(out1: *MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0x1000003d1; + out1[1] = 0x0; + out1[2] = 0x0; + out1[3] = 0x0; +} + +/// The function msat returns the saturated representation of the prime modulus. +/// +/// Postconditions: +/// twos_complement_eval out1 = m +/// 0 ≤ eval out1 < m +/// +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn msat(out1: *[5]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xfffffffefffffc2f; + out1[1] = 0xffffffffffffffff; + out1[2] = 0xffffffffffffffff; + out1[3] = 0xffffffffffffffff; + out1[4] = 0x0; +} + +/// The function divstep computes a divstep. +/// +/// Preconditions: +/// 0 ≤ eval arg4 < m +/// 0 ≤ eval arg5 < m +/// Postconditions: +/// out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1) +/// twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2) +/// twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋) +/// eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m) +/// eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m) +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out2 < m +/// 0 ≤ eval out3 < m +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *[4]u64, out5: *[4]u64, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: [4]u64, arg5: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (~arg1), 0x1); + const x3 = (@truncate(u1, (x1 >> 63)) & @truncate(u1, ((arg3[0]) & 0x1))); + var x4: u64 = undefined; + var x5: u1 = undefined; + addcarryxU64(&x4, &x5, 0x0, (~arg1), 0x1); + var x6: u64 = undefined; + cmovznzU64(&x6, x3, arg1, x4); + var x7: u64 = undefined; + cmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); + var x8: u64 = undefined; + cmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); + var x9: u64 = undefined; + cmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); + var x10: u64 = undefined; + cmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); + var x11: u64 = undefined; + cmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, 0x1, (~(arg2[0]))); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, 0x0, (~(arg2[1]))); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, 0x0, (~(arg2[2]))); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, x17, 0x0, (~(arg2[3]))); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, 0x0, (~(arg2[4]))); + var x22: u64 = undefined; + cmovznzU64(&x22, x3, (arg3[0]), x12); + var x23: u64 = undefined; + cmovznzU64(&x23, x3, (arg3[1]), x14); + var x24: u64 = undefined; + cmovznzU64(&x24, x3, (arg3[2]), x16); + var x25: u64 = undefined; + cmovznzU64(&x25, x3, (arg3[3]), x18); + var x26: u64 = undefined; + cmovznzU64(&x26, x3, (arg3[4]), x20); + var x27: u64 = undefined; + cmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); + var x28: u64 = undefined; + cmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); + var x29: u64 = undefined; + cmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); + var x30: u64 = undefined; + cmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, 0x0, x27, x27); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, x28, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + addcarryxU64(&x35, &x36, x34, x29, x29); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, x36, x30, x30); + var x39: u64 = undefined; + var x40: u1 = undefined; + subborrowxU64(&x39, &x40, 0x0, x31, 0xfffffffefffffc2f); + var x41: u64 = undefined; + var x42: u1 = undefined; + subborrowxU64(&x41, &x42, x40, x33, 0xffffffffffffffff); + var x43: u64 = undefined; + var x44: u1 = undefined; + subborrowxU64(&x43, &x44, x42, x35, 0xffffffffffffffff); + var x45: u64 = undefined; + var x46: u1 = undefined; + subborrowxU64(&x45, &x46, x44, x37, 0xffffffffffffffff); + var x47: u64 = undefined; + var x48: u1 = undefined; + subborrowxU64(&x47, &x48, x46, @as(u64, x38), 0x0); + const x49 = (arg4[3]); + const x50 = (arg4[2]); + const x51 = (arg4[1]); + const x52 = (arg4[0]); + var x53: u64 = undefined; + var x54: u1 = undefined; + subborrowxU64(&x53, &x54, 0x0, 0x0, x52); + var x55: u64 = undefined; + var x56: u1 = undefined; + subborrowxU64(&x55, &x56, x54, 0x0, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + subborrowxU64(&x57, &x58, x56, 0x0, x50); + var x59: u64 = undefined; + var x60: u1 = undefined; + subborrowxU64(&x59, &x60, x58, 0x0, x49); + var x61: u64 = undefined; + cmovznzU64(&x61, x60, 0x0, 0xffffffffffffffff); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x53, (x61 & 0xfffffffefffffc2f)); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x55, x61); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x57, x61); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x59, x61); + var x70: u64 = undefined; + cmovznzU64(&x70, x3, (arg5[0]), x62); + var x71: u64 = undefined; + cmovznzU64(&x71, x3, (arg5[1]), x64); + var x72: u64 = undefined; + cmovznzU64(&x72, x3, (arg5[2]), x66); + var x73: u64 = undefined; + cmovznzU64(&x73, x3, (arg5[3]), x68); + const x74 = @truncate(u1, (x22 & 0x1)); + var x75: u64 = undefined; + cmovznzU64(&x75, x74, 0x0, x7); + var x76: u64 = undefined; + cmovznzU64(&x76, x74, 0x0, x8); + var x77: u64 = undefined; + cmovznzU64(&x77, x74, 0x0, x9); + var x78: u64 = undefined; + cmovznzU64(&x78, x74, 0x0, x10); + var x79: u64 = undefined; + cmovznzU64(&x79, x74, 0x0, x11); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, 0x0, x22, x75); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x23, x76); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x24, x77); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x25, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x26, x79); + var x90: u64 = undefined; + cmovznzU64(&x90, x74, 0x0, x27); + var x91: u64 = undefined; + cmovznzU64(&x91, x74, 0x0, x28); + var x92: u64 = undefined; + cmovznzU64(&x92, x74, 0x0, x29); + var x93: u64 = undefined; + cmovznzU64(&x93, x74, 0x0, x30); + var x94: u64 = undefined; + var x95: u1 = undefined; + addcarryxU64(&x94, &x95, 0x0, x70, x90); + var x96: u64 = undefined; + var x97: u1 = undefined; + addcarryxU64(&x96, &x97, x95, x71, x91); + var x98: u64 = undefined; + var x99: u1 = undefined; + addcarryxU64(&x98, &x99, x97, x72, x92); + var x100: u64 = undefined; + var x101: u1 = undefined; + addcarryxU64(&x100, &x101, x99, x73, x93); + var x102: u64 = undefined; + var x103: u1 = undefined; + subborrowxU64(&x102, &x103, 0x0, x94, 0xfffffffefffffc2f); + var x104: u64 = undefined; + var x105: u1 = undefined; + subborrowxU64(&x104, &x105, x103, x96, 0xffffffffffffffff); + var x106: u64 = undefined; + var x107: u1 = undefined; + subborrowxU64(&x106, &x107, x105, x98, 0xffffffffffffffff); + var x108: u64 = undefined; + var x109: u1 = undefined; + subborrowxU64(&x108, &x109, x107, x100, 0xffffffffffffffff); + var x110: u64 = undefined; + var x111: u1 = undefined; + subborrowxU64(&x110, &x111, x109, @as(u64, x101), 0x0); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, 0x0, x6, 0x1); + const x114 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); + const x115 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); + const x116 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); + const x117 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); + const x118 = ((x88 & 0x8000000000000000) | (x88 >> 1)); + var x119: u64 = undefined; + cmovznzU64(&x119, x48, x39, x31); + var x120: u64 = undefined; + cmovznzU64(&x120, x48, x41, x33); + var x121: u64 = undefined; + cmovznzU64(&x121, x48, x43, x35); + var x122: u64 = undefined; + cmovznzU64(&x122, x48, x45, x37); + var x123: u64 = undefined; + cmovznzU64(&x123, x111, x102, x94); + var x124: u64 = undefined; + cmovznzU64(&x124, x111, x104, x96); + var x125: u64 = undefined; + cmovznzU64(&x125, x111, x106, x98); + var x126: u64 = undefined; + cmovznzU64(&x126, x111, x108, x100); + out1.