diff --git a/lib/std/crypto.zig b/lib/std/crypto.zig index e4ec50f5b7..af23af9460 100644 --- a/lib/std/crypto.zig +++ b/lib/std/crypto.zig @@ -67,6 +67,7 @@ pub const dh = struct { pub const ecc = struct { pub const Curve25519 = @import("crypto/25519/curve25519.zig").Curve25519; pub const Edwards25519 = @import("crypto/25519/edwards25519.zig").Edwards25519; + pub const P256 = @import("crypto/pcurves/p256.zig").P256; pub const Ristretto255 = @import("crypto/25519/ristretto255.zig").Ristretto255; }; diff --git a/lib/std/crypto/pcurves/p256.zig b/lib/std/crypto/pcurves/p256.zig new file mode 100644 index 0000000000..0b1c584fa9 --- /dev/null +++ b/lib/std/crypto/pcurves/p256.zig @@ -0,0 +1,412 @@ +// SPDX-License-Identifier: MIT +// Copyright (c) 2015-2021 Zig Contributors +// This file is part of [zig](https://ziglang.org/), which is MIT licensed. +// The MIT license requires this copyright notice to be included in all copies +// and substantial portions of the software. + +const std = @import("std"); +const builtin = std.builtin; +const crypto = std.crypto; +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 P256. +pub const P256 = struct { + /// The underlying prime field. + pub const Fe = @import("p256/field.zig").Fe; + /// Field arithmetic mod the order of the main subgroup. + pub const scalar = @import("p256/scalar.zig"); + + x: Fe, + y: Fe, + z: Fe = Fe.one, + + is_base: bool = false, + + /// The P256 base point. + pub const basePoint = P256{ + .x = try Fe.fromInt(48439561293906451759052585252797914202762949526041747995844080717082404635286), + .y = try Fe.fromInt(36134250956749795798585127919587881956611106672985015071877198253568414405109), + .z = Fe.one, + .is_base = true, + }; + + /// The P256 neutral element. + pub const identityElement = P256{ .x = Fe.zero, .y = Fe.one, .z = Fe.zero }; + + pub const B = try Fe.fromInt(41058363725152142129326129780047268409114441015993725554835256314039467401291); + + /// Reject the neutral element. + pub fn rejectIdentity(p: P256) 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(x: Fe, y: Fe) EncodingError!P256 { + const x3AxB = x.sq().mul(x).sub(x).sub(x).sub(x).add(B); + const yy = y.sq(); + if (!x3AxB.equivalent(yy)) { + return error.InvalidEncoding; + } + const p: P256 = .{ .x = x, .y = y, .z = Fe.one }; + return p; + } + + /// Create a point from serialized affine coordinates. + pub fn fromSerializedAffineCoordinates(xs: [32]u8, ys: [32]u8, endian: builtin.Endian) (NonCanonicalError || EncodingError)!P256 { + const x = try Fe.fromBytes(xs, endian); + const y = try Fe.fromBytes(ys, endian); + return fromAffineCoordinates(x, y); + } + + /// Recover the Y coordinate from the X coordinate. + pub fn recoverY(x: Fe, is_odd: bool) NotSquareError!Fe { + const x3AxB = x.sq().mul(x).sub(x).sub(x).sub(x).add(B); + var y = try x3AxB.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)!P256 { + 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 P256.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 P256{ .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 P256.fromAffineCoordinates(x, y); + }, + else => return error.InvalidEncoding, + } + } + + /// Serialize a point using the compressed SEC-1 format. + pub fn toCompressedSec1(p: P256) [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: P256) [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() P256 { + const n = scalar.random(.Little); + return basePoint.mul(n, .Little) catch unreachable; + } + + /// Flip the sign of the X coordinate. + pub fn neg(p: P256) P256 { + return .{ .x = p.x, .y = p.y.neg(), .z = p.z }; + } + + /// Double a P256 point. + // Algorithm 6 from https://eprint.iacr.org/2015/1060.pdf + pub fn dbl(p: P256) P256 { + var t0 = p.x.sq(); + var t1 = p.y.sq(); + var t2 = p.z.sq(); + var t3 = p.x.mul(p.y); + t3 = t3.dbl(); + var Z3 = p.x.mul(p.z); + Z3 = Z3.add(Z3); + var Y3 = B.mul(t2); + Y3 = Y3.sub(Z3); + var X3 = Y3.dbl(); + Y3 = X3.add(Y3); + X3 = t1.sub(Y3); + Y3 = t1.add(Y3); + Y3 = X3.mul(Y3); + X3 = X3.mul(t3); + t3 = t2.dbl(); + t2 = t2.add(t3); + Z3 = B.mul(Z3); + Z3 = Z3.sub(t2); + Z3 = Z3.sub(t0); + t3 = Z3.dbl(); + Z3 = Z3.add(t3); + t3 = t0.dbl(); + t0 = t3.add(t0); + t0 = t0.sub(t2); + t0 = t0.mul(Z3); + Y3 = Y3.add(t0); + t0 = p.y.mul(p.z); + t0 = t0.dbl(); + Z3 = t0.mul(Z3); + X3 = X3.sub(Z3); + Z3 = t0.mul(t1); + Z3 = Z3.dbl().dbl(); + return .{ + .x = X3, + .y = Y3, + .z = Z3, + }; + } + + /// Add P256 points, the second being specified using affine coordinates. + // Algorithm 5 from https://eprint.iacr.org/2015/1060.pdf + pub fn addMixed(p: P256, q: struct { x: Fe, y: Fe }) P256 { + 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.y); + 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 Z3 = B.mul(p.z); + var X3 = Y3.sub(Z3); + Z3 = X3.dbl(); + X3 = X3.add(Z3); + Z3 = t1.sub(X3); + X3 = t1.dbl(); + Y3 = B.mul(Y3); + t1 = p.z.add(p.z); + var t2 = t1.add(p.z); + Y3 = Y3.sub(t2); + Y3 = Y3.sub(t0); + t1 = Y3.dbl(); + Y3 = t1.add(Y3); + t1 = t0.dbl(); + t0 = t1.add(t0); + t0 = t0.sub(t2); + t1 = t4.mul(Y3); + t2 = t0.mul(Y3); + Y3 = X3.mul(Z3); + Y3 = Y3.add(t2); + X3 = t3.mul(X3); + X3 = X3.sub(t1); + Z3 = t4.mul(Z3); + t1 = t3.mul(t0); + Z3 = Z3.add(t1); + return .{ + .x = X3, + .y = Y3, + .z = Z3, + }; + } + + // Add P256 points. + // Algorithm 4 from https://eprint.iacr.org/2015/1060.pdf + pub fn add(p: P256, q: P256) P256 { + 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); + var Z3 = B.mul(t2); + X3 = Y3.sub(Z3); + Z3 = X3.dbl(); + X3 = X3.add(Z3); + Z3 = t1.sub(X3); + X3 = t1.add(X3); + Y3 = B.mul(Y3); + t1 = t2.dbl(); + t2 = t1.add(t2); + Y3 = Y3.sub(t2); + Y3 = Y3.sub(t0); + t1 = Y3.dbl(); + Y3 = t1.add(Y3); + t1 = t0.dbl(); + t0 = t1.add(t0); + t0 = t0.sub(t2); + t1 = t4.mul(Y3); + t2 = t0.mul(Y3); + Y3 = X3.mul(Z3); + Y3 = Y3.add(t2); + X3 = t3.mul(X3); + X3 = X3.sub(t1); + Z3 = t4.mul(Z3); + t1 = t3.mul(t0); + Z3 = Z3.add(t1); + return .{ + .x = X3, + .y = Y3, + .z = Z3, + }; + } + + // Subtract P256 points. + pub fn sub(p: P256, q: P256) P256 { + return p.add(q.neg()); + } + + /// Return affine coordinates. + pub fn affineCoordinates(p: P256) struct { x: Fe, y: Fe } { + const zinv = p.z.invert(); + const ret = .{ + .x = p.x.mul(zinv), + .y = p.y.mul(zinv), + }; + return ret; + } + + /// Return true if both coordinate sets represent the same point. + pub fn equivalent(a: P256, b: P256) bool { + if (a.sub(b).rejectIdentity()) { + return false; + } else |_| { + return true; + } + } + + fn cMov(p: *P256, a: P256, 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: [n]P256, b: u8) P256 { + var t = P256.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: [9]P256, s: [32]u8, comptime vartime: bool) IdentityElementError!P256 { + std.debug.assert(vartime); + const e = slide(s); + var q = P256.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: [16]P256, s: [32]u8, comptime vartime: bool) IdentityElementError!P256 { + var q = P256.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: P256, comptime count: usize) [1 + count]P256 { + var pc: [1 + count]P256 = undefined; + pc[0] = P256.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; + } + + /// Multiply an elliptic curve point by a scalar. + /// Return error.IdentityElement if the result is the identity element. + pub fn mul(p: P256, s_: [32]u8, endian: builtin.Endian) IdentityElementError!P256 { + const s = if (endian == .Little) s_ else Fe.orderSwap(s_); + const pc = if (p.is_base) precompute(P256.basePoint, 15) else pc: { + try p.rejectIdentity(); + const xpc = precompute(p, 15); + break :pc xpc; + }; + 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: P256, s_: [32]u8, endian: builtin.Endian) IdentityElementError!P256 { + const s = if (endian == .Little) s_ else Fe.orderSwap(s_); + const pc = if (p.is_base) precompute(P256.basePoint, 8) else pc: { + try p.rejectIdentity(); + const xpc = precompute(p, 8); + break :pc xpc; + }; + return pcMul(pc, s, true); + } +}; + +test "p256" { + _ = @import("tests.zig"); +} diff --git a/lib/std/crypto/pcurves/p256/field.zig b/lib/std/crypto/pcurves/p256/field.zig new file mode 100644 index 0000000000..68659e4601 --- /dev/null +++ b/lib/std/crypto/pcurves/p256/field.zig @@ -0,0 +1,261 @@ +// SPDX-License-Identifier: MIT +// Copyright (c) 2015-2021 Zig Contributors +// This file is part of [zig](https://ziglang.org/), which is MIT licensed. +// The MIT license requires this copyright notice to be included in all copies +// and substantial portions of the software. + +const std = @import("std"); +const builtin = std.builtin; +const crypto = std.crypto; +const debug = std.debug; +const mem = std.mem; +const meta = std.meta; + +const fiat = @import("p256_64.zig"); + +const NonCanonicalError = crypto.errors.NonCanonicalError; +const NotSquareError = crypto.errors.NotSquareError; + +const Limbs = fiat.Limbs; + +/// A field element, internally stored in Montgomery domain. +pub const Fe = struct { + limbs: Limbs, + + /// Field size. + pub const field_order = 115792089210356248762697446949407573530086143415290314195533631308867097853951; + + /// Numer of bits that can be saturated without overflowing. + pub const saturated_bits = 255; + + /// Zero. + pub const zero: Fe = Fe{ .limbs = mem.zeroes(Limbs) }; + + /// One. + pub const one = comptime one: { + var fe: Fe = undefined; + fiat.p256SetOne(&fe.limbs); + break :one fe; + }; + + /// Reject non-canonical encodings of an element. + pub fn rejectNonCanonical(s_: [32]u8, endian: builtin.Endian) NonCanonicalError!void { + var s = if (endian == .Little) s_ else orderSwap(s_); + const field_order_s = comptime fos: { + var fos: [32]u8 = undefined; + mem.writeIntLittle(u256, &fos, field_order); + break :fos fos; + }; + if (crypto.utils.timingSafeCompare(u8, &s, &field_order_s, .Little) != .lt) { + return error.NonCanonical; + } + } + + /// Swap the endianness of an encoded element. + pub fn orderSwap(s: [32]u8) [32]u8 { + var t = s; + for (s) |x, i| t[t.len - 1 - i] = x; + return t; + } + + /// Unpack a field element. + pub fn fromBytes(s_: [32]u8, endian: builtin.Endian) NonCanonicalError!Fe { + var s = if (endian == .Little) s_ else orderSwap(s_); + try rejectNonCanonical(s, .Little); + var limbs_z: Limbs = undefined; + fiat.p256FromBytes(&limbs_z, s); + var limbs: Limbs = undefined; + fiat.p256ToMontgomery(&limbs, limbs_z); + return Fe{ .limbs = limbs }; + } + + /// Pack a field element. + pub fn toBytes(fe: Fe, endian: builtin.Endian) [32]u8 { + var limbs_z: Limbs = undefined; + fiat.p256FromMontgomery(&limbs_z, fe.limbs); + var s: [32]u8 = undefined; + fiat.p256ToBytes(&s, limbs_z); + return if (endian == .Little) s else orderSwap(s); + } + + /// Create a field element from an integer. + pub fn fromInt(comptime x: u256) NonCanonicalError!Fe { + var s: [32]u8 = undefined; + mem.writeIntLittle(u256, &s, x); + return fromBytes(s, .Little); + } + + /// Return the field element as an integer. + pub fn toInt(fe: Fe) u256 { + const s = fe.toBytes(.Little); + return mem.readIntLittle(u256, &s); + } + + /// Return true if the field element is zero. + pub fn isZero(fe: Fe) bool { + var z: @TypeOf(fe.limbs[0]) = undefined; + fiat.p256Nonzero(&z, fe.limbs); + return z == 0; + } + + /// Return true if both field elements are equivalent. + pub fn equivalent(a: Fe, b: Fe) bool { + return a.sub(b).isZero(); + } + + /// Return true if the element is odd. + pub fn isOdd(fe: Fe) bool { + const s = fe.toBytes(.Little); + return @truncate(u1, s[0]) != 0; + } + + /// Conditonally replace a field element with `a` if `c` is positive. + pub fn cMov(fe: *Fe, a: Fe, c: u1) void { + fiat.p256Selectznz(&fe.limbs, c, fe.limbs, a.limbs); + } + + /// Add field elements. + pub fn add(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Add(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Subtract field elements. + pub fn sub(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Sub(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Double a field element. + pub fn dbl(a: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Add(&fe.limbs, a.limbs, a.limbs); + return fe; + } + + /// Multiply field elements. + pub fn mul(a: Fe, b: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Mul(&fe.limbs, a.limbs, b.limbs); + return fe; + } + + /// Square a field element. + pub fn sq(a: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Square(&fe.limbs, a.limbs); + return fe; + } + + /// Square a field element n times. + fn sqn(a: Fe, comptime n: comptime_int) Fe { + var i: usize = 0; + var fe = a; + while (i < n) : (i += 1) { + fe = fe.sq(); + } + return fe; + } + + /// Compute a^n. + pub fn pow(a: Fe, comptime T: type, comptime n: T) Fe { + var fe = one; + var x: T = n; + var t = a; + while (true) { + if (@truncate(u1, x) != 0) fe = fe.mul(t); + x >>= 1; + if (x == 0) break; + t = t.sq(); + } + return fe; + } + + /// Negate a field element. + pub fn neg(a: Fe) Fe { + var fe: Fe = undefined; + fiat.p256Opp(&fe.limbs, a.limbs); + return fe; + } + + /// Return the inverse of a field element, or 0 if a=0. + // Field inversion from https://eprint.iacr.org/2021/549.pdf + pub fn invert(a: Fe) Fe { + const len_prime = 256; + const iterations = (49 * len_prime + 57) / 17; + const Word = @TypeOf(a.limbs[0]); + const XLimbs = [a.limbs.len + 1]Word; + + var d: Word = 1; + var f: XLimbs = undefined; + fiat.p256Msat(&f); + + var g: XLimbs = undefined; + fiat.p256FromMontgomery(g[0..a.limbs.len], a.limbs); + g[g.len - 1] = 0; + + var r: Limbs = undefined; + fiat.p256SetOne(&r); + var v = mem.zeroes(Limbs); + + var precomp: Limbs = undefined; + fiat.p256DivstepPrecomp(&precomp); + + var out1: Word = undefined; + var out2: XLimbs = undefined; + var out3: XLimbs = undefined; + var out4: Limbs = undefined; + var out5: Limbs = undefined; + + var i: usize = 0; + while (i < iterations - iterations % 2) : (i += 2) { + fiat.p256Divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); + fiat.p256Divstep(&d, &f, &g, &v, &r, out1, out2, out3, out4, out5); + } + if (iterations % 2 != 0) { + fiat.p256Divstep(&out1, &out2, &out3, &out4, &out5, d, f, g, v, r); + mem.copy(Word, &v, &out4); + mem.copy(Word, &f, &out2); + } + var v_opp: Limbs = undefined; + fiat.p256Opp(&v_opp, v); + fiat.p256Selectznz(&v, @truncate(u1, f[f.len - 1] >> (meta.bitCount(Word) - 1)), v, v_opp); + var fe: Fe = undefined; + fiat.p256Mul(&fe.limbs, v, precomp); + return fe; + } + + /// Return true if the field element is a square. + pub fn isSquare(x2: Fe) bool { + const t110 = x2.mul(x2.sq()).sq(); + const t111 = x2.mul(t110); + const t111111 = t111.mul(x2.mul(t110).sqn(3)); + const x15 = t111111.sqn(6).mul(t111111).sqn(3).mul(t111); + const x16 = x15.sq().mul(x2); + const x53 = x16.sqn(16).mul(x16).sqn(15); + const x47 = x15.mul(x53); + const ls = x47.mul(((x53.sqn(17).mul(x2)).sqn(143).mul(x47)).sqn(47)).sq().mul(x2); // Legendre symbol, (p-1)/2 + return ls.equivalent(Fe.one); + } + + // x=x2^((field_order+1)/4) w/ field order=3 (mod 4). + fn uncheckedSqrt(x2: Fe) Fe { + comptime debug.assert(field_order % 4 == 3); + const t11 = x2.mul(x2.sq()); + const t1111 = t11.mul(t11.sqn(2)); + const t11111111 = t1111.mul(t1111.sqn(4)); + const x16 = t11111111.sqn(8).mul(t11111111); + return x16.sqn(16).mul(x16).sqn(32).mul(x2).sqn(96).mul(x2).sqn(94); + } + + /// Compute the square root of `x2`, returning `error.NotSquare` if `x2` was not a square. + pub fn sqrt(x2: Fe) NotSquareError!Fe { + const x = x2.uncheckedSqrt(); + if (x.sq().equivalent(x2)) { + return x; + } + return error.NotSquare; + } +}; diff --git a/lib/std/crypto/pcurves/p256/p256_64.zig b/lib/std/crypto/pcurves/p256/p256_64.zig new file mode 100644 index 0000000000..9f3d6c22f8 --- /dev/null +++ b/lib/std/crypto/pcurves/p256/p256_64.zig @@ -0,0 +1,1774 @@ +// SPDX-License-Identifier: MIT +// Copyright (c) 2015-2021 Zig Contributors +// This file is part of [zig](https://ziglang.org/), which is MIT licensed. +// The MIT license requires this copyright notice to be included in all copies +// and substantial portions of the software. + +// Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --lang Zig --internal-static --public-function-case camelCase --private-function-case camelCase p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp +// curve description: p256 +// 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 = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") +// +// 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) + +pub const Limbs = [4]u64; + +/// The function p256AddcarryxU64 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] +fn p256AddcarryxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + 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 p256SubborrowxU64 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] +fn p256SubborrowxU64(out1: *u64, out2: *u1, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + 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 p256MulxU64 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] +fn p256MulxU64(out1: *u64, out2: *u64, arg1: u64, arg2: u64) callconv(.Inline) void { + const x = @as(u128, arg1) * @as(u128, arg2); + out1.* = @truncate(u64, x); + out2.* = @truncate(u64, x >> 64); +} + +/// The function p256CmovznzU64 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] +fn p256CmovznzU64(out1: *u64, arg1: u1, arg2: u64, arg3: u64) callconv(.Inline) void { + const mask = 0 -% @as(u64, arg1); + out1.