* = x112; + out2[0] = x7; + out2[1] = x8; + out2[2] = x9; + out2[3] = x10; + out2[4] = x11; + out3[0] = x114; + out3[1] = x115; + out3[2] = x116; + out3[3] = x117; + out3[4] = x118; + out4[0] = x119; + out4[1] = x120; + out4[2] = x121; + out4[3] = x122; + out5[0] = x123; + out5[1] = x124; + out5[2] = x125; + out5[3] = x126; +} + +/// The function divstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form). +/// +/// Postconditions: +/// eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if ⌊log2 m⌋ + 1 < 46 then ⌊(49 * (⌊log2 m⌋ + 1) + 80) / 17⌋ else ⌊(49 * (⌊log2 m⌋ + 1) + 57) / 17⌋) +/// 0 ≤ eval out1 < m +/// +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstepPrecomp(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xf201a41831525e0a; + out1[1] = 0x9953f9ddcd648d85; + out1[2] = 0xe86029463db210a9; + out1[3] = 0x24fb8a3104b03709; +} diff --git a/lib/std/crypto/pcurves/secp256k1/secp256k1_scalar_64.zig b/lib/std/crypto/pcurves/secp256k1/secp256k1_scalar_64.zig new file mode 100644 index 0000000000..8e9687f0a1 --- /dev/null +++ b/lib/std/crypto/pcurves/secp256k1/secp256k1_scalar_64.zig @@ -0,0 +1,2024 @@ +// Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase --public-type-case UpperCamelCase --private-type-case UpperCamelCase --no-prefix-fiat --package-name secp256k1_scalar '' 64 '2^256 - 432420386565659656852420866394968145599' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp +// curve description (via package name): secp256k1_scalar +// machine_wordsize = 64 (from "64") +// requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp +// m = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 (from "2^256 - 432420386565659656852420866394968145599") +// +// NOTE: In addition to the bounds specified above each function, all +// functions synthesized for this Montgomery arithmetic require the +// input to be strictly less than the prime modulus (m), and also +// require the input to be in the unique saturated representation. +// All functions also ensure that these two properties are true of +// return values. +// +// Computed values: +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +const std = @import("std"); +const mode = @import("builtin").mode; // Checked arithmetic is disabled in non-debug modes to avoid side channels + +// The type MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const MontgomeryDomainFieldElement = [4]u64; + +// The type NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub const NonMontgomeryDomainFieldElement = [4]u64; + +/// The function addcarryxU64 is an addition with carry. +/// +/// Postconditions: +/// out1 = (arg1 + arg2 + arg3) mod 2^64 +/// out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +inline fn addcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @addWithOverflow(u64, arg2, arg3, &t); + const carry2 = @addWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function subborrowxU64 is a subtraction with borrow. +/// +/// Postconditions: +/// out1 = (-arg1 + arg2 + -arg3) mod 2^64 +/// out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0x1] +inline fn subborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + var t: u64 = undefined; + const carry1 = @subWithOverflow(u64, arg2, arg3, &t); + const carry2 = @subWithOverflow(u64, t, arg1, out1); + out2.* = @boolToInt(carry1) | @boolToInt(carry2); +} + +/// The function mulxU64 is a multiplication, returning the full double-width result. +/// +/// Postconditions: +/// out1 = (arg1 * arg2) mod 2^64 +/// out2 = ⌊arg1 * arg2 / 2^64⌋ +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [0x0 ~> 0xffffffffffffffff] +inline fn mulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) void { + @setRuntimeSafety(mode == .Debug); + + const x = @as(u128, arg1) * @as(u128, arg2); + out1.* = @truncate(u64, x); + out2.* = @truncate(u64, x >> 64); +} + +/// The function cmovznzU64 is a single-word conditional move. +/// +/// Postconditions: +/// out1 = (if arg1 = 0 then arg2 else arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [0x0 ~> 0xffffffffffffffff] +/// arg3: [0x0 ~> 0xffffffffffffffff] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +inline fn cmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) void { + @setRuntimeSafety(mode == .Debug); + + const mask = 0 -% @as(u64, arg1); + out1.* = (mask & arg3) | ((~mask) & arg2); +} + +/// The function mul multiplies two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn mul(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg2[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg2[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg2[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg2[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (@as(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0x4b0dff665588b13f); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffffffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xfffffffffffffffe); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xbaaedce6af48a03b); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xbfd25e8cd0364141); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (@as(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg2[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg2[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg2[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg2[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (@as(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, @as(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0x4b0dff665588b13f); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffffffffffff); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xfffffffffffffffe); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xbaaedce6af48a03b); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xbfd25e8cd0364141); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (@as(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (@as(u64, x98) + @as(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg2[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg2[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg2[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg2[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (@as(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0x4b0dff665588b13f); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffffffffffff); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xfffffffffffffffe); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xbaaedce6af48a03b); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xbfd25e8cd0364141); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (@as(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (@as(u64, x151) + @as(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg2[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg2[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg2[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg2[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (@as(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0x4b0dff665588b13f); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffffffffffff); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xfffffffffffffffe); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xbaaedce6af48a03b); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xbfd25e8cd0364141); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (@as(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (@as(u64, x204) + @as(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xbfd25e8cd0364141); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xbaaedce6af48a03b); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xfffffffffffffffe); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffffffffffff); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, 0x0); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function square squares a field element in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn square(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, (arg1[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, (arg1[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, (arg1[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, (arg1[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + const x19 = (@as(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + mulxU64(&x20, &x21, x11, 0x4b0dff665588b13f); + var x22: u64 = undefined; + var x23: u64 = undefined; + mulxU64(&x22, &x23, x20, 0xffffffffffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + mulxU64(&x24, &x25, x20, 0xfffffffffffffffe); + var x26: u64 = undefined; + var x27: u64 = undefined; + mulxU64(&x26, &x27, x20, 0xbaaedce6af48a03b); + var x28: u64 = undefined; + var x29: u64 = undefined; + mulxU64(&x28, &x29, x20, 0xbfd25e8cd0364141); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, 0x0, x29, x26); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x27, x24); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x25, x22); + const x36 = (@as(u64, x35) + x23); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, 0x0, x11, x28); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x13, x30); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x15, x32); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, x17, x34); + var x45: u64 = undefined; + var x46: u1 = undefined; + addcarryxU64(&x45, &x46, x44, x19, x36); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, (arg1[3])); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, (arg1[2])); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, (arg1[1])); + var x53: u64 = undefined; + var x54: u64 = undefined; + mulxU64(&x53, &x54, x1, (arg1[0])); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, 0x0, x54, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x52, x49); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, x58, x50, x47); + const x61 = (@as(u64, x60) + x48); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x39, x53); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x41, x55); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x43, x57); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x45, x59); + var x70: u64 = undefined; + var x71: u1 = undefined; + addcarryxU64(&x70, &x71, x69, @as(u64, x46), x61); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x62, 0x4b0dff665588b13f); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x72, 0xffffffffffffffff); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x72, 0xfffffffffffffffe); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x72, 0xbaaedce6af48a03b); + var x80: u64 = undefined; + var x81: u64 = undefined; + mulxU64(&x80, &x81, x72, 0xbfd25e8cd0364141); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, 0x0, x81, x78); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x79, x76); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x77, x74); + const x88 = (@as(u64, x87) + x75); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, 0x0, x62, x80); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, x64, x82); + var x93: u64 = undefined; + var x94: u1 = undefined; + addcarryxU64(&x93, &x94, x92, x66, x84); + var x95: u64 = undefined; + var x96: u1 = undefined; + addcarryxU64(&x95, &x96, x94, x68, x86); + var x97: u64 = undefined; + var x98: u1 = undefined; + addcarryxU64(&x97, &x98, x96, x70, x88); + const x99 = (@as(u64, x98) + @as(u64, x71)); + var x100: u64 = undefined; + var x101: u64 = undefined; + mulxU64(&x100, &x101, x2, (arg1[3])); + var x102: u64 = undefined; + var x103: u64 = undefined; + mulxU64(&x102, &x103, x2, (arg1[2])); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x2, (arg1[1])); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x2, (arg1[0])); + var x108: u64 = undefined; + var x109: u1 = undefined; + addcarryxU64(&x108, &x109, 0x0, x107, x104); + var x110: u64 = undefined; + var x111: u1 = undefined; + addcarryxU64(&x110, &x111, x109, x105, x102); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, x111, x103, x100); + const x114 = (@as(u64, x113) + x101); + var x115: u64 = undefined; + var x116: u1 = undefined; + addcarryxU64(&x115, &x116, 0x0, x91, x106); + var x117: u64 = undefined; + var x118: u1 = undefined; + addcarryxU64(&x117, &x118, x116, x93, x108); + var x119: u64 = undefined; + var x120: u1 = undefined; + addcarryxU64(&x119, &x120, x118, x95, x110); + var x121: u64 = undefined; + var x122: u1 = undefined; + addcarryxU64(&x121, &x122, x120, x97, x112); + var x123: u64 = undefined; + var x124: u1 = undefined; + addcarryxU64(&x123, &x124, x122, x99, x114); + var x125: u64 = undefined; + var x126: u64 = undefined; + mulxU64(&x125, &x126, x115, 0x4b0dff665588b13f); + var x127: u64 = undefined; + var x128: u64 = undefined; + mulxU64(&x127, &x128, x125, 0xffffffffffffffff); + var x129: u64 = undefined; + var x130: u64 = undefined; + mulxU64(&x129, &x130, x125, 0xfffffffffffffffe); + var x131: u64 = undefined; + var x132: u64 = undefined; + mulxU64(&x131, &x132, x125, 0xbaaedce6af48a03b); + var x133: u64 = undefined; + var x134: u64 = undefined; + mulxU64(&x133, &x134, x125, 0xbfd25e8cd0364141); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, 0x0, x134, x131); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x132, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, x130, x127); + const x141 = (@as(u64, x140) + x128); + var x142: u64 = undefined; + var x143: u1 = undefined; + addcarryxU64(&x142, &x143, 0x0, x115, x133); + var x144: u64 = undefined; + var x145: u1 = undefined; + addcarryxU64(&x144, &x145, x143, x117, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + addcarryxU64(&x146, &x147, x145, x119, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + addcarryxU64(&x148, &x149, x147, x121, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + addcarryxU64(&x150, &x151, x149, x123, x141); + const x152 = (@as(u64, x151) + @as(u64, x124)); + var x153: u64 = undefined; + var x154: u64 = undefined; + mulxU64(&x153, &x154, x3, (arg1[3])); + var x155: u64 = undefined; + var x156: u64 = undefined; + mulxU64(&x155, &x156, x3, (arg1[2])); + var x157: u64 = undefined; + var x158: u64 = undefined; + mulxU64(&x157, &x158, x3, (arg1[1])); + var x159: u64 = undefined; + var x160: u64 = undefined; + mulxU64(&x159, &x160, x3, (arg1[0])); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, 0x0, x160, x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + addcarryxU64(&x163, &x164, x162, x158, x155); + var x165: u64 = undefined; + var x166: u1 = undefined; + addcarryxU64(&x165, &x166, x164, x156, x153); + const x167 = (@as(u64, x166) + x154); + var x168: u64 = undefined; + var x169: u1 = undefined; + addcarryxU64(&x168, &x169, 0x0, x144, x159); + var x170: u64 = undefined; + var x171: u1 = undefined; + addcarryxU64(&x170, &x171, x169, x146, x161); + var x172: u64 = undefined; + var x173: u1 = undefined; + addcarryxU64(&x172, &x173, x171, x148, x163); + var x174: u64 = undefined; + var x175: u1 = undefined; + addcarryxU64(&x174, &x175, x173, x150, x165); + var x176: u64 = undefined; + var x177: u1 = undefined; + addcarryxU64(&x176, &x177, x175, x152, x167); + var x178: u64 = undefined; + var x179: u64 = undefined; + mulxU64(&x178, &x179, x168, 0x4b0dff665588b13f); + var x180: u64 = undefined; + var x181: u64 = undefined; + mulxU64(&x180, &x181, x178, 0xffffffffffffffff); + var x182: u64 = undefined; + var x183: u64 = undefined; + mulxU64(&x182, &x183, x178, 0xfffffffffffffffe); + var x184: u64 = undefined; + var x185: u64 = undefined; + mulxU64(&x184, &x185, x178, 0xbaaedce6af48a03b); + var x186: u64 = undefined; + var x187: u64 = undefined; + mulxU64(&x186, &x187, x178, 0xbfd25e8cd0364141); + var x188: u64 = undefined; + var x189: u1 = undefined; + addcarryxU64(&x188, &x189, 0x0, x187, x184); + var x190: u64 = undefined; + var x191: u1 = undefined; + addcarryxU64(&x190, &x191, x189, x185, x182); + var x192: u64 = undefined; + var x193: u1 = undefined; + addcarryxU64(&x192, &x193, x191, x183, x180); + const x194 = (@as(u64, x193) + x181); + var x195: u64 = undefined; + var x196: u1 = undefined; + addcarryxU64(&x195, &x196, 0x0, x168, x186); + var x197: u64 = undefined; + var x198: u1 = undefined; + addcarryxU64(&x197, &x198, x196, x170, x188); + var x199: u64 = undefined; + var x200: u1 = undefined; + addcarryxU64(&x199, &x200, x198, x172, x190); + var x201: u64 = undefined; + var x202: u1 = undefined; + addcarryxU64(&x201, &x202, x200, x174, x192); + var x203: u64 = undefined; + var x204: u1 = undefined; + addcarryxU64(&x203, &x204, x202, x176, x194); + const x205 = (@as(u64, x204) + @as(u64, x177)); + var x206: u64 = undefined; + var x207: u1 = undefined; + subborrowxU64(&x206, &x207, 0x0, x197, 0xbfd25e8cd0364141); + var x208: u64 = undefined; + var x209: u1 = undefined; + subborrowxU64(&x208, &x209, x207, x199, 0xbaaedce6af48a03b); + var x210: u64 = undefined; + var x211: u1 = undefined; + subborrowxU64(&x210, &x211, x209, x201, 0xfffffffffffffffe); + var x212: u64 = undefined; + var x213: u1 = undefined; + subborrowxU64(&x212, &x213, x211, x203, 0xffffffffffffffff); + var x214: u64 = undefined; + var x215: u1 = undefined; + subborrowxU64(&x214, &x215, x213, x205, 0x0); + var x216: u64 = undefined; + cmovznzU64(&x216, x215, x206, x197); + var x217: u64 = undefined; + cmovznzU64(&x217, x215, x208, x199); + var x218: u64 = undefined; + cmovznzU64(&x218, x215, x210, x201); + var x219: u64 = undefined; + cmovznzU64(&x219, x215, x212, x203); + out1[0] = x216; + out1[1] = x217; + out1[2] = x218; + out1[3] = x219; +} + +/// The function add adds two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn add(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + addcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + addcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + addcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + var x10: u1 = undefined; + subborrowxU64(&x9, &x10, 0x0, x1, 0xbfd25e8cd0364141); + var x11: u64 = undefined; + var x12: u1 = undefined; + subborrowxU64(&x11, &x12, x10, x3, 0xbaaedce6af48a03b); + var x13: u64 = undefined; + var x14: u1 = undefined; + subborrowxU64(&x13, &x14, x12, x5, 0xfffffffffffffffe); + var x15: u64 = undefined; + var x16: u1 = undefined; + subborrowxU64(&x15, &x16, x14, x7, 0xffffffffffffffff); + var x17: u64 = undefined; + var x18: u1 = undefined; + subborrowxU64(&x17, &x18, x16, @as(u64, x8), 0x0); + var x19: u64 = undefined; + cmovznzU64(&x19, x18, x9, x1); + var x20: u64 = undefined; + cmovznzU64(&x20, x18, x11, x3); + var x21: u64 = undefined; + cmovznzU64(&x21, x18, x13, x5); + var x22: u64 = undefined; + cmovznzU64(&x22, x18, x15, x7); + out1[0] = x19; + out1[1] = x20; + out1[2] = x21; + out1[3] = x22; +} + +/// The function sub subtracts two field elements in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// 0 ≤ eval arg2 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +/// 0 ≤ eval out1 < m +/// +pub fn sub(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement, arg2: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, 0x0, 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xbfd25e8cd0364141)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xbaaedce6af48a03b)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, (x9 & 0xfffffffffffffffe)); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x9); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function opp negates a field element in the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m +/// 0 ≤ eval out1 < m +/// +pub fn opp(out1: *MontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + subborrowxU64(&x1, &x2, 0x0, 0x0, (arg1[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + subborrowxU64(&x3, &x4, x2, 0x0, (arg1[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + subborrowxU64(&x5, &x6, x4, 0x0, (arg1[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + subborrowxU64(&x7, &x8, x6, 0x0, (arg1[3])); + var x9: u64 = undefined; + cmovznzU64(&x9, x8, 0x0, 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + addcarryxU64(&x10, &x11, 0x0, x1, (x9 & 0xbfd25e8cd0364141)); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, x11, x3, (x9 & 0xbaaedce6af48a03b)); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x5, (x9 & 0xfffffffffffffffe)); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x9); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function fromMontgomery translates a field element out of the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m +/// 0 ≤ eval out1 < m +/// +pub fn fromMontgomery(out1: *NonMontgomeryDomainFieldElement, arg1: MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[0]); + var x2: u64 = undefined; + var x3: u64 = undefined; + mulxU64(&x2, &x3, x1, 0x4b0dff665588b13f); + var x4: u64 = undefined; + var x5: u64 = undefined; + mulxU64(&x4, &x5, x2, 0xffffffffffffffff); + var x6: u64 = undefined; + var x7: u64 = undefined; + mulxU64(&x6, &x7, x2, 0xfffffffffffffffe); + var x8: u64 = undefined; + var x9: u64 = undefined; + mulxU64(&x8, &x9, x2, 0xbaaedce6af48a03b); + var x10: u64 = undefined; + var x11: u64 = undefined; + mulxU64(&x10, &x11, x2, 0xbfd25e8cd0364141); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, x11, x8); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, x9, x6); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, x7, x4); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, 0x0, x1, x10); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, 0x0, x12); + var x22: u64 = undefined; + var x23: u1 = undefined; + addcarryxU64(&x22, &x23, x21, 0x0, x14); + var x24: u64 = undefined; + var x25: u1 = undefined; + addcarryxU64(&x24, &x25, x23, 0x0, x16); + var x26: u64 = undefined; + var x27: u1 = undefined; + addcarryxU64(&x26, &x27, x25, 0x0, (@as(u64, x17) + x5)); + var x28: u64 = undefined; + var x29: u1 = undefined; + addcarryxU64(&x28, &x29, 0x0, x20, (arg1[1])); + var x30: u64 = undefined; + var x31: u1 = undefined; + addcarryxU64(&x30, &x31, x29, x22, 0x0); + var x32: u64 = undefined; + var x33: u1 = undefined; + addcarryxU64(&x32, &x33, x31, x24, 0x0); + var x34: u64 = undefined; + var x35: u1 = undefined; + addcarryxU64(&x34, &x35, x33, x26, 0x0); + var x36: u64 = undefined; + var x37: u64 = undefined; + mulxU64(&x36, &x37, x28, 0x4b0dff665588b13f); + var x38: u64 = undefined; + var x39: u64 = undefined; + mulxU64(&x38, &x39, x36, 0xffffffffffffffff); + var x40: u64 = undefined; + var x41: u64 = undefined; + mulxU64(&x40, &x41, x36, 0xfffffffffffffffe); + var x42: u64 = undefined; + var x43: u64 = undefined; + mulxU64(&x42, &x43, x36, 0xbaaedce6af48a03b); + var x44: u64 = undefined; + var x45: u64 = undefined; + mulxU64(&x44, &x45, x36, 0xbfd25e8cd0364141); + var x46: u64 = undefined; + var x47: u1 = undefined; + addcarryxU64(&x46, &x47, 0x0, x45, x42); + var x48: u64 = undefined; + var x49: u1 = undefined; + addcarryxU64(&x48, &x49, x47, x43, x40); + var x50: u64 = undefined; + var x51: u1 = undefined; + addcarryxU64(&x50, &x51, x49, x41, x38); + var x52: u64 = undefined; + var x53: u1 = undefined; + addcarryxU64(&x52, &x53, 0x0, x28, x44); + var x54: u64 = undefined; + var x55: u1 = undefined; + addcarryxU64(&x54, &x55, x53, x30, x46); + var x56: u64 = undefined; + var x57: u1 = undefined; + addcarryxU64(&x56, &x57, x55, x32, x48); + var x58: u64 = undefined; + var x59: u1 = undefined; + addcarryxU64(&x58, &x59, x57, x34, x50); + var x60: u64 = undefined; + var x61: u1 = undefined; + addcarryxU64(&x60, &x61, x59, (@as(u64, x35) + @as(u64, x27)), (@as(u64, x51) + x39)); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x54, (arg1[2])); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x56, 0x0); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x58, 0x0); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x60, 0x0); + var x70: u64 = undefined; + var x71: u64 = undefined; + mulxU64(&x70, &x71, x62, 0x4b0dff665588b13f); + var x72: u64 = undefined; + var x73: u64 = undefined; + mulxU64(&x72, &x73, x70, 0xffffffffffffffff); + var x74: u64 = undefined; + var x75: u64 = undefined; + mulxU64(&x74, &x75, x70, 0xfffffffffffffffe); + var x76: u64 = undefined; + var x77: u64 = undefined; + mulxU64(&x76, &x77, x70, 0xbaaedce6af48a03b); + var x78: u64 = undefined; + var x79: u64 = undefined; + mulxU64(&x78, &x79, x70, 0xbfd25e8cd0364141); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, 0x0, x79, x76); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x77, x74); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x75, x72); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, 0x0, x62, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x64, x80); + var x90: u64 = undefined; + var x91: u1 = undefined; + addcarryxU64(&x90, &x91, x89, x66, x82); + var x92: u64 = undefined; + var x93: u1 = undefined; + addcarryxU64(&x92, &x93, x91, x68, x84); + var x94: u64 = undefined; + var x95: u1 = undefined; + addcarryxU64(&x94, &x95, x93, (@as(u64, x69) + @as(u64, x61)), (@as(u64, x85) + x73)); + var x96: u64 = undefined; + var x97: u1 = undefined; + addcarryxU64(&x96, &x97, 0x0, x88, (arg1[3])); + var x98: u64 = undefined; + var x99: u1 = undefined; + addcarryxU64(&x98, &x99, x97, x90, 0x0); + var x100: u64 = undefined; + var x101: u1 = undefined; + addcarryxU64(&x100, &x101, x99, x92, 0x0); + var x102: u64 = undefined; + var x103: u1 = undefined; + addcarryxU64(&x102, &x103, x101, x94, 0x0); + var x104: u64 = undefined; + var x105: u64 = undefined; + mulxU64(&x104, &x105, x96, 0x4b0dff665588b13f); + var x106: u64 = undefined; + var x107: u64 = undefined; + mulxU64(&x106, &x107, x104, 0xffffffffffffffff); + var x108: u64 = undefined; + var x109: u64 = undefined; + mulxU64(&x108, &x109, x104, 0xfffffffffffffffe); + var x110: u64 = undefined; + var x111: u64 = undefined; + mulxU64(&x110, &x111, x104, 0xbaaedce6af48a03b); + var x112: u64 = undefined; + var x113: u64 = undefined; + mulxU64(&x112, &x113, x104, 0xbfd25e8cd0364141); + var x114: u64 = undefined; + var x115: u1 = undefined; + addcarryxU64(&x114, &x115, 0x0, x113, x110); + var x116: u64 = undefined; + var x117: u1 = undefined; + addcarryxU64(&x116, &x117, x115, x111, x108); + var x118: u64 = undefined; + var x119: u1 = undefined; + addcarryxU64(&x118, &x119, x117, x109, x106); + var x120: u64 = undefined; + var x121: u1 = undefined; + addcarryxU64(&x120, &x121, 0x0, x96, x112); + var x122: u64 = undefined; + var x123: u1 = undefined; + addcarryxU64(&x122, &x123, x121, x98, x114); + var