* = (mask & arg3) | ((~mask) & arg2); +} + +/// The function p256Mul 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Mul(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { + const x1: u64 = (arg1[1]); + const x2: u64 = (arg1[2]); + const x3: u64 = (arg1[3]); + const x4: u64 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + p256MulxU64(&x5, &x6, x4, (arg2[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + p256MulxU64(&x7, &x8, x4, (arg2[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + p256MulxU64(&x9, &x10, x4, (arg2[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + p256MulxU64(&x11, &x12, x4, (arg2[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + p256AddcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + p256AddcarryxU64(&x17, &x18, x16, x8, x5); + const x19: u64 = (@intCast(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + p256MulxU64(&x20, &x21, x11, 0xffffffff00000001); + var x22: u64 = undefined; + var x23: u64 = undefined; + p256MulxU64(&x22, &x23, x11, 0xffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + p256MulxU64(&x24, &x25, x11, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u1 = undefined; + p256AddcarryxU64(&x26, &x27, 0x0, x25, x22); + const x28: u64 = (@intCast(u64, x27) + x23); + var x29: u64 = undefined; + var x30: u1 = undefined; + p256AddcarryxU64(&x29, &x30, 0x0, x11, x24); + var x31: u64 = undefined; + var x32: u1 = undefined; + p256AddcarryxU64(&x31, &x32, x30, x13, x26); + var x33: u64 = undefined; + var x34: u1 = undefined; + p256AddcarryxU64(&x33, &x34, x32, x15, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + p256AddcarryxU64(&x35, &x36, x34, x17, x20); + var x37: u64 = undefined; + var x38: u1 = undefined; + p256AddcarryxU64(&x37, &x38, x36, x19, x21); + var x39: u64 = undefined; + var x40: u64 = undefined; + p256MulxU64(&x39, &x40, x1, (arg2[3])); + var x41: u64 = undefined; + var x42: u64 = undefined; + p256MulxU64(&x41, &x42, x1, (arg2[2])); + var x43: u64 = undefined; + var x44: u64 = undefined; + p256MulxU64(&x43, &x44, x1, (arg2[1])); + var x45: u64 = undefined; + var x46: u64 = undefined; + p256MulxU64(&x45, &x46, x1, (arg2[0])); + var x47: u64 = undefined; + var x48: u1 = undefined; + p256AddcarryxU64(&x47, &x48, 0x0, x46, x43); + var x49: u64 = undefined; + var x50: u1 = undefined; + p256AddcarryxU64(&x49, &x50, x48, x44, x41); + var x51: u64 = undefined; + var x52: u1 = undefined; + p256AddcarryxU64(&x51, &x52, x50, x42, x39); + const x53: u64 = (@intCast(u64, x52) + x40); + var x54: u64 = undefined; + var x55: u1 = undefined; + p256AddcarryxU64(&x54, &x55, 0x0, x31, x45); + var x56: u64 = undefined; + var x57: u1 = undefined; + p256AddcarryxU64(&x56, &x57, x55, x33, x47); + var x58: u64 = undefined; + var x59: u1 = undefined; + p256AddcarryxU64(&x58, &x59, x57, x35, x49); + var x60: u64 = undefined; + var x61: u1 = undefined; + p256AddcarryxU64(&x60, &x61, x59, x37, x51); + var x62: u64 = undefined; + var x63: u1 = undefined; + p256AddcarryxU64(&x62, &x63, x61, @intCast(u64, x38), x53); + var x64: u64 = undefined; + var x65: u64 = undefined; + p256MulxU64(&x64, &x65, x54, 0xffffffff00000001); + var x66: u64 = undefined; + var x67: u64 = undefined; + p256MulxU64(&x66, &x67, x54, 0xffffffff); + var x68: u64 = undefined; + var x69: u64 = undefined; + p256MulxU64(&x68, &x69, x54, 0xffffffffffffffff); + var x70: u64 = undefined; + var x71: u1 = undefined; + p256AddcarryxU64(&x70, &x71, 0x0, x69, x66); + const x72: u64 = (@intCast(u64, x71) + x67); + var x73: u64 = undefined; + var x74: u1 = undefined; + p256AddcarryxU64(&x73, &x74, 0x0, x54, x68); + var x75: u64 = undefined; + var x76: u1 = undefined; + p256AddcarryxU64(&x75, &x76, x74, x56, x70); + var x77: u64 = undefined; + var x78: u1 = undefined; + p256AddcarryxU64(&x77, &x78, x76, x58, x72); + var x79: u64 = undefined; + var x80: u1 = undefined; + p256AddcarryxU64(&x79, &x80, x78, x60, x64); + var x81: u64 = undefined; + var x82: u1 = undefined; + p256AddcarryxU64(&x81, &x82, x80, x62, x65); + const x83: u64 = (@intCast(u64, x82) + @intCast(u64, x63)); + var x84: u64 = undefined; + var x85: u64 = undefined; + p256MulxU64(&x84, &x85, x2, (arg2[3])); + var x86: u64 = undefined; + var x87: u64 = undefined; + p256MulxU64(&x86, &x87, x2, (arg2[2])); + var x88: u64 = undefined; + var x89: u64 = undefined; + p256MulxU64(&x88, &x89, x2, (arg2[1])); + var x90: u64 = undefined; + var x91: u64 = undefined; + p256MulxU64(&x90, &x91, x2, (arg2[0])); + var x92: u64 = undefined; + var x93: u1 = undefined; + p256AddcarryxU64(&x92, &x93, 0x0, x91, x88); + var x94: u64 = undefined; + var x95: u1 = undefined; + p256AddcarryxU64(&x94, &x95, x93, x89, x86); + var x96: u64 = undefined; + var x97: u1 = undefined; + p256AddcarryxU64(&x96, &x97, x95, x87, x84); + const x98: u64 = (@intCast(u64, x97) + x85); + var x99: u64 = undefined; + var x100: u1 = undefined; + p256AddcarryxU64(&x99, &x100, 0x0, x75, x90); + var x101: u64 = undefined; + var x102: u1 = undefined; + p256AddcarryxU64(&x101, &x102, x100, x77, x92); + var x103: u64 = undefined; + var x104: u1 = undefined; + p256AddcarryxU64(&x103, &x104, x102, x79, x94); + var x105: u64 = undefined; + var x106: u1 = undefined; + p256AddcarryxU64(&x105, &x106, x104, x81, x96); + var x107: u64 = undefined; + var x108: u1 = undefined; + p256AddcarryxU64(&x107, &x108, x106, x83, x98); + var x109: u64 = undefined; + var x110: u64 = undefined; + p256MulxU64(&x109, &x110, x99, 0xffffffff00000001); + var x111: u64 = undefined; + var x112: u64 = undefined; + p256MulxU64(&x111, &x112, x99, 0xffffffff); + var x113: u64 = undefined; + var x114: u64 = undefined; + p256MulxU64(&x113, &x114, x99, 0xffffffffffffffff); + var x115: u64 = undefined; + var x116: u1 = undefined; + p256AddcarryxU64(&x115, &x116, 0x0, x114, x111); + const x117: u64 = (@intCast(u64, x116) + x112); + var x118: u64 = undefined; + var x119: u1 = undefined; + p256AddcarryxU64(&x118, &x119, 0x0, x99, x113); + var x120: u64 = undefined; + var x121: u1 = undefined; + p256AddcarryxU64(&x120, &x121, x119, x101, x115); + var x122: u64 = undefined; + var x123: u1 = undefined; + p256AddcarryxU64(&x122, &x123, x121, x103, x117); + var x124: u64 = undefined; + var x125: u1 = undefined; + p256AddcarryxU64(&x124, &x125, x123, x105, x109); + var x126: u64 = undefined; + var x127: u1 = undefined; + p256AddcarryxU64(&x126, &x127, x125, x107, x110); + const x128: u64 = (@intCast(u64, x127) + @intCast(u64, x108)); + var x129: u64 = undefined; + var x130: u64 = undefined; + p256MulxU64(&x129, &x130, x3, (arg2[3])); + var x131: u64 = undefined; + var x132: u64 = undefined; + p256MulxU64(&x131, &x132, x3, (arg2[2])); + var x133: u64 = undefined; + var x134: u64 = undefined; + p256MulxU64(&x133, &x134, x3, (arg2[1])); + var x135: u64 = undefined; + var x136: u64 = undefined; + p256MulxU64(&x135, &x136, x3, (arg2[0])); + var x137: u64 = undefined; + var x138: u1 = undefined; + p256AddcarryxU64(&x137, &x138, 0x0, x136, x133); + var x139: u64 = undefined; + var x140: u1 = undefined; + p256AddcarryxU64(&x139, &x140, x138, x134, x131); + var x141: u64 = undefined; + var x142: u1 = undefined; + p256AddcarryxU64(&x141, &x142, x140, x132, x129); + const x143: u64 = (@intCast(u64, x142) + x130); + var x144: u64 = undefined; + var x145: u1 = undefined; + p256AddcarryxU64(&x144, &x145, 0x0, x120, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + p256AddcarryxU64(&x146, &x147, x145, x122, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + p256AddcarryxU64(&x148, &x149, x147, x124, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + p256AddcarryxU64(&x150, &x151, x149, x126, x141); + var x152: u64 = undefined; + var x153: u1 = undefined; + p256AddcarryxU64(&x152, &x153, x151, x128, x143); + var x154: u64 = undefined; + var x155: u64 = undefined; + p256MulxU64(&x154, &x155, x144, 0xffffffff00000001); + var x156: u64 = undefined; + var x157: u64 = undefined; + p256MulxU64(&x156, &x157, x144, 0xffffffff); + var x158: u64 = undefined; + var x159: u64 = undefined; + p256MulxU64(&x158, &x159, x144, 0xffffffffffffffff); + var x160: u64 = undefined; + var x161: u1 = undefined; + p256AddcarryxU64(&x160, &x161, 0x0, x159, x156); + const x162: u64 = (@intCast(u64, x161) + x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + p256AddcarryxU64(&x163, &x164, 0x0, x144, x158); + var x165: u64 = undefined; + var x166: u1 = undefined; + p256AddcarryxU64(&x165, &x166, x164, x146, x160); + var x167: u64 = undefined; + var x168: u1 = undefined; + p256AddcarryxU64(&x167, &x168, x166, x148, x162); + var x169: u64 = undefined; + var x170: u1 = undefined; + p256AddcarryxU64(&x169, &x170, x168, x150, x154); + var x171: u64 = undefined; + var x172: u1 = undefined; + p256AddcarryxU64(&x171, &x172, x170, x152, x155); + const x173: u64 = (@intCast(u64, x172) + @intCast(u64, x153)); + var x174: u64 = undefined; + var x175: u1 = undefined; + p256SubborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); + var x176: u64 = undefined; + var x177: u1 = undefined; + p256SubborrowxU64(&x176, &x177, x175, x167, 0xffffffff); + var x178: u64 = undefined; + var x179: u1 = undefined; + p256SubborrowxU64(&x178, &x179, x177, x169, @intCast(u64, 0x0)); + var x180: u64 = undefined; + var x181: u1 = undefined; + p256SubborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); + var x182: u64 = undefined; + var x183: u1 = undefined; + p256SubborrowxU64(&x182, &x183, x181, x173, @intCast(u64, 0x0)); + var x184: u64 = undefined; + p256CmovznzU64(&x184, x183, x174, x165); + var x185: u64 = undefined; + p256CmovznzU64(&x185, x183, x176, x167); + var x186: u64 = undefined; + p256CmovznzU64(&x186, x183, x178, x169); + var x187: u64 = undefined; + p256CmovznzU64(&x187, x183, x180, x171); + out1[0] = x184; + out1[1] = x185; + out1[2] = x186; + out1[3] = x187; +} + +/// The function p256Square 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Square(out1: *Limbs, arg1: Limbs) void { + const x1: u64 = (arg1[1]); + const x2: u64 = (arg1[2]); + const x3: u64 = (arg1[3]); + const x4: u64 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + p256MulxU64(&x5, &x6, x4, (arg1[3])); + var x7: u64 = undefined; + var x8: u64 = undefined; + p256MulxU64(&x7, &x8, x4, (arg1[2])); + var x9: u64 = undefined; + var x10: u64 = undefined; + p256MulxU64(&x9, &x10, x4, (arg1[1])); + var x11: u64 = undefined; + var x12: u64 = undefined; + p256MulxU64(&x11, &x12, x4, (arg1[0])); + var x13: u64 = undefined; + var x14: u1 = undefined; + p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + p256AddcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + p256AddcarryxU64(&x17, &x18, x16, x8, x5); + const x19: u64 = (@intCast(u64, x18) + x6); + var x20: u64 = undefined; + var x21: u64 = undefined; + p256MulxU64(&x20, &x21, x11, 0xffffffff00000001); + var x22: u64 = undefined; + var x23: u64 = undefined; + p256MulxU64(&x22, &x23, x11, 0xffffffff); + var x24: u64 = undefined; + var x25: u64 = undefined; + p256MulxU64(&x24, &x25, x11, 0xffffffffffffffff); + var x26: u64 = undefined; + var x27: u1 = undefined; + p256AddcarryxU64(&x26, &x27, 0x0, x25, x22); + const x28: u64 = (@intCast(u64, x27) + x23); + var x29: u64 = undefined; + var x30: u1 = undefined; + p256AddcarryxU64(&x29, &x30, 0x0, x11, x24); + var x31: u64 = undefined; + var x32: u1 = undefined; + p256AddcarryxU64(&x31, &x32, x30, x13, x26); + var x33: u64 = undefined; + var x34: u1 = undefined; + p256AddcarryxU64(&x33, &x34, x32, x15, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + p256AddcarryxU64(&x35, &x36, x34, x17, x20); + var x37: u64 = undefined; + var x38: u1 = undefined; + p256AddcarryxU64(&x37, &x38, x36, x19, x21); + var x39: u64 = undefined; + var x40: u64 = undefined; + p256MulxU64(&x39, &x40, x1, (arg1[3])); + var x41: u64 = undefined; + var x42: u64 = undefined; + p256MulxU64(&x41, &x42, x1, (arg1[2])); + var x43: u64 = undefined; + var x44: u64 = undefined; + p256MulxU64(&x43, &x44, x1, (arg1[1])); + var x45: u64 = undefined; + var x46: u64 = undefined; + p256MulxU64(&x45, &x46, x1, (arg1[0])); + var x47: u64 = undefined; + var x48: u1 = undefined; + p256AddcarryxU64(&x47, &x48, 0x0, x46, x43); + var x49: u64 = undefined; + var x50: u1 = undefined; + p256AddcarryxU64(&x49, &x50, x48, x44, x41); + var x51: u64 = undefined; + var x52: u1 = undefined; + p256AddcarryxU64(&x51, &x52, x50, x42, x39); + const x53: u64 = (@intCast(u64, x52) + x40); + var x54: u64 = undefined; + var x55: u1 = undefined; + p256AddcarryxU64(&x54, &x55, 0x0, x31, x45); + var x56: u64 = undefined; + var x57: u1 = undefined; + p256AddcarryxU64(&x56, &x57, x55, x33, x47); + var x58: u64 = undefined; + var x59: u1 = undefined; + p256AddcarryxU64(&x58, &x59, x57, x35, x49); + var x60: u64 = undefined; + var x61: u1 = undefined; + p256AddcarryxU64(&x60, &x61, x59, x37, x51); + var x62: u64 = undefined; + var x63: u1 = undefined; + p256AddcarryxU64(&x62, &x63, x61, @intCast(u64, x38), x53); + var x64: u64 = undefined; + var x65: u64 = undefined; + p256MulxU64(&x64, &x65, x54, 0xffffffff00000001); + var x66: u64 = undefined; + var x67: u64 = undefined; + p256MulxU64(&x66, &x67, x54, 0xffffffff); + var x68: u64 = undefined; + var x69: u64 = undefined; + p256MulxU64(&x68, &x69, x54, 0xffffffffffffffff); + var x70: u64 = undefined; + var x71: u1 = undefined; + p256AddcarryxU64(&x70, &x71, 0x0, x69, x66); + const x72: u64 = (@intCast(u64, x71) + x67); + var x73: u64 = undefined; + var x74: u1 = undefined; + p256AddcarryxU64(&x73, &x74, 0x0, x54, x68); + var x75: u64 = undefined; + var x76: u1 = undefined; + p256AddcarryxU64(&x75, &x76, x74, x56, x70); + var x77: u64 = undefined; + var x78: u1 = undefined; + p256AddcarryxU64(&x77, &x78, x76, x58, x72); + var x79: u64 = undefined; + var x80: u1 = undefined; + p256AddcarryxU64(&x79, &x80, x78, x60, x64); + var x81: u64 = undefined; + var x82: u1 = undefined; + p256AddcarryxU64(&x81, &x82, x80, x62, x65); + const x83: u64 = (@intCast(u64, x82) + @intCast(u64, x63)); + var x84: u64 = undefined; + var x85: u64 = undefined; + p256MulxU64(&x84, &x85, x2, (arg1[3])); + var x86: u64 = undefined; + var x87: u64 = undefined; + p256MulxU64(&x86, &x87, x2, (arg1[2])); + var x88: u64 = undefined; + var x89: u64 = undefined; + p256MulxU64(&x88, &x89, x2, (arg1[1])); + var x90: u64 = undefined; + var x91: u64 = undefined; + p256MulxU64(&x90, &x91, x2, (arg1[0])); + var x92: u64 = undefined; + var x93: u1 = undefined; + p256AddcarryxU64(&x92, &x93, 0x0, x91, x88); + var x94: u64 = undefined; + var x95: u1 = undefined; + p256AddcarryxU64(&x94, &x95, x93, x89, x86); + var x96: u64 = undefined; + var x97: u1 = undefined; + p256AddcarryxU64(&x96, &x97, x95, x87, x84); + const x98: u64 = (@intCast(u64, x97) + x85); + var x99: u64 = undefined; + var x100: u1 = undefined; + p256AddcarryxU64(&x99, &x100, 0x0, x75, x90); + var x101: u64 = undefined; + var x102: u1 = undefined; + p256AddcarryxU64(&x101, &x102, x100, x77, x92); + var x103: u64 = undefined; + var x104: u1 = undefined; + p256AddcarryxU64(&x103, &x104, x102, x79, x94); + var x105: u64 = undefined; + var x106: u1 = undefined; + p256AddcarryxU64(&x105, &x106, x104, x81, x96); + var x107: u64 = undefined; + var x108: u1 = undefined; + p256AddcarryxU64(&x107, &x108, x106, x83, x98); + var x109: u64 = undefined; + var x110: u64 = undefined; + p256MulxU64(&x109, &x110, x99, 0xffffffff00000001); + var x111: u64 = undefined; + var x112: u64 = undefined; + p256MulxU64(&x111, &x112, x99, 0xffffffff); + var x113: u64 = undefined; + var x114: u64 = undefined; + p256MulxU64(&x113, &x114, x99, 0xffffffffffffffff); + var x115: u64 = undefined; + var x116: u1 = undefined; + p256AddcarryxU64(&x115, &x116, 0x0, x114, x111); + const x117: u64 = (@intCast(u64, x116) + x112); + var x118: u64 = undefined; + var x119: u1 = undefined; + p256AddcarryxU64(&x118, &x119, 0x0, x99, x113); + var x120: u64 = undefined; + var x121: u1 = undefined; + p256AddcarryxU64(&x120, &x121, x119, x101, x115); + var x122: u64 = undefined; + var x123: u1 = undefined; + p256AddcarryxU64(&x122, &x123, x121, x103, x117); + var x124: u64 = undefined; + var x125: u1 = undefined; + p256AddcarryxU64(&x124, &x125, x123, x105, x109); + var x126: u64 = undefined; + var x127: u1 = undefined; + p256AddcarryxU64(&x126, &x127, x125, x107, x110); + const x128: u64 = (@intCast(u64, x127) + @intCast(u64, x108)); + var x129: u64 = undefined; + var x130: u64 = undefined; + p256MulxU64(&x129, &x130, x3, (arg1[3])); + var x131: u64 = undefined; + var x132: u64 = undefined; + p256MulxU64(&x131, &x132, x3, (arg1[2])); + var x133: u64 = undefined; + var x134: u64 = undefined; + p256MulxU64(&x133, &x134, x3, (arg1[1])); + var x135: u64 = undefined; + var x136: u64 = undefined; + p256MulxU64(&x135, &x136, x3, (arg1[0])); + var x137: u64 = undefined; + var x138: u1 = undefined; + p256AddcarryxU64(&x137, &x138, 0x0, x136, x133); + var x139: u64 = undefined; + var x140: u1 = undefined; + p256AddcarryxU64(&x139, &x140, x138, x134, x131); + var x141: u64 = undefined; + var x142: u1 = undefined; + p256AddcarryxU64(&x141, &x142, x140, x132, x129); + const x143: u64 = (@intCast(u64, x142) + x130); + var x144: u64 = undefined; + var x145: u1 = undefined; + p256AddcarryxU64(&x144, &x145, 0x0, x120, x135); + var x146: u64 = undefined; + var x147: u1 = undefined; + p256AddcarryxU64(&x146, &x147, x145, x122, x137); + var x148: u64 = undefined; + var x149: u1 = undefined; + p256AddcarryxU64(&x148, &x149, x147, x124, x139); + var x150: u64 = undefined; + var x151: u1 = undefined; + p256AddcarryxU64(&x150, &x151, x149, x126, x141); + var x152: u64 = undefined; + var x153: u1 = undefined; + p256AddcarryxU64(&x152, &x153, x151, x128, x143); + var x154: u64 = undefined; + var x155: u64 = undefined; + p256MulxU64(&x154, &x155, x144, 0xffffffff00000001); + var x156: u64 = undefined; + var x157: u64 = undefined; + p256MulxU64(&x156, &x157, x144, 0xffffffff); + var x158: u64 = undefined; + var x159: u64 = undefined; + p256MulxU64(&x158, &x159, x144, 0xffffffffffffffff); + var x160: u64 = undefined; + var x161: u1 = undefined; + p256AddcarryxU64(&x160, &x161, 0x0, x159, x156); + const x162: u64 = (@intCast(u64, x161) + x157); + var x163: u64 = undefined; + var x164: u1 = undefined; + p256AddcarryxU64(&x163, &x164, 0x0, x144, x158); + var x165: u64 = undefined; + var x166: u1 = undefined; + p256AddcarryxU64(&x165, &x166, x164, x146, x160); + var x167: u64 = undefined; + var x168: u1 = undefined; + p256AddcarryxU64(&x167, &x168, x166, x148, x162); + var x169: u64 = undefined; + var x170: u1 = undefined; + p256AddcarryxU64(&x169, &x170, x168, x150, x154); + var x171: u64 = undefined; + var x172: u1 = undefined; + p256AddcarryxU64(&x171, &x172, x170, x152, x155); + const x173: u64 = (@intCast(u64, x172) + @intCast(u64, x153)); + var x174: u64 = undefined; + var x175: u1 = undefined; + p256SubborrowxU64(&x174, &x175, 0x0, x165, 0xffffffffffffffff); + var x176: u64 = undefined; + var x177: u1 = undefined; + p256SubborrowxU64(&x176, &x177, x175, x167, 0xffffffff); + var x178: u64 = undefined; + var x179: u1 = undefined; + p256SubborrowxU64(&x178, &x179, x177, x169, @intCast(u64, 0x0)); + var x180: u64 = undefined; + var x181: u1 = undefined; + p256SubborrowxU64(&x180, &x181, x179, x171, 0xffffffff00000001); + var x182: u64 = undefined; + var x183: u1 = undefined; + p256SubborrowxU64(&x182, &x183, x181, x173, @intCast(u64, 0x0)); + var x184: u64 = undefined; + p256CmovznzU64(&x184, x183, x174, x165); + var x185: u64 = undefined; + p256CmovznzU64(&x185, x183, x176, x167); + var x186: u64 = undefined; + p256CmovznzU64(&x186, x183, x178, x169); + var x187: u64 = undefined; + p256CmovznzU64(&x187, x183, x180, x171); + out1[0] = x184; + out1[1] = x185; + out1[2] = x186; + out1[3] = x187; +} + +/// The function p256Add 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Add(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { + var x1: u64 = undefined; + var x2: u1 = undefined; + p256AddcarryxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + p256AddcarryxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + p256AddcarryxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + p256AddcarryxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + var x10: u1 = undefined; + p256SubborrowxU64(&x9, &x10, 0x0, x1, 0xffffffffffffffff); + var x11: u64 = undefined; + var x12: u1 = undefined; + p256SubborrowxU64(&x11, &x12, x10, x3, 0xffffffff); + var x13: u64 = undefined; + var x14: u1 = undefined; + p256SubborrowxU64(&x13, &x14, x12, x5, @intCast(u64, 0x0)); + var x15: u64 = undefined; + var x16: u1 = undefined; + p256SubborrowxU64(&x15, &x16, x14, x7, 0xffffffff00000001); + var x17: u64 = undefined; + var x18: u1 = undefined; + p256SubborrowxU64(&x17, &x18, x16, @intCast(u64, x8), @intCast(u64, 0x0)); + var x19: u64 = undefined; + p256CmovznzU64(&x19, x18, x9, x1); + var x20: u64 = undefined; + p256CmovznzU64(&x20, x18, x11, x3); + var x21: u64 = undefined; + p256CmovznzU64(&x21, x18, x13, x5); + var x22: u64 = undefined; + p256CmovznzU64(&x22, x18, x15, x7); + out1[0] = x19; + out1[1] = x20; + out1[2] = x21; + out1[3] = x22; +} + +/// The function p256Sub 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Sub(out1: *Limbs, arg1: Limbs, arg2: Limbs) void { + var x1: u64 = undefined; + var x2: u1 = undefined; + p256SubborrowxU64(&x1, &x2, 0x0, (arg1[0]), (arg2[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + p256SubborrowxU64(&x3, &x4, x2, (arg1[1]), (arg2[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + p256SubborrowxU64(&x5, &x6, x4, (arg1[2]), (arg2[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + p256SubborrowxU64(&x7, &x8, x6, (arg1[3]), (arg2[3])); + var x9: u64 = undefined; + p256CmovznzU64(&x9, x8, @intCast(u64, 0x0), 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + p256AddcarryxU64(&x10, &x11, 0x0, x1, x9); + var x12: u64 = undefined; + var x13: u1 = undefined; + p256AddcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); + var x14: u64 = undefined; + var x15: u1 = undefined; + p256AddcarryxU64(&x14, &x15, x13, x5, @intCast(u64, 0x0)); + var x16: u64 = undefined; + var x17: u1 = undefined; + p256AddcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function p256Opp 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Opp(out1: *Limbs, arg1: Limbs) void { + var x1: u64 = undefined; + var x2: u1 = undefined; + p256SubborrowxU64(&x1, &x2, 0x0, @intCast(u64, 0x0), (arg1[0])); + var x3: u64 = undefined; + var x4: u1 = undefined; + p256SubborrowxU64(&x3, &x4, x2, @intCast(u64, 0x0), (arg1[1])); + var x5: u64 = undefined; + var x6: u1 = undefined; + p256SubborrowxU64(&x5, &x6, x4, @intCast(u64, 0x0), (arg1[2])); + var x7: u64 = undefined; + var x8: u1 = undefined; + p256SubborrowxU64(&x7, &x8, x6, @intCast(u64, 0x0), (arg1[3])); + var x9: u64 = undefined; + p256CmovznzU64(&x9, x8, @intCast(u64, 0x0), 0xffffffffffffffff); + var x10: u64 = undefined; + var x11: u1 = undefined; + p256AddcarryxU64(&x10, &x11, 0x0, x1, x9); + var x12: u64 = undefined; + var x13: u1 = undefined; + p256AddcarryxU64(&x12, &x13, x11, x3, (x9 & 0xffffffff)); + var x14: u64 = undefined; + var x15: u1 = undefined; + p256AddcarryxU64(&x14, &x15, x13, x5, @intCast(u64, 0x0)); + var x16: u64 = undefined; + var x17: u1 = undefined; + p256AddcarryxU64(&x16, &x17, x15, x7, (x9 & 0xffffffff00000001)); + out1[0] = x10; + out1[1] = x12; + out1[2] = x14; + out1[3] = x16; +} + +/// The function p256FromMontgomery 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256FromMontgomery(out1: *Limbs, arg1: Limbs) void { + const x1: u64 = (arg1[0]); + var x2: u64 = undefined; + var x3: u64 = undefined; + p256MulxU64(&x2, &x3, x1, 0xffffffff00000001); + var x4: u64 = undefined; + var x5: u64 = undefined; + p256MulxU64(&x4, &x5, x1, 0xffffffff); + var x6: u64 = undefined; + var x7: u64 = undefined; + p256MulxU64(&x6, &x7, x1, 0xffffffffffffffff); + var x8: u64 = undefined; + var x9: u1 = undefined; + p256AddcarryxU64(&x8, &x9, 0x0, x7, x4); + var x10: u64 = undefined; + var x11: u1 = undefined; + p256AddcarryxU64(&x10, &x11, 0x0, x1, x6); + var x12: u64 = undefined; + var x13: u1 = undefined; + p256AddcarryxU64(&x12, &x13, x11, @intCast(u64, 0x0), x8); + var x14: u64 = undefined; + var x15: u1 = undefined; + p256AddcarryxU64(&x14, &x15, 0x0, x12, (arg1[1])); + var x16: u64 = undefined; + var x17: u64 = undefined; + p256MulxU64(&x16, &x17, x14, 0xffffffff00000001); + var x18: u64 = undefined; + var x19: u64 = undefined; + p256MulxU64(&x18, &x19, x14, 0xffffffff); + var x20: u64 = undefined; + var x21: u64 = undefined; + p256MulxU64(&x20, &x21, x14, 0xffffffffffffffff); + var x22: u64 = undefined; + var x23: u1 = undefined; + p256AddcarryxU64(&x22, &x23, 0x0, x21, x18); + var x24: u64 = undefined; + var x25: u1 = undefined; + p256AddcarryxU64(&x24, &x25, 0x0, x14, x20); + var x26: u64 = undefined; + var x27: u1 = undefined; + p256AddcarryxU64(&x26, &x27, x25, (@intCast(u64, x15) + (@intCast(u64, x13) + (@intCast(u64, x9) + x5))), x22); + var x28: u64 = undefined; + var x29: u1 = undefined; + p256AddcarryxU64(&x28, &x29, x27, x2, (@intCast(u64, x23) + x19)); + var x30: u64 = undefined; + var x31: u1 = undefined; + p256AddcarryxU64(&x30, &x31, x29, x3, x16); + var x32: u64 = undefined; + var x33: u1 = undefined; + p256AddcarryxU64(&x32, &x33, 0x0, x26, (arg1[2])); + var x34: u64 = undefined; + var x35: u1 = undefined; + p256AddcarryxU64(&x34, &x35, x33, x28, @intCast(u64, 0x0)); + var x36: u64 = undefined; + var x37: u1 = undefined; + p256AddcarryxU64(&x36, &x37, x35, x30, @intCast(u64, 0x0)); + var x38: u64 = undefined; + var x39: u64 = undefined; + p256MulxU64(&x38, &x39, x32, 0xffffffff00000001); + var x40: u64 = undefined; + var x41: u64 = undefined; + p256MulxU64(&x40, &x41, x32, 0xffffffff); + var x42: u64 = undefined; + var x43: u64 = undefined; + p256MulxU64(&x42, &x43, x32, 0xffffffffffffffff); + var x44: u64 = undefined; + var x45: u1 = undefined; + p256AddcarryxU64(&x44, &x45, 0x0, x43, x40); + var x46: u64 = undefined; + var x47: u1 = undefined; + p256AddcarryxU64(&x46, &x47, 0x0, x32, x42); + var x48: u64 = undefined; + var x49: u1 = undefined; + p256AddcarryxU64(&x48, &x49, x47, x34, x44); + var x50: u64 = undefined; + var x51: u1 = undefined; + p256AddcarryxU64(&x50, &x51, x49, x36, (@intCast(u64, x45) + x41)); + var x52: u64 = undefined; + var x53: u1 = undefined; + p256AddcarryxU64(&x52, &x53, x51, (@intCast(u64, x37) + (@intCast(u64, x31) + x17)), x38); + var x54: u64 = undefined; + var x55: u1 = undefined; + p256AddcarryxU64(&x54, &x55, 0x0, x48, (arg1[3])); + var x56: u64 = undefined; + var x57: u1 = undefined; + p256AddcarryxU64(&x56, &x57, x55, x50, @intCast(u64, 0x0)); + var x58: u64 = undefined; + var x59: u1 = undefined; + p256AddcarryxU64(&x58, &x59, x57, x52, @intCast(u64, 