x124: u64 = undefined; + var x125: u1 = undefined; + addcarryxU64(&x124, &x125, x123, x100, x116); + var x126: u64 = undefined; + var x127: u1 = undefined; + addcarryxU64(&x126, &x127, x125, x102, x118); + var x128: u64 = undefined; + var x129: u1 = undefined; + addcarryxU64(&x128, &x129, x127, (@as(u64, x103) + @as(u64, x95)), (@as(u64, x119) + x107)); + var x130: u64 = undefined; + var x131: u1 = undefined; + subborrowxU64(&x130, &x131, 0x0, x122, 0xbfd25e8cd0364141); + var x132: u64 = undefined; + var x133: u1 = undefined; + subborrowxU64(&x132, &x133, x131, x124, 0xbaaedce6af48a03b); + var x134: u64 = undefined; + var x135: u1 = undefined; + subborrowxU64(&x134, &x135, x133, x126, 0xfffffffffffffffe); + var x136: u64 = undefined; + var x137: u1 = undefined; + subborrowxU64(&x136, &x137, x135, x128, 0xffffffffffffffff); + var x138: u64 = undefined; + var x139: u1 = undefined; + subborrowxU64(&x138, &x139, x137, @as(u64, x129), 0x0); + var x140: u64 = undefined; + cmovznzU64(&x140, x139, x130, x122); + var x141: u64 = undefined; + cmovznzU64(&x141, x139, x132, x124); + var x142: u64 = undefined; + cmovznzU64(&x142, x139, x134, x126); + var x143: u64 = undefined; + cmovznzU64(&x143, x139, x136, x128); + out1[0] = x140; + out1[1] = x141; + out1[2] = x142; + out1[3] = x143; +} + +/// The function toMontgomery translates a field element into the Montgomery domain. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// eval (from_montgomery out1) mod m = eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +pub fn toMontgomery(out1: *MontgomeryDomainFieldElement, arg1: NonMontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[1]); + const x2 = (arg1[2]); + const x3 = (arg1[3]); + const x4 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + mulxU64(&x5, &x6, x4, 0x9d671cd581c69bc5); + var x7: u64 = undefined; + var x8: u64 = undefined; + mulxU64(&x7, &x8, x4, 0xe697f5e45bcd07c6); + var x9: u64 = undefined; + var x10: u64 = undefined; + mulxU64(&x9, &x10, x4, 0x741496c20e7cf878); + var x11: u64 = undefined; + var x12: u64 = undefined; + mulxU64(&x11, &x12, x4, 0x896cf21467d7d140); + var x13: u64 = undefined; + var x14: u1 = undefined; + addcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + addcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + addcarryxU64(&x17, &x18, x16, x8, x5); + var x19: u64 = undefined; + var x20: u64 = undefined; + mulxU64(&x19, &x20, x11, 0x4b0dff665588b13f); + var x21: u64 = undefined; + var x22: u64 = undefined; + mulxU64(&x21, &x22, x19, 0xffffffffffffffff); + var x23: u64 = undefined; + var x24: u64 = undefined; + mulxU64(&x23, &x24, x19, 0xfffffffffffffffe); + var x25: u64 = undefined; + var x26: u64 = undefined; + mulxU64(&x25, &x26, x19, 0xbaaedce6af48a03b); + var x27: u64 = undefined; + var x28: u64 = undefined; + mulxU64(&x27, &x28, x19, 0xbfd25e8cd0364141); + var x29: u64 = undefined; + var x30: u1 = undefined; + addcarryxU64(&x29, &x30, 0x0, x28, x25); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, x30, x26, x23); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, x24, x21); + var x35: u64 = undefined; + var x36: u1 = undefined; + addcarryxU64(&x35, &x36, 0x0, x11, x27); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, x36, x13, x29); + var x39: u64 = undefined; + var x40: u1 = undefined; + addcarryxU64(&x39, &x40, x38, x15, x31); + var x41: u64 = undefined; + var x42: u1 = undefined; + addcarryxU64(&x41, &x42, x40, x17, x33); + var x43: u64 = undefined; + var x44: u1 = undefined; + addcarryxU64(&x43, &x44, x42, (@as(u64, x18) + x6), (@as(u64, x34) + x22)); + var x45: u64 = undefined; + var x46: u64 = undefined; + mulxU64(&x45, &x46, x1, 0x9d671cd581c69bc5); + var x47: u64 = undefined; + var x48: u64 = undefined; + mulxU64(&x47, &x48, x1, 0xe697f5e45bcd07c6); + var x49: u64 = undefined; + var x50: u64 = undefined; + mulxU64(&x49, &x50, x1, 0x741496c20e7cf878); + var x51: u64 = undefined; + var x52: u64 = undefined; + mulxU64(&x51, &x52, x1, 0x896cf21467d7d140); + var x53: u64 = undefined; + var x54: u1 = undefined; + addcarryxU64(&x53, &x54, 0x0, x52, x49); + var x55: u64 = undefined; + var x56: u1 = undefined; + addcarryxU64(&x55, &x56, x54, x50, x47); + var x57: u64 = undefined; + var x58: u1 = undefined; + addcarryxU64(&x57, &x58, x56, x48, x45); + var x59: u64 = undefined; + var x60: u1 = undefined; + addcarryxU64(&x59, &x60, 0x0, x37, x51); + var x61: u64 = undefined; + var x62: u1 = undefined; + addcarryxU64(&x61, &x62, x60, x39, x53); + var x63: u64 = undefined; + var x64: u1 = undefined; + addcarryxU64(&x63, &x64, x62, x41, x55); + var x65: u64 = undefined; + var x66: u1 = undefined; + addcarryxU64(&x65, &x66, x64, x43, x57); + var x67: u64 = undefined; + var x68: u64 = undefined; + mulxU64(&x67, &x68, x59, 0x4b0dff665588b13f); + var x69: u64 = undefined; + var x70: u64 = undefined; + mulxU64(&x69, &x70, x67, 0xffffffffffffffff); + var x71: u64 = undefined; + var x72: u64 = undefined; + mulxU64(&x71, &x72, x67, 0xfffffffffffffffe); + var x73: u64 = undefined; + var x74: u64 = undefined; + mulxU64(&x73, &x74, x67, 0xbaaedce6af48a03b); + var x75: u64 = undefined; + var x76: u64 = undefined; + mulxU64(&x75, &x76, x67, 0xbfd25e8cd0364141); + var x77: u64 = undefined; + var x78: u1 = undefined; + addcarryxU64(&x77, &x78, 0x0, x76, x73); + var x79: u64 = undefined; + var x80: u1 = undefined; + addcarryxU64(&x79, &x80, x78, x74, x71); + var x81: u64 = undefined; + var x82: u1 = undefined; + addcarryxU64(&x81, &x82, x80, x72, x69); + var x83: u64 = undefined; + var x84: u1 = undefined; + addcarryxU64(&x83, &x84, 0x0, x59, x75); + var x85: u64 = undefined; + var x86: u1 = undefined; + addcarryxU64(&x85, &x86, x84, x61, x77); + var x87: u64 = undefined; + var x88: u1 = undefined; + addcarryxU64(&x87, &x88, x86, x63, x79); + var x89: u64 = undefined; + var x90: u1 = undefined; + addcarryxU64(&x89, &x90, x88, x65, x81); + var x91: u64 = undefined; + var x92: u1 = undefined; + addcarryxU64(&x91, &x92, x90, ((@as(u64, x66) + @as(u64, x44)) + (@as(u64, x58) + x46)), (@as(u64, x82) + x70)); + var x93: u64 = undefined; + var x94: u64 = undefined; + mulxU64(&x93, &x94, x2, 0x9d671cd581c69bc5); + var x95: u64 = undefined; + var x96: u64 = undefined; + mulxU64(&x95, &x96, x2, 0xe697f5e45bcd07c6); + var x97: u64 = undefined; + var x98: u64 = undefined; + mulxU64(&x97, &x98, x2, 0x741496c20e7cf878); + var x99: u64 = undefined; + var x100: u64 = undefined; + mulxU64(&x99, &x100, x2, 0x896cf21467d7d140); + var x101: u64 = undefined; + var x102: u1 = undefined; + addcarryxU64(&x101, &x102, 0x0, x100, x97); + var x103: u64 = undefined; + var x104: u1 = undefined; + addcarryxU64(&x103, &x104, x102, x98, x95); + var x105: u64 = undefined; + var x106: u1 = undefined; + addcarryxU64(&x105, &x106, x104, x96, x93); + var x107: u64 = undefined; + var x108: u1 = undefined; + addcarryxU64(&x107, &x108, 0x0, x85, x99); + var x109: u64 = undefined; + var x110: u1 = undefined; + addcarryxU64(&x109, &x110, x108, x87, x101); + var x111: u64 = undefined; + var x112: u1 = undefined; + addcarryxU64(&x111, &x112, x110, x89, x103); + var x113: u64 = undefined; + var x114: u1 = undefined; + addcarryxU64(&x113, &x114, x112, x91, x105); + var x115: u64 = undefined; + var x116: u64 = undefined; + mulxU64(&x115, &x116, x107, 0x4b0dff665588b13f); + var x117: u64 = undefined; + var x118: u64 = undefined; + mulxU64(&x117, &x118, x115, 0xffffffffffffffff); + var x119: u64 = undefined; + var x120: u64 = undefined; + mulxU64(&x119, &x120, x115, 0xfffffffffffffffe); + var x121: u64 = undefined; + var x122: u64 = undefined; + mulxU64(&x121, &x122, x115, 0xbaaedce6af48a03b); + var x123: u64 = undefined; + var x124: u64 = undefined; + mulxU64(&x123, &x124, x115, 0xbfd25e8cd0364141); + var x125: u64 = undefined; + var x126: u1 = undefined; + addcarryxU64(&x125, &x126, 0x0, x124, x121); + var x127: u64 = undefined; + var x128: u1 = undefined; + addcarryxU64(&x127, &x128, x126, x122, x119); + var x129: u64 = undefined; + var x130: u1 = undefined; + addcarryxU64(&x129, &x130, x128, x120, x117); + var x131: u64 = undefined; + var x132: u1 = undefined; + addcarryxU64(&x131, &x132, 0x0, x107, x123); + var x133: u64 = undefined; + var x134: u1 = undefined; + addcarryxU64(&x133, &x134, x132, x109, x125); + var x135: u64 = undefined; + var x136: u1 = undefined; + addcarryxU64(&x135, &x136, x134, x111, x127); + var x137: u64 = undefined; + var x138: u1 = undefined; + addcarryxU64(&x137, &x138, x136, x113, x129); + var x139: u64 = undefined; + var x140: u1 = undefined; + addcarryxU64(&x139, &x140, x138, ((@as(u64, x114) + @as(u64, x92)) + (@as(u64, x106) + x94)), (@as(u64, x130) + x118)); + var x141: u64 = undefined; + var x142: u64 = undefined; + mulxU64(&x141, &x142, x3, 0x9d671cd581c69bc5); + var x143: u64 = undefined; + var x144: u64 = undefined; + mulxU64(&x143, &x144, x3, 0xe697f5e45bcd07c6); + var x145: u64 = undefined; + var x146: u64 = undefined; + mulxU64(&x145, &x146, x3, 0x741496c20e7cf878); + var x147: u64 = undefined; + var x148: u64 = undefined; + mulxU64(&x147, &x148, x3, 0x896cf21467d7d140); + var x149: u64 = undefined; + var x150: u1 = undefined; + addcarryxU64(&x149, &x150, 0x0, x148, x145); + var x151: u64 = undefined; + var x152: u1 = undefined; + addcarryxU64(&x151, &x152, x150, x146, x143); + var x153: u64 = undefined; + var x154: u1 = undefined; + addcarryxU64(&x153, &x154, x152, x144, x141); + var x155: u64 = undefined; + var x156: u1 = undefined; + addcarryxU64(&x155, &x156, 0x0, x133, x147); + var x157: u64 = undefined; + var x158: u1 = undefined; + addcarryxU64(&x157, &x158, x156, x135, x149); + var x159: u64 = undefined; + var x160: u1 = undefined; + addcarryxU64(&x159, &x160, x158, x137, x151); + var x161: u64 = undefined; + var x162: u1 = undefined; + addcarryxU64(&x161, &x162, x160, x139, x153); + var x163: u64 = undefined; + var x164: u64 = undefined; + mulxU64(&x163, &x164, x155, 0x4b0dff665588b13f); + var x165: u64 = undefined; + var x166: u64 = undefined; + mulxU64(&x165, &x166, x163, 0xffffffffffffffff); + var x167: u64 = undefined; + var x168: u64 = undefined; + mulxU64(&x167, &x168, x163, 0xfffffffffffffffe); + var x169: u64 = undefined; + var x170: u64 = undefined; + mulxU64(&x169, &x170, x163, 0xbaaedce6af48a03b); + var x171: u64 = undefined; + var x172: u64 = undefined; + mulxU64(&x171, &x172, x163, 0xbfd25e8cd0364141); + var x173: u64 = undefined; + var x174: u1 = undefined; + addcarryxU64(&x173, &x174, 0x0, x172, x169); + var x175: u64 = undefined; + var x176: u1 = undefined; + addcarryxU64(&x175, &x176, x174, x170, x167); + var x177: u64 = undefined; + var x178: u1 = undefined; + addcarryxU64(&x177, &x178, x176, x168, x165); + var x179: u64 = undefined; + var x180: u1 = undefined; + addcarryxU64(&x179, &x180, 0x0, x155, x171); + var x181: u64 = undefined; + var x182: u1 = undefined; + addcarryxU64(&x181, &x182, x180, x157, x173); + var x183: u64 = undefined; + var x184: u1 = undefined; + addcarryxU64(&x183, &x184, x182, x159, x175); + var x185: u64 = undefined; + var x186: u1 = undefined; + addcarryxU64(&x185, &x186, x184, x161, x177); + var x187: u64 = undefined; + var x188: u1 = undefined; + addcarryxU64(&x187, &x188, x186, ((@as(u64, x162) + @as(u64, x140)) + (@as(u64, x154) + x142)), (@as(u64, x178) + x166)); + var x189: u64 = undefined; + var x190: u1 = undefined; + subborrowxU64(&x189, &x190, 0x0, x181, 0xbfd25e8cd0364141); + var x191: u64 = undefined; + var x192: u1 = undefined; + subborrowxU64(&x191, &x192, x190, x183, 0xbaaedce6af48a03b); + var x193: u64 = undefined; + var x194: u1 = undefined; + subborrowxU64(&x193, &x194, x192, x185, 0xfffffffffffffffe); + var x195: u64 = undefined; + var x196: u1 = undefined; + subborrowxU64(&x195, &x196, x194, x187, 0xffffffffffffffff); + var x197: u64 = undefined; + var x198: u1 = undefined; + subborrowxU64(&x197, &x198, x196, @as(u64, x188), 0x0); + var x199: u64 = undefined; + cmovznzU64(&x199, x198, x189, x181); + var x200: u64 = undefined; + cmovznzU64(&x200, x198, x191, x183); + var x201: u64 = undefined; + cmovznzU64(&x201, x198, x193, x185); + var x202: u64 = undefined; + cmovznzU64(&x202, x198, x195, x187); + out1[0] = x199; + out1[1] = x200; + out1[2] = x201; + out1[3] = x202; +} + +/// The function nonzero outputs a single non-zero word if the input is non-zero and zero otherwise. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +pub fn nonzero(out1: *u64, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); + out1.* = x1; +} + +/// The function selectznz is a multi-limb conditional select. +/// +/// Postconditions: +/// out1 = (if arg1 = 0 then arg2 else arg3) +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0x1] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn selectznz(out1: *[4]u64, arg1: u1, arg2: [4]u64, arg3: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + cmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); + var x2: u64 = undefined; + cmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); + var x3: u64 = undefined; + cmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); + var x4: u64 = undefined; + cmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); + out1[0] = x1; + out1[1] = x2; + out1[2] = x3; + out1[3] = x4; +} + +/// The function toBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +/// +/// Preconditions: +/// 0 ≤ eval arg1 < m +/// Postconditions: +/// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31] +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +pub fn toBytes(out1: *[32]u8, arg1: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (arg1[3]); + const x2 = (arg1[2]); + const x3 = (arg1[1]); + const x4 = (arg1[0]); + const x5 = @truncate(u8, (x4 & 0xff)); + const x6 = (x4 >> 8); + const x7 = @truncate(u8, (x6 & 0xff)); + const x8 = (x6 >> 8); + const x9 = @truncate(u8, (x8 & 0xff)); + const x10 = (x8 >> 8); + const x11 = @truncate(u8, (x10 & 0xff)); + const x12 = (x10 >> 8); + const x13 = @truncate(u8, (x12 & 0xff)); + const x14 = (x12 >> 8); + const x15 = @truncate(u8, (x14 & 0xff)); + const x16 = (x14 >> 8); + const x17 = @truncate(u8, (x16 & 0xff)); + const x18 = @truncate(u8, (x16 >> 8)); + const x19 = @truncate(u8, (x3 & 0xff)); + const x20 = (x3 >> 8); + const x21 = @truncate(u8, (x20 & 0xff)); + const x22 = (x20 >> 8); + const x23 = @truncate(u8, (x22 & 0xff)); + const x24 = (x22 >> 8); + const x25 = @truncate(u8, (x24 & 0xff)); + const x26 = (x24 >> 8); + const x27 = @truncate(u8, (x26 & 0xff)); + const x28 = (x26 >> 8); + const x29 = @truncate(u8, (x28 & 0xff)); + const x30 = (x28 >> 8); + const x31 = @truncate(u8, (x30 & 0xff)); + const x32 = @truncate(u8, (x30 >> 8)); + const x33 = @truncate(u8, (x2 & 0xff)); + const x34 = (x2 >> 8); + const x35 = @truncate(u8, (x34 & 0xff)); + const x36 = (x34 >> 8); + const x37 = @truncate(u8, (x36 & 0xff)); + const x38 = (x36 >> 8); + const x39 = @truncate(u8, (x38 & 0xff)); + const x40 = (x38 >> 8); + const x41 = @truncate(u8, (x40 & 0xff)); + const x42 = (x40 >> 8); + const x43 = @truncate(u8, (x42 & 0xff)); + const x44 = (x42 >> 8); + const x45 = @truncate(u8, (x44 & 0xff)); + const x46 = @truncate(u8, (x44 >> 8)); + const x47 = @truncate(u8, (x1 & 0xff)); + const x48 = (x1 >> 8); + const x49 = @truncate(u8, (x48 & 0xff)); + const x50 = (x48 >> 8); + const x51 = @truncate(u8, (x50 & 0xff)); + const x52 = (x50 >> 8); + const x53 = @truncate(u8, (x52 & 0xff)); + const x54 = (x52 >> 8); + const x55 = @truncate(u8, (x54 & 0xff)); + const x56 = (x54 >> 8); + const x57 = @truncate(u8, (x56 & 0xff)); + const x58 = (x56 >> 8); + const x59 = @truncate(u8, (x58 & 0xff)); + const x60 = @truncate(u8, (x58 >> 8)); + out1[0] = x5; + out1[1] = x7; + out1[2] = x9; + out1[3] = x11; + out1[4] = x13; + out1[5] = x15; + out1[6] = x17; + out1[7] = x18; + out1[8] = x19; + out1[9] = x21; + out1[10] = x23; + out1[11] = x25; + out1[12] = x27; + out1[13] = x29; + out1[14] = x31; + out1[15] = x32; + out1[16] = x33; + out1[17] = x35; + out1[18] = x37; + out1[19] = x39; + out1[20] = x41; + out1[21] = x43; + out1[22] = x45; + out1[23] = x46; + out1[24] = x47; + out1[25] = x49; + out1[26] = x51; + out1[27] = x53; + out1[28] = x55; + out1[29] = x57; + out1[30] = x59; + out1[31] = x60; +} + +/// The function fromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +/// +/// Preconditions: +/// 0 ≤ bytes_eval arg1 < m +/// Postconditions: +/// eval out1 mod m = bytes_eval arg1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn fromBytes(out1: *[4]u64, arg1: [32]u8) void { + @setRuntimeSafety(mode == .Debug); + + const x1 = (@as(u64, (arg1[31])) << 56); + const x2 = (@as(u64, (arg1[30])) << 48); + const x3 = (@as(u64, (arg1[29])) << 40); + const x4 = (@as(u64, (arg1[28])) << 32); + const x5 = (@as(u64, (arg1[27])) << 24); + const x6 = (@as(u64, (arg1[26])) << 16); + const x7 = (@as(u64, (arg1[25])) << 8); + const x8 = (arg1[24]); + const x9 = (@as(u64, (arg1[23])) << 56); + const x10 = (@as(u64, (arg1[22])) << 48); + const x11 = (@as(u64, (arg1[21])) << 40); + const x12 = (@as(u64, (arg1[20])) << 32); + const x13 = (@as(u64, (arg1[19])) << 24); + const x14 = (@as(u64, (arg1[18])) << 16); + const x15 = (@as(u64, (arg1[17])) << 8); + const x16 = (arg1[16]); + const x17 = (@as(u64, (arg1[15])) << 56); + const x18 = (@as(u64, (arg1[14])) << 48); + const x19 = (@as(u64, (arg1[13])) << 40); + const x20 = (@as(u64, (arg1[12])) << 32); + const x21 = (@as(u64, (arg1[11])) << 24); + const x22 = (@as(u64, (arg1[10])) << 16); + const x23 = (@as(u64, (arg1[9])) << 8); + const x24 = (arg1[8]); + const x25 = (@as(u64, (arg1[7])) << 56); + const x26 = (@as(u64, (arg1[6])) << 48); + const x27 = (@as(u64, (arg1[5])) << 40); + const x28 = (@as(u64, (arg1[4])) << 32); + const x29 = (@as(u64, (arg1[3])) << 24); + const x30 = (@as(u64, (arg1[2])) << 16); + const x31 = (@as(u64, (arg1[1])) << 8); + const x32 = (arg1[0]); + const x33 = (x31 + @as(u64, x32)); + const x34 = (x30 + x33); + const x35 = (x29 + x34); + const x36 = (x28 + x35); + const x37 = (x27 + x36); + const x38 = (x26 + x37); + const x39 = (x25 + x38); + const x40 = (x23 + @as(u64, x24)); + const x41 = (x22 + x40); + const x42 = (x21 + x41); + const x43 = (x20 + x42); + const x44 = (x19 + x43); + const x45 = (x18 + x44); + const x46 = (x17 + x45); + const x47 = (x15 + @as(u64, x16)); + const x48 = (x14 + x47); + const x49 = (x13 + x48); + const x50 = (x12 + x49); + const x51 = (x11 + x50); + const x52 = (x10 + x51); + const x53 = (x9 + x52); + const x54 = (x7 + @as(u64, x8)); + const x55 = (x6 + x54); + const x56 = (x5 + x55); + const x57 = (x4 + x56); + const x58 = (x3 + x57); + const x59 = (x2 + x58); + const x60 = (x1 + x59); + out1[0] = x39; + out1[1] = x46; + out1[2] = x53; + out1[3] = x60; +} + +/// The function setOne returns the field element one in the Montgomery domain. +/// +/// Postconditions: +/// eval (from_montgomery out1) mod m = 1 mod m +/// 0 ≤ eval out1 < m +/// +pub fn setOne(out1: *MontgomeryDomainFieldElement) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0x402da1732fc9bebf; + out1[1] = 0x4551231950b75fc4; + out1[2] = 0x1; + out1[3] = 0x0; +} + +/// The function msat returns the saturated representation of the prime modulus. +/// +/// Postconditions: +/// twos_complement_eval out1 = m +/// 0 ≤ eval out1 < m +/// +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn msat(out1: *[5]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xbfd25e8cd0364141; + out1[1] = 0xbaaedce6af48a03b; + out1[2] = 0xfffffffffffffffe; + out1[3] = 0xffffffffffffffff; + out1[4] = 0x0; +} + +/// The function divstep computes a divstep. +/// +/// Preconditions: +/// 0 ≤ eval arg4 < m +/// 0 ≤ eval arg5 < m +/// Postconditions: +/// out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1) +/// twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2) +/// twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋) +/// eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m) +/// eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m) +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out5 < m +/// 0 ≤ eval out2 < m +/// 0 ≤ eval out3 < m +/// +/// Input Bounds: +/// arg1: [0x0 ~> 0xffffffffffffffff] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [0x0 ~> 0xffffffffffffffff] +/// out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *[4]u64, out5: *[4]u64, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: [4]u64, arg5: [4]u64) void { + @setRuntimeSafety(mode == .Debug); + + var x1: u64 = undefined; + var x2: u1 = undefined; + addcarryxU64(&x1, &x2, 0x0, (~arg1), 0x1); + const x3 = (@truncate(u1, (x1 >> 63)) & @truncate(u1, ((arg3[0]) & 0x1))); + var x4: u64 = undefined; + var x5: u1 = undefined; + addcarryxU64(&x4, &x5, 0x0, (~arg1), 0x1); + var x6: u64 = undefined; + cmovznzU64(&x6, x3, arg1, x4); + var x7: u64 = undefined; + cmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); + var x8: u64 = undefined; + cmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); + var x9: u64 = undefined; + cmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); + var x10: u64 = undefined; + cmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); + var x11: u64 = undefined; + cmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); + var x12: u64 = undefined; + var x13: u1 = undefined; + addcarryxU64(&x12, &x13, 0x0, 0x1, (~(arg2[0]))); + var x14: u64 = undefined; + var x15: u1 = undefined; + addcarryxU64(&x14, &x15, x13, 0x0, (~(arg2[1]))); + var x16: u64 = undefined; + var x17: u1 = undefined; + addcarryxU64(&x16, &x17, x15, 0x0, (~(arg2[2]))); + var x18: u64 = undefined; + var x19: u1 = undefined; + addcarryxU64(&x18, &x19, x17, 0x0, (~(arg2[3]))); + var x20: u64 = undefined; + var x21: u1 = undefined; + addcarryxU64(&x20, &x21, x19, 0x0, (~(arg2[4]))); + var x22: u64 = undefined; + cmovznzU64(&x22, x3, (arg3[0]), x12); + var x23: u64 = undefined; + cmovznzU64(&x23, x3, (arg3[1]), x14); + var x24: u64 = undefined; + cmovznzU64(&x24, x3, (arg3[2]), x16); + var x25: u64 = undefined; + cmovznzU64(&x25, x3, (arg3[3]), x18); + var x26: u64 = undefined; + cmovznzU64(&x26, x3, (arg3[4]), x20); + var x27: u64 = undefined; + cmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); + var x28: u64 = undefined; + cmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); + var x29: u64 = undefined; + cmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); + var x30: u64 = undefined; + cmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); + var x31: u64 = undefined; + var x32: u1 = undefined; + addcarryxU64(&x31, &x32, 0x0, x27, x27); + var x33: u64 = undefined; + var x34: u1 = undefined; + addcarryxU64(&x33, &x34, x32, x28, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + addcarryxU64(&x35, &x36, x34, x29, x29); + var x37: u64 = undefined; + var x38: u1 = undefined; + addcarryxU64(&x37, &x38, x36, x30, x30); + var x39: u64 = undefined; + var x40: u1 = undefined; + subborrowxU64(&x39, &x40, 0x0, x31, 0xbfd25e8cd0364141); + var x41: u64 = undefined; + var x42: u1 = undefined; + subborrowxU64(&x41, &x42, x40, x33, 0xbaaedce6af48a03b); + var x43: u64 = undefined; + var x44: u1 = undefined; + subborrowxU64(&x43, &x44, x42, x35, 0xfffffffffffffffe); + var x45: u64 = undefined; + var x46: u1 = undefined; + subborrowxU64(&x45, &x46, x44, x37, 0xffffffffffffffff); + var x47: u64 = undefined; + var x48: u1 = undefined; + subborrowxU64(&x47, &x48, x46, @as(u64, x38), 0x0); + const x49 = (arg4[3]); + const x50 = (arg4[2]); + const x51 = (arg4[1]); + const x52 = (arg4[0]); + var x53: u64 = undefined; + var x54: u1 = undefined; + subborrowxU64(&x53, &x54, 0x0, 0x0, x52); + var x55: u64 = undefined; + var x56: u1 = undefined; + subborrowxU64(&x55, &x56, x54, 0x0, x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + subborrowxU64(&x57, &x58, x56, 0x0, x50); + var x59: u64 = undefined; + var x60: u1 = undefined; + subborrowxU64(&x59, &x60, x58, 0x0, x49); + var x61: u64 = undefined; + cmovznzU64(&x61, x60, 0x0, 0xffffffffffffffff); + var x62: u64 = undefined; + var x63: u1 = undefined; + addcarryxU64(&x62, &x63, 0x0, x53, (x61 & 0xbfd25e8cd0364141)); + var x64: u64 = undefined; + var x65: u1 = undefined; + addcarryxU64(&x64, &x65, x63, x55, (x61 & 0xbaaedce6af48a03b)); + var x66: u64 = undefined; + var x67: u1 = undefined; + addcarryxU64(&x66, &x67, x65, x57, (x61 & 0xfffffffffffffffe)); + var x68: u64 = undefined; + var x69: u1 = undefined; + addcarryxU64(&x68, &x69, x67, x59, x61); + var x70: u64 = undefined; + cmovznzU64(&x70, x3, (arg5[0]), x62); + var x71: u64 = undefined; + cmovznzU64(&x71, x3, (arg5[1]), x64); + var x72: u64 = undefined; + cmovznzU64(&x72, x3, (arg5[2]), x66); + var x73: u64 = undefined; + cmovznzU64(&x73, x3, (arg5[3]), x68); + const x74 = @truncate(u1, (x22 & 0x1)); + var x75: u64 = undefined; + cmovznzU64(&x75, x74, 0x0, x7); + var x76: u64 = undefined; + cmovznzU64(&x76, x74, 0x0, x8); + var x77: u64 = undefined; + cmovznzU64(&x77, x74, 0x0, x9); + var x78: u64 = undefined; + cmovznzU64(&x78, x74, 0x0, x10); + var x79: u64 = undefined; + cmovznzU64(&x79, x74, 0x0, x11); + var x80: u64 = undefined; + var x81: u1 = undefined; + addcarryxU64(&x80, &x81, 0x0, x22, x75); + var x82: u64 = undefined; + var x83: u1 = undefined; + addcarryxU64(&x82, &x83, x81, x23, x76); + var x84: u64 = undefined; + var x85: u1 = undefined; + addcarryxU64(&x84, &x85, x83, x24, x77); + var x86: u64 = undefined; + var x87: u1 = undefined; + addcarryxU64(&x86, &x87, x85, x25, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + addcarryxU64(&x88, &x89, x87, x26, x79); + var x90: u64 = undefined; + cmovznzU64(&x90, x74, 0x0, x27); + var x91: u64 = undefined; + cmovznzU64(&x91, x74, 0x0, x28); + var x92: u64 = undefined; + cmovznzU64(&x92, x74, 0x0, x29); + var x93: u64 = undefined; + cmovznzU64(&x93, x74, 0x0, x30); + var x94: u64 = undefined; + var x95: u1 = undefined; + addcarryxU64(&x94, &x95, 0x0, x70, x90); + var x96: u64 = undefined; + var x97: u1 = undefined; + addcarryxU64(&x96, &x97, x95, x71, x91); + var x98: u64 = undefined; + var x99: u1 = undefined; + addcarryxU64(&x98, &x99, x97, x72, x92); + var x100: u64 = undefined; + var x101: u1 = undefined; + addcarryxU64(&x100, &x101, x99, x73, x93); + var x102: u64 = undefined; + var x103: u1 = undefined; + subborrowxU64(&x102, &x103, 0x0, x94, 0xbfd25e8cd0364141); + var x104: u64 = undefined; + var x105: u1 = undefined; + subborrowxU64(&x104, &x105, x103, x96, 0xbaaedce6af48a03b); + var x106: u64 = undefined; + var x107: u1 = undefined; + subborrowxU64(&x106, &x107, x105, x98, 0xfffffffffffffffe); + var x108: u64 = undefined; + var x109: u1 = undefined; + subborrowxU64(&x108, &x109, x107, x100, 0xffffffffffffffff); + var x110: u64 = undefined; + var x111: u1 = undefined; + subborrowxU64(&x110, &x111, x109, @as(u64, x101), 0x0); + var x112: u64 = undefined; + var x113: u1 = undefined; + addcarryxU64(&x112, &x113, 0x0, x6, 0x1); + const x114 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); + const x115 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); + const x116 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); + const x117 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); + const x118 = ((x88 & 0x8000000000000000) | (x88 >> 1)); + var x119: u64 = undefined; + cmovznzU64(&x119, x48, x39, x31); + var x120: u64 = undefined; + cmovznzU64(&x120, x48, x41, x33); + var x121: u64 = undefined; + cmovznzU64(&x121, x48, x43, x35); + var x122: u64 = undefined; + cmovznzU64(&x122, x48, x45, x37); + var x123: u64 = undefined; + cmovznzU64(&x123, x111, x102, x94); + var x124: u64 = undefined; + cmovznzU64(&x124, x111, x104, x96); + var x125: u64 = undefined; + cmovznzU64(&x125, x111, x106, x98); + var x126: u64 = undefined; + cmovznzU64(&x126, x111, x108, x100); + out1.* = x112; + out2[0] = x7; + out2[1] = x8; + out2[2] = x9; + out2[3] = x10; + out2[4] = x11; + out3[0] = x114; + out3[1] = x115; + out3[2] = x116; + out3[3] = x117; + out3[4] = x118; + out4[0] = x119; + out4[1] = x120; + out4[2] = x121; + out4[3] = x122; + out5[0] = x123; + out5[1] = x124; + out5[2] = x125; + out5[3] = x126; +} + +/// The function divstepPrecomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form). +/// +/// Postconditions: +/// eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if ⌊log2 m⌋ + 1 < 46 then ⌊(49 * (⌊log2 m⌋ + 1) + 80) / 17⌋ else ⌊(49 * (⌊log2 m⌋ + 1) + 57) / 17⌋) +/// 0 ≤ eval out1 < m +/// +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn divstepPrecomp(out1: *[4]u64) void { + @setRuntimeSafety(mode == .Debug); + + out1[0] = 0xd7431a4d2b9cb4e9; + out1[1] = 0xab67d35a32d9c503; + out1[2] = 0xadf6c7e5859ce35f; + out1[3] = 0x615441451df6c379; +} diff --git a/lib/std/crypto/pcurves/tests/secp256k1.zig b/lib/std/crypto/pcurves/tests/secp256k1.zig new file mode 100644 index 0000000000..32fca87691 --- /dev/null +++ b/lib/std/crypto/pcurves/tests/secp256k1.zig @@ -0,0 +1,137 @@ +const std = @import("std"); +const fmt = std.fmt; +const testing = std.testing; + +const Secp256k1 = @import("../secp256k1.zig").Secp256k1; + +test "secp256k1 ECDH key exchange" { + const dha = Secp256k1.scalar.random(.Little); + const dhb = Secp256k1.scalar.random(.Little); + const dhA = try Secp256k1.basePoint.mul(dha, .Little); + const dhB = try Secp256k1.basePoint.mul(dhb, .Little); + const shareda = try dhA.mul(dhb, .Little); + const sharedb = try dhB.mul(dha, .Little); + try testing.expect(shareda.equivalent(sharedb)); +} + +test "secp256k1 ECDH key exchange including public multiplication" { + const dha = Secp256k1.scalar.random(.Little); + const dhb = Secp256k1.scalar.random(.Little); + const dhA = try Secp256k1.basePoint.mul(dha, .Little); + const dhB = try Secp256k1.basePoint.mulPublic(dhb, .Little); + const shareda = try dhA.mul(dhb, .Little); + const sharedb = try dhB.mulPublic(dha, .Little); + try testing.expect(shareda.equivalent(sharedb)); +} + +test "secp256k1 point from affine coordinates" { + const xh = "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"; + const yh = "483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"; + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + var ys: [32]u8 = undefined; + _ = try fmt.hexToBytes(&ys, yh); + var p = try Secp256k1.fromSerializedAffineCoordinates(xs, ys, .Big); + try testing.expect(p.equivalent(Secp256k1.basePoint)); +} + +test "secp256k1 test vectors" { + const expected = [_][]const u8{ + "0000000000000000000000000000000000000000000000000000000000000000", + "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798", + "c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5", + "f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9", + "e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13", + "2f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4", + "fff97bd5755eeea420453a14355235d382f6472f8568a18b2f057a1460297556", + "5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc", + "2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01", + "acd484e2f0c7f65309ad178a9f559abde09796974c57e714c35f110dfc27ccbe", + }; + var p = Secp256k1.identityElement; + for (expected) |xh| { + const x = p.affineCoordinates().x; + p = p.add(Secp256k1.basePoint); + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + try testing.expectEqualSlices(u8, &x.toBytes(.Big), &xs); + } +} + +test "secp256k1 test vectors - doubling" { + const expected = [_][]const u8{ + "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798", + "c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5", + "e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13", + "2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01", + "e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a", + }; + var p = Secp256k1.basePoint; + for (expected) |xh| { + const x = p.affineCoordinates().x; + p = p.dbl(); + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + try testing.expectEqualSlices(u8, &x.toBytes(.Big), &xs); + } +} + +test "secp256k1 compressed sec1 encoding/decoding" { + const p = Secp256k1.random(); + const s = p.toCompressedSec1(); + const q = try Secp256k1.fromSec1(&s); + try testing.expect(p.equivalent(q)); +} + +test "secp256k1 uncompressed sec1 encoding/decoding" { + const p = Secp256k1.random(); + const s = p.toUncompressedSec1(); + const q = try Secp256k1.fromSec1(&s); + try testing.expect(p.equivalent(q)); +} + +test "secp256k1 public key is the neutral element" { + const n = Secp256k1.scalar.Scalar.zero.toBytes(.Little); + const p = Secp256k1.random(); + try testing.expectError(error.IdentityElement, p.mul(n, .Little)); +} + +test "secp256k1 public key is the neutral element (public verification)" { + const n = Secp256k1.scalar.Scalar.zero.toBytes(.Little); + const p = Secp256k1.random(); + try testing.expectError(error.IdentityElement, p.mulPublic(n, .Little)); +} + +test "secp256k1 field element non-canonical encoding" { + const s = [_]u8{0xff} ** 32; + try testing.expectError(error.NonCanonical, Secp256k1.Fe.fromBytes(s, .Little)); +} + +test "secp256k1 neutral element decoding" { + try testing.expectError(error.InvalidEncoding, Secp256k1.fromAffineCoordinates(.{ .x = Secp256k1.Fe.zero, .y = Secp256k1.Fe.zero })); + const p = try Secp256k1.fromAffineCoordinates(.{ .x = Secp256k1.Fe.zero, .y = Secp256k1.Fe.one }); + try testing.expectError(error.IdentityElement, p.rejectIdentity()); +} + +test "secp256k1 double base multiplication" { + const p1 = Secp256k1.basePoint; + const p2 = Secp256k1.basePoint.dbl(); + const s1 = [_]u8{0x01} ** 32; + const s2 = [_]u8{0x02} ** 32; + const pr1 = try Secp256k1.mulDoubleBasePublic(p1, s1, p2, s2, .Little); + const pr2 = (try p1.mul(s1, .Little)).add(try p2.mul(s2, .Little)); + try testing.expect(pr1.equivalent(pr2)); +} + +test "secp256k1 scalar inverse" { + const expected = "08d0684a0fe8ea978b68a29e4b4ffdbd19eeb59db25301cf23ecbe568e1f9822"; + var out: [32]u8 = undefined; + _ = try std.fmt.hexToBytes(&out, expected); + + const scalar = try Secp256k1.scalar.Scalar.fromBytes(.{ + 0x94, 0xa1, 0xbb, 0xb1, 0x4b, 0x90, 0x6a, 0x61, 0xa2, 0x80, 0xf2, 0x45, 0xf9, 0xe9, 0x3c, 0x7f, + 0x3b, 0x4a, 0x62, 0x47, 0x82, 0x4f, 0x5d, 0x33, 0xb9, 0x67, 0x07, 0x87, 0x64, 0x2a, 0x68, 0xde, + }, .Big); + const inverse = scalar.invert(); + try std.testing.expectEqualSlices(u8, &out, &inverse.toBytes(.Big)); +}