0x0)); + var x60: u64 = undefined; + var x61: u64 = undefined; + p256MulxU64(&x60, &x61, x54, 0xffffffff00000001); + var x62: u64 = undefined; + var x63: u64 = undefined; + p256MulxU64(&x62, &x63, x54, 0xffffffff); + var x64: u64 = undefined; + var x65: u64 = undefined; + p256MulxU64(&x64, &x65, x54, 0xffffffffffffffff); + var x66: u64 = undefined; + var x67: u1 = undefined; + p256AddcarryxU64(&x66, &x67, 0x0, x65, x62); + var x68: u64 = undefined; + var x69: u1 = undefined; + p256AddcarryxU64(&x68, &x69, 0x0, x54, x64); + var x70: u64 = undefined; + var x71: u1 = undefined; + p256AddcarryxU64(&x70, &x71, x69, x56, x66); + var x72: u64 = undefined; + var x73: u1 = undefined; + p256AddcarryxU64(&x72, &x73, x71, x58, (@intCast(u64, x67) + x63)); + var x74: u64 = undefined; + var x75: u1 = undefined; + p256AddcarryxU64(&x74, &x75, x73, (@intCast(u64, x59) + (@intCast(u64, x53) + x39)), x60); + const x76: u64 = (@intCast(u64, x75) + x61); + var x77: u64 = undefined; + var x78: u1 = undefined; + p256SubborrowxU64(&x77, &x78, 0x0, x70, 0xffffffffffffffff); + var x79: u64 = undefined; + var x80: u1 = undefined; + p256SubborrowxU64(&x79, &x80, x78, x72, 0xffffffff); + var x81: u64 = undefined; + var x82: u1 = undefined; + p256SubborrowxU64(&x81, &x82, x80, x74, @intCast(u64, 0x0)); + var x83: u64 = undefined; + var x84: u1 = undefined; + p256SubborrowxU64(&x83, &x84, x82, x76, 0xffffffff00000001); + var x85: u64 = undefined; + var x86: u1 = undefined; + p256SubborrowxU64(&x85, &x86, x84, @intCast(u64, 0x0), @intCast(u64, 0x0)); + var x87: u64 = undefined; + p256CmovznzU64(&x87, x86, x77, x70); + var x88: u64 = undefined; + p256CmovznzU64(&x88, x86, x79, x72); + var x89: u64 = undefined; + p256CmovznzU64(&x89, x86, x81, x74); + var x90: u64 = undefined; + p256CmovznzU64(&x90, x86, x83, x76); + out1[0] = x87; + out1[1] = x88; + out1[2] = x89; + out1[3] = x90; +} + +/// The function p256ToMontgomery 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 +/// +/// Input Bounds: +/// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256ToMontgomery(out1: *Limbs, arg1: Limbs) void { + const x1: u64 = (arg1[1]); + const x2: u64 = (arg1[2]); + const x3: u64 = (arg1[3]); + const x4: u64 = (arg1[0]); + var x5: u64 = undefined; + var x6: u64 = undefined; + p256MulxU64(&x5, &x6, x4, 0x4fffffffd); + var x7: u64 = undefined; + var x8: u64 = undefined; + p256MulxU64(&x7, &x8, x4, 0xfffffffffffffffe); + var x9: u64 = undefined; + var x10: u64 = undefined; + p256MulxU64(&x9, &x10, x4, 0xfffffffbffffffff); + var x11: u64 = undefined; + var x12: u64 = undefined; + p256MulxU64(&x11, &x12, x4, 0x3); + var x13: u64 = undefined; + var x14: u1 = undefined; + p256AddcarryxU64(&x13, &x14, 0x0, x12, x9); + var x15: u64 = undefined; + var x16: u1 = undefined; + p256AddcarryxU64(&x15, &x16, x14, x10, x7); + var x17: u64 = undefined; + var x18: u1 = undefined; + p256AddcarryxU64(&x17, &x18, x16, x8, x5); + var x19: u64 = undefined; + var x20: u64 = undefined; + p256MulxU64(&x19, &x20, x11, 0xffffffff00000001); + var x21: u64 = undefined; + var x22: u64 = undefined; + p256MulxU64(&x21, &x22, x11, 0xffffffff); + var x23: u64 = undefined; + var x24: u64 = undefined; + p256MulxU64(&x23, &x24, x11, 0xffffffffffffffff); + var x25: u64 = undefined; + var x26: u1 = undefined; + p256AddcarryxU64(&x25, &x26, 0x0, x24, x21); + var x27: u64 = undefined; + var x28: u1 = undefined; + p256AddcarryxU64(&x27, &x28, 0x0, x11, x23); + var x29: u64 = undefined; + var x30: u1 = undefined; + p256AddcarryxU64(&x29, &x30, x28, x13, x25); + var x31: u64 = undefined; + var x32: u1 = undefined; + p256AddcarryxU64(&x31, &x32, x30, x15, (@intCast(u64, x26) + x22)); + var x33: u64 = undefined; + var x34: u1 = undefined; + p256AddcarryxU64(&x33, &x34, x32, x17, x19); + var x35: u64 = undefined; + var x36: u1 = undefined; + p256AddcarryxU64(&x35, &x36, x34, (@intCast(u64, x18) + x6), x20); + var x37: u64 = undefined; + var x38: u64 = undefined; + p256MulxU64(&x37, &x38, x1, 0x4fffffffd); + var x39: u64 = undefined; + var x40: u64 = undefined; + p256MulxU64(&x39, &x40, x1, 0xfffffffffffffffe); + var x41: u64 = undefined; + var x42: u64 = undefined; + p256MulxU64(&x41, &x42, x1, 0xfffffffbffffffff); + var x43: u64 = undefined; + var x44: u64 = undefined; + p256MulxU64(&x43, &x44, x1, 0x3); + var x45: u64 = undefined; + var x46: u1 = undefined; + p256AddcarryxU64(&x45, &x46, 0x0, x44, x41); + var x47: u64 = undefined; + var x48: u1 = undefined; + p256AddcarryxU64(&x47, &x48, x46, x42, x39); + var x49: u64 = undefined; + var x50: u1 = undefined; + p256AddcarryxU64(&x49, &x50, x48, x40, x37); + var x51: u64 = undefined; + var x52: u1 = undefined; + p256AddcarryxU64(&x51, &x52, 0x0, x29, x43); + var x53: u64 = undefined; + var x54: u1 = undefined; + p256AddcarryxU64(&x53, &x54, x52, x31, x45); + var x55: u64 = undefined; + var x56: u1 = undefined; + p256AddcarryxU64(&x55, &x56, x54, x33, x47); + var x57: u64 = undefined; + var x58: u1 = undefined; + p256AddcarryxU64(&x57, &x58, x56, x35, x49); + var x59: u64 = undefined; + var x60: u64 = undefined; + p256MulxU64(&x59, &x60, x51, 0xffffffff00000001); + var x61: u64 = undefined; + var x62: u64 = undefined; + p256MulxU64(&x61, &x62, x51, 0xffffffff); + var x63: u64 = undefined; + var x64: u64 = undefined; + p256MulxU64(&x63, &x64, x51, 0xffffffffffffffff); + var x65: u64 = undefined; + var x66: u1 = undefined; + p256AddcarryxU64(&x65, &x66, 0x0, x64, x61); + var x67: u64 = undefined; + var x68: u1 = undefined; + p256AddcarryxU64(&x67, &x68, 0x0, x51, x63); + var x69: u64 = undefined; + var x70: u1 = undefined; + p256AddcarryxU64(&x69, &x70, x68, x53, x65); + var x71: u64 = undefined; + var x72: u1 = undefined; + p256AddcarryxU64(&x71, &x72, x70, x55, (@intCast(u64, x66) + x62)); + var x73: u64 = undefined; + var x74: u1 = undefined; + p256AddcarryxU64(&x73, &x74, x72, x57, x59); + var x75: u64 = undefined; + var x76: u1 = undefined; + p256AddcarryxU64(&x75, &x76, x74, ((@intCast(u64, x58) + @intCast(u64, x36)) + (@intCast(u64, x50) + x38)), x60); + var x77: u64 = undefined; + var x78: u64 = undefined; + p256MulxU64(&x77, &x78, x2, 0x4fffffffd); + var x79: u64 = undefined; + var x80: u64 = undefined; + p256MulxU64(&x79, &x80, x2, 0xfffffffffffffffe); + var x81: u64 = undefined; + var x82: u64 = undefined; + p256MulxU64(&x81, &x82, x2, 0xfffffffbffffffff); + var x83: u64 = undefined; + var x84: u64 = undefined; + p256MulxU64(&x83, &x84, x2, 0x3); + var x85: u64 = undefined; + var x86: u1 = undefined; + p256AddcarryxU64(&x85, &x86, 0x0, x84, x81); + var x87: u64 = undefined; + var x88: u1 = undefined; + p256AddcarryxU64(&x87, &x88, x86, x82, x79); + var x89: u64 = undefined; + var x90: u1 = undefined; + p256AddcarryxU64(&x89, &x90, x88, x80, x77); + var x91: u64 = undefined; + var x92: u1 = undefined; + p256AddcarryxU64(&x91, &x92, 0x0, x69, x83); + var x93: u64 = undefined; + var x94: u1 = undefined; + p256AddcarryxU64(&x93, &x94, x92, x71, x85); + var x95: u64 = undefined; + var x96: u1 = undefined; + p256AddcarryxU64(&x95, &x96, x94, x73, x87); + var x97: u64 = undefined; + var x98: u1 = undefined; + p256AddcarryxU64(&x97, &x98, x96, x75, x89); + var x99: u64 = undefined; + var x100: u64 = undefined; + p256MulxU64(&x99, &x100, x91, 0xffffffff00000001); + var x101: u64 = undefined; + var x102: u64 = undefined; + p256MulxU64(&x101, &x102, x91, 0xffffffff); + var x103: u64 = undefined; + var x104: u64 = undefined; + p256MulxU64(&x103, &x104, x91, 0xffffffffffffffff); + var x105: u64 = undefined; + var x106: u1 = undefined; + p256AddcarryxU64(&x105, &x106, 0x0, x104, x101); + var x107: u64 = undefined; + var x108: u1 = undefined; + p256AddcarryxU64(&x107, &x108, 0x0, x91, x103); + var x109: u64 = undefined; + var x110: u1 = undefined; + p256AddcarryxU64(&x109, &x110, x108, x93, x105); + var x111: u64 = undefined; + var x112: u1 = undefined; + p256AddcarryxU64(&x111, &x112, x110, x95, (@intCast(u64, x106) + x102)); + var x113: u64 = undefined; + var x114: u1 = undefined; + p256AddcarryxU64(&x113, &x114, x112, x97, x99); + var x115: u64 = undefined; + var x116: u1 = undefined; + p256AddcarryxU64(&x115, &x116, x114, ((@intCast(u64, x98) + @intCast(u64, x76)) + (@intCast(u64, x90) + x78)), x100); + var x117: u64 = undefined; + var x118: u64 = undefined; + p256MulxU64(&x117, &x118, x3, 0x4fffffffd); + var x119: u64 = undefined; + var x120: u64 = undefined; + p256MulxU64(&x119, &x120, x3, 0xfffffffffffffffe); + var x121: u64 = undefined; + var x122: u64 = undefined; + p256MulxU64(&x121, &x122, x3, 0xfffffffbffffffff); + var x123: u64 = undefined; + var x124: u64 = undefined; + p256MulxU64(&x123, &x124, x3, 0x3); + var x125: u64 = undefined; + var x126: u1 = undefined; + p256AddcarryxU64(&x125, &x126, 0x0, x124, x121); + var x127: u64 = undefined; + var x128: u1 = undefined; + p256AddcarryxU64(&x127, &x128, x126, x122, x119); + var x129: u64 = undefined; + var x130: u1 = undefined; + p256AddcarryxU64(&x129, &x130, x128, x120, x117); + var x131: u64 = undefined; + var x132: u1 = undefined; + p256AddcarryxU64(&x131, &x132, 0x0, x109, x123); + var x133: u64 = undefined; + var x134: u1 = undefined; + p256AddcarryxU64(&x133, &x134, x132, x111, x125); + var x135: u64 = undefined; + var x136: u1 = undefined; + p256AddcarryxU64(&x135, &x136, x134, x113, x127); + var x137: u64 = undefined; + var x138: u1 = undefined; + p256AddcarryxU64(&x137, &x138, x136, x115, x129); + var x139: u64 = undefined; + var x140: u64 = undefined; + p256MulxU64(&x139, &x140, x131, 0xffffffff00000001); + var x141: u64 = undefined; + var x142: u64 = undefined; + p256MulxU64(&x141, &x142, x131, 0xffffffff); + var x143: u64 = undefined; + var x144: u64 = undefined; + p256MulxU64(&x143, &x144, x131, 0xffffffffffffffff); + var x145: u64 = undefined; + var x146: u1 = undefined; + p256AddcarryxU64(&x145, &x146, 0x0, x144, x141); + var x147: u64 = undefined; + var x148: u1 = undefined; + p256AddcarryxU64(&x147, &x148, 0x0, x131, x143); + var x149: u64 = undefined; + var x150: u1 = undefined; + p256AddcarryxU64(&x149, &x150, x148, x133, x145); + var x151: u64 = undefined; + var x152: u1 = undefined; + p256AddcarryxU64(&x151, &x152, x150, x135, (@intCast(u64, x146) + x142)); + var x153: u64 = undefined; + var x154: u1 = undefined; + p256AddcarryxU64(&x153, &x154, x152, x137, x139); + var x155: u64 = undefined; + var x156: u1 = undefined; + p256AddcarryxU64(&x155, &x156, x154, ((@intCast(u64, x138) + @intCast(u64, x116)) + (@intCast(u64, x130) + x118)), x140); + var x157: u64 = undefined; + var x158: u1 = undefined; + p256SubborrowxU64(&x157, &x158, 0x0, x149, 0xffffffffffffffff); + var x159: u64 = undefined; + var x160: u1 = undefined; + p256SubborrowxU64(&x159, &x160, x158, x151, 0xffffffff); + var x161: u64 = undefined; + var x162: u1 = undefined; + p256SubborrowxU64(&x161, &x162, x160, x153, @intCast(u64, 0x0)); + var x163: u64 = undefined; + var x164: u1 = undefined; + p256SubborrowxU64(&x163, &x164, x162, x155, 0xffffffff00000001); + var x165: u64 = undefined; + var x166: u1 = undefined; + p256SubborrowxU64(&x165, &x166, x164, @intCast(u64, x156), @intCast(u64, 0x0)); + var x167: u64 = undefined; + p256CmovznzU64(&x167, x166, x157, x149); + var x168: u64 = undefined; + p256CmovznzU64(&x168, x166, x159, x151); + var x169: u64 = undefined; + p256CmovznzU64(&x169, x166, x161, x153); + var x170: u64 = undefined; + p256CmovznzU64(&x170, x166, x163, x155); + out1[0] = x167; + out1[1] = x168; + out1[2] = x169; + out1[3] = x170; +} + +/// The function p256Nonzero 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 p256Nonzero(out1: *u64, arg1: Limbs) void { + const x1: u64 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3])))); + out1.* = x1; +} + +/// The function p256Selectznz is a multi-limb conditional select. +/// Postconditions: +/// eval out1 = (if arg1 = 0 then eval arg2 else eval 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 p256Selectznz(out1: *Limbs, arg1: u1, arg2: Limbs, arg3: Limbs) void { + var x1: u64 = undefined; + p256CmovznzU64(&x1, arg1, (arg2[0]), (arg3[0])); + var x2: u64 = undefined; + p256CmovznzU64(&x2, arg1, (arg2[1]), (arg3[1])); + var x3: u64 = undefined; + p256CmovznzU64(&x3, arg1, (arg2[2]), (arg3[2])); + var x4: u64 = undefined; + p256CmovznzU64(&x4, arg1, (arg2[3]), (arg3[3])); + out1[0] = x1; + out1[1] = x2; + out1[2] = x3; + out1[3] = x4; +} + +/// The function p256ToBytes 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 p256ToBytes(out1: *[32]u8, arg1: Limbs) void { + const x1: u64 = (arg1[3]); + const x2: u64 = (arg1[2]); + const x3: u64 = (arg1[1]); + const x4: u64 = (arg1[0]); + const x5: u8 = @intCast(u8, (x4 & @intCast(u64, 0xff))); + const x6: u64 = (x4 >> 8); + const x7: u8 = @intCast(u8, (x6 & @intCast(u64, 0xff))); + const x8: u64 = (x6 >> 8); + const x9: u8 = @intCast(u8, (x8 & @intCast(u64, 0xff))); + const x10: u64 = (x8 >> 8); + const x11: u8 = @intCast(u8, (x10 & @intCast(u64, 0xff))); + const x12: u64 = (x10 >> 8); + const x13: u8 = @intCast(u8, (x12 & @intCast(u64, 0xff))); + const x14: u64 = (x12 >> 8); + const x15: u8 = @intCast(u8, (x14 & @intCast(u64, 0xff))); + const x16: u64 = (x14 >> 8); + const x17: u8 = @intCast(u8, (x16 & @intCast(u64, 0xff))); + const x18: u8 = @intCast(u8, (x16 >> 8)); + const x19: u8 = @intCast(u8, (x3 & @intCast(u64, 0xff))); + const x20: u64 = (x3 >> 8); + const x21: u8 = @intCast(u8, (x20 & @intCast(u64, 0xff))); + const x22: u64 = (x20 >> 8); + const x23: u8 = @intCast(u8, (x22 & @intCast(u64, 0xff))); + const x24: u64 = (x22 >> 8); + const x25: u8 = @intCast(u8, (x24 & @intCast(u64, 0xff))); + const x26: u64 = (x24 >> 8); + const x27: u8 = @intCast(u8, (x26 & @intCast(u64, 0xff))); + const x28: u64 = (x26 >> 8); + const x29: u8 = @intCast(u8, (x28 & @intCast(u64, 0xff))); + const x30: u64 = (x28 >> 8); + const x31: u8 = @intCast(u8, (x30 & @intCast(u64, 0xff))); + const x32: u8 = @intCast(u8, (x30 >> 8)); + const x33: u8 = @intCast(u8, (x2 & @intCast(u64, 0xff))); + const x34: u64 = (x2 >> 8); + const x35: u8 = @intCast(u8, (x34 & @intCast(u64, 0xff))); + const x36: u64 = (x34 >> 8); + const x37: u8 = @intCast(u8, (x36 & @intCast(u64, 0xff))); + const x38: u64 = (x36 >> 8); + const x39: u8 = @intCast(u8, (x38 & @intCast(u64, 0xff))); + const x40: u64 = (x38 >> 8); + const x41: u8 = @intCast(u8, (x40 & @intCast(u64, 0xff))); + const x42: u64 = (x40 >> 8); + const x43: u8 = @intCast(u8, (x42 & @intCast(u64, 0xff))); + const x44: u64 = (x42 >> 8); + const x45: u8 = @intCast(u8, (x44 & @intCast(u64, 0xff))); + const x46: u8 = @intCast(u8, (x44 >> 8)); + const x47: u8 = @intCast(u8, (x1 & @intCast(u64, 0xff))); + const x48: u64 = (x1 >> 8); + const x49: u8 = @intCast(u8, (x48 & @intCast(u64, 0xff))); + const x50: u64 = (x48 >> 8); + const x51: u8 = @intCast(u8, (x50 & @intCast(u64, 0xff))); + const x52: u64 = (x50 >> 8); + const x53: u8 = @intCast(u8, (x52 & @intCast(u64, 0xff))); + const x54: u64 = (x52 >> 8); + const x55: u8 = @intCast(u8, (x54 & @intCast(u64, 0xff))); + const x56: u64 = (x54 >> 8); + const x57: u8 = @intCast(u8, (x56 & @intCast(u64, 0xff))); + const x58: u64 = (x56 >> 8); + const x59: u8 = @intCast(u8, (x58 & @intCast(u64, 0xff))); + const x60: u8 = @intCast(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 p256FromBytes 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 p256FromBytes(out1: *Limbs, arg1: [32]u8) void { + const x1: u64 = (@intCast(u64, (arg1[31])) << 56); + const x2: u64 = (@intCast(u64, (arg1[30])) << 48); + const x3: u64 = (@intCast(u64, (arg1[29])) << 40); + const x4: u64 = (@intCast(u64, (arg1[28])) << 32); + const x5: u64 = (@intCast(u64, (arg1[27])) << 24); + const x6: u64 = (@intCast(u64, (arg1[26])) << 16); + const x7: u64 = (@intCast(u64, (arg1[25])) << 8); + const x8: u8 = (arg1[24]); + const x9: u64 = (@intCast(u64, (arg1[23])) << 56); + const x10: u64 = (@intCast(u64, (arg1[22])) << 48); + const x11: u64 = (@intCast(u64, (arg1[21])) << 40); + const x12: u64 = (@intCast(u64, (arg1[20])) << 32); + const x13: u64 = (@intCast(u64, (arg1[19])) << 24); + const x14: u64 = (@intCast(u64, (arg1[18])) << 16); + const x15: u64 = (@intCast(u64, (arg1[17])) << 8); + const x16: u8 = (arg1[16]); + const x17: u64 = (@intCast(u64, (arg1[15])) << 56); + const x18: u64 = (@intCast(u64, (arg1[14])) << 48); + const x19: u64 = (@intCast(u64, (arg1[13])) << 40); + const x20: u64 = (@intCast(u64, (arg1[12])) << 32); + const x21: u64 = (@intCast(u64, (arg1[11])) << 24); + const x22: u64 = (@intCast(u64, (arg1[10])) << 16); + const x23: u64 = (@intCast(u64, (arg1[9])) << 8); + const x24: u8 = (arg1[8]); + const x25: u64 = (@intCast(u64, (arg1[7])) << 56); + const x26: u64 = (@intCast(u64, (arg1[6])) << 48); + const x27: u64 = (@intCast(u64, (arg1[5])) << 40); + const x28: u64 = (@intCast(u64, (arg1[4])) << 32); + const x29: u64 = (@intCast(u64, (arg1[3])) << 24); + const x30: u64 = (@intCast(u64, (arg1[2])) << 16); + const x31: u64 = (@intCast(u64, (arg1[1])) << 8); + const x32: u8 = (arg1[0]); + const x33: u64 = (x31 + @intCast(u64, x32)); + const x34: u64 = (x30 + x33); + const x35: u64 = (x29 + x34); + const x36: u64 = (x28 + x35); + const x37: u64 = (x27 + x36); + const x38: u64 = (x26 + x37); + const x39: u64 = (x25 + x38); + const x40: u64 = (x23 + @intCast(u64, x24)); + const x41: u64 = (x22 + x40); + const x42: u64 = (x21 + x41); + const x43: u64 = (x20 + x42); + const x44: u64 = (x19 + x43); + const x45: u64 = (x18 + x44); + const x46: u64 = (x17 + x45); + const x47: u64 = (x15 + @intCast(u64, x16)); + const x48: u64 = (x14 + x47); + const x49: u64 = (x13 + x48); + const x50: u64 = (x12 + x49); + const x51: u64 = (x11 + x50); + const x52: u64 = (x10 + x51); + const x53: u64 = (x9 + x52); + const x54: u64 = (x7 + @intCast(u64, x8)); + const x55: u64 = (x6 + x54); + const x56: u64 = (x5 + x55); + const x57: u64 = (x4 + x56); + const x58: u64 = (x3 + x57); + const x59: u64 = (x2 + x58); + const x60: u64 = (x1 + x59); + out1[0] = x39; + out1[1] = x46; + out1[2] = x53; + out1[3] = x60; +} + +/// The function p256SetOne returns the field element one in the Montgomery domain. +/// Postconditions: +/// eval (from_montgomery out1) mod m = 1 mod m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256SetOne(out1: *Limbs) void { + out1[0] = @intCast(u64, 0x1); + out1[1] = 0xffffffff00000000; + out1[2] = 0xffffffffffffffff; + out1[3] = 0xfffffffe; +} + +/// The function p256Msat returns the saturated representation of the prime modulus. +/// Postconditions: +/// twos_complement_eval out1 = m +/// 0 ≤ eval out1 < m +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256Msat(out1: *[5]u64) void { + out1[0] = 0xffffffffffffffff; + out1[1] = 0xffffffff; + out1[2] = @intCast(u64, 0x0); + out1[3] = 0xffffffff00000001; + out1[4] = @intCast(u64, 0x0); +} + +/// The function p256Divstep 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 p256Divstep(out1: *u64, out2: *[5]u64, out3: *[5]u64, out4: *Limbs, out5: *Limbs, arg1: u64, arg2: [5]u64, arg3: [5]u64, arg4: Limbs, arg5: Limbs) void { + var x1: u64 = undefined; + var x2: u1 = undefined; + p256AddcarryxU64(&x1, &x2, 0x0, (~arg1), @intCast(u64, 0x1)); + const x3: u1 = (@intCast(u1, (x1 >> 63)) & @intCast(u1, ((arg3[0]) & @intCast(u64, 0x1)))); + var x4: u64 = undefined; + var x5: u1 = undefined; + p256AddcarryxU64(&x4, &x5, 0x0, (~arg1), @intCast(u64, 0x1)); + var x6: u64 = undefined; + p256CmovznzU64(&x6, x3, arg1, x4); + var x7: u64 = undefined; + p256CmovznzU64(&x7, x3, (arg2[0]), (arg3[0])); + var x8: u64 = undefined; + p256CmovznzU64(&x8, x3, (arg2[1]), (arg3[1])); + var x9: u64 = undefined; + p256CmovznzU64(&x9, x3, (arg2[2]), (arg3[2])); + var x10: u64 = undefined; + p256CmovznzU64(&x10, x3, (arg2[3]), (arg3[3])); + var x11: u64 = undefined; + p256CmovznzU64(&x11, x3, (arg2[4]), (arg3[4])); + var x12: u64 = undefined; + var x13: u1 = undefined; + p256AddcarryxU64(&x12, &x13, 0x0, @intCast(u64, 0x1), (~(arg2[0]))); + var x14: u64 = undefined; + var x15: u1 = undefined; + p256AddcarryxU64(&x14, &x15, x13, @intCast(u64, 0x0), (~(arg2[1]))); + var x16: u64 = undefined; + var x17: u1 = undefined; + p256AddcarryxU64(&x16, &x17, x15, @intCast(u64, 0x0), (~(arg2[2]))); + var x18: u64 = undefined; + var x19: u1 = undefined; + p256AddcarryxU64(&x18, &x19, x17, @intCast(u64, 0x0), (~(arg2[3]))); + var x20: u64 = undefined; + var x21: u1 = undefined; + p256AddcarryxU64(&x20, &x21, x19, @intCast(u64, 0x0), (~(arg2[4]))); + var x22: u64 = undefined; + p256CmovznzU64(&x22, x3, (arg3[0]), x12); + var x23: u64 = undefined; + p256CmovznzU64(&x23, x3, (arg3[1]), x14); + var x24: u64 = undefined; + p256CmovznzU64(&x24, x3, (arg3[2]), x16); + var x25: u64 = undefined; + p256CmovznzU64(&x25, x3, (arg3[3]), x18); + var x26: u64 = undefined; + p256CmovznzU64(&x26, x3, (arg3[4]), x20); + var x27: u64 = undefined; + p256CmovznzU64(&x27, x3, (arg4[0]), (arg5[0])); + var x28: u64 = undefined; + p256CmovznzU64(&x28, x3, (arg4[1]), (arg5[1])); + var x29: u64 = undefined; + p256CmovznzU64(&x29, x3, (arg4[2]), (arg5[2])); + var x30: u64 = undefined; + p256CmovznzU64(&x30, x3, (arg4[3]), (arg5[3])); + var x31: u64 = undefined; + var x32: u1 = undefined; + p256AddcarryxU64(&x31, &x32, 0x0, x27, x27); + var x33: u64 = undefined; + var x34: u1 = undefined; + p256AddcarryxU64(&x33, &x34, x32, x28, x28); + var x35: u64 = undefined; + var x36: u1 = undefined; + p256AddcarryxU64(&x35, &x36, x34, x29, x29); + var x37: u64 = undefined; + var x38: u1 = undefined; + p256AddcarryxU64(&x37, &x38, x36, x30, x30); + var x39: u64 = undefined; + var x40: u1 = undefined; + p256SubborrowxU64(&x39, &x40, 0x0, x31, 0xffffffffffffffff); + var x41: u64 = undefined; + var x42: u1 = undefined; + p256SubborrowxU64(&x41, &x42, x40, x33, 0xffffffff); + var x43: u64 = undefined; + var x44: u1 = undefined; + p256SubborrowxU64(&x43, &x44, x42, x35, @intCast(u64, 0x0)); + var x45: u64 = undefined; + var x46: u1 = undefined; + p256SubborrowxU64(&x45, &x46, x44, x37, 0xffffffff00000001); + var x47: u64 = undefined; + var x48: u1 = undefined; + p256SubborrowxU64(&x47, &x48, x46, @intCast(u64, x38), @intCast(u64, 0x0)); + const x49: u64 = (arg4[3]); + const x50: u64 = (arg4[2]); + const x51: u64 = (arg4[1]); + const x52: u64 = (arg4[0]); + var x53: u64 = undefined; + var x54: u1 = undefined; + p256SubborrowxU64(&x53, &x54, 0x0, @intCast(u64, 0x0), x52); + var x55: u64 = undefined; + var x56: u1 = undefined; + p256SubborrowxU64(&x55, &x56, x54, @intCast(u64, 0x0), x51); + var x57: u64 = undefined; + var x58: u1 = undefined; + p256SubborrowxU64(&x57, &x58, x56, @intCast(u64, 0x0), x50); + var x59: u64 = undefined; + var x60: u1 = undefined; + p256SubborrowxU64(&x59, &x60, x58, @intCast(u64, 0x0), x49); + var x61: u64 = undefined; + p256CmovznzU64(&x61, x60, @intCast(u64, 0x0), 0xffffffffffffffff); + var x62: u64 = undefined; + var x63: u1 = undefined; + p256AddcarryxU64(&x62, &x63, 0x0, x53, x61); + var x64: u64 = undefined; + var x65: u1 = undefined; + p256AddcarryxU64(&x64, &x65, x63, x55, (x61 & 0xffffffff)); + var x66: u64 = undefined; + var x67: u1 = undefined; + p256AddcarryxU64(&x66, &x67, x65, x57, @intCast(u64, 0x0)); + var x68: u64 = undefined; + var x69: u1 = undefined; + p256AddcarryxU64(&x68, &x69, x67, x59, (x61 & 0xffffffff00000001)); + var x70: u64 = undefined; + p256CmovznzU64(&x70, x3, (arg5[0]), x62); + var x71: u64 = undefined; + p256CmovznzU64(&x71, x3, (arg5[1]), x64); + var x72: u64 = undefined; + p256CmovznzU64(&x72, x3, (arg5[2]), x66); + var x73: u64 = undefined; + p256CmovznzU64(&x73, x3, (arg5[3]), x68); + const x74: u1 = @intCast(u1, (x22 & @intCast(u64, 0x1))); + var x75: u64 = undefined; + p256CmovznzU64(&x75, x74, @intCast(u64, 0x0), x7); + var x76: u64 = undefined; + p256CmovznzU64(&x76, x74, @intCast(u64, 0x0), x8); + var x77: u64 = undefined; + p256CmovznzU64(&x77, x74, @intCast(u64, 0x0), x9); + var x78: u64 = undefined; + p256CmovznzU64(&x78, x74, @intCast(u64, 0x0), x10); + var x79: u64 = undefined; + p256CmovznzU64(&x79, x74, @intCast(u64, 0x0), x11); + var x80: u64 = undefined; + var x81: u1 = undefined; + p256AddcarryxU64(&x80, &x81, 0x0, x22, x75); + var x82: u64 = undefined; + var x83: u1 = undefined; + p256AddcarryxU64(&x82, &x83, x81, x23, x76); + var x84: u64 = undefined; + var x85: u1 = undefined; + p256AddcarryxU64(&x84, &x85, x83, x24, x77); + var x86: u64 = undefined; + var x87: u1 = undefined; + p256AddcarryxU64(&x86, &x87, x85, x25, x78); + var x88: u64 = undefined; + var x89: u1 = undefined; + p256AddcarryxU64(&x88, &x89, x87, x26, x79); + var x90: u64 = undefined; + p256CmovznzU64(&x90, x74, @intCast(u64, 0x0), x27); + var x91: u64 = undefined; + p256CmovznzU64(&x91, x74, @intCast(u64, 0x0), x28); + var x92: u64 = undefined; + p256CmovznzU64(&x92, x74, @intCast(u64, 0x0), x29); + var x93: u64 = undefined; + p256CmovznzU64(&x93, x74, @intCast(u64, 0x0), x30); + var x94: u64 = undefined; + var x95: u1 = undefined; + p256AddcarryxU64(&x94, &x95, 0x0, x70, x90); + var x96: u64 = undefined; + var x97: u1 = undefined; + p256AddcarryxU64(&x96, &x97, x95, x71, x91); + var x98: u64 = undefined; + var x99: u1 = undefined; + p256AddcarryxU64(&x98, &x99, x97, x72, x92); + var x100: u64 = undefined; + var x101: u1 = undefined; + p256AddcarryxU64(&x100, &x101, x99, x73, x93); + var x102: u64 = undefined; + var x103: u1 = undefined; + p256SubborrowxU64(&x102, &x103, 0x0, x94, 0xffffffffffffffff); + var x104: u64 = undefined; + var x105: u1 = undefined; + p256SubborrowxU64(&x104, &x105, x103, x96, 0xffffffff); + var x106: u64 = undefined; + var x107: u1 = undefined; + p256SubborrowxU64(&x106, &x107, x105, x98, @intCast(u64, 0x0)); + var x108: u64 = undefined; + var x109: u1 = undefined; + p256SubborrowxU64(&x108, &x109, x107, x100, 0xffffffff00000001); + var x110: u64 = undefined; + var x111: u1 = undefined; + p256SubborrowxU64(&x110, &x111, x109, @intCast(u64, x101), @intCast(u64, 0x0)); + var x112: u64 = undefined; + var x113: u1 = undefined; + p256AddcarryxU64(&x112, &x113, 0x0, x6, @intCast(u64, 0x1)); + const x114: u64 = ((x80 >> 1) | ((x82 << 63) & 0xffffffffffffffff)); + const x115: u64 = ((x82 >> 1) | ((x84 << 63) & 0xffffffffffffffff)); + const x116: u64 = ((x84 >> 1) | ((x86 << 63) & 0xffffffffffffffff)); + const x117: u64 = ((x86 >> 1) | ((x88 << 63) & 0xffffffffffffffff)); + const x118: u64 = ((x88 & 0x8000000000000000) | (x88 >> 1)); + var x119: u64 = undefined; + p256CmovznzU64(&x119, x48, x39, x31); + var x120: u64 = undefined; + p256CmovznzU64(&x120, x48, x41, x33); + var x121: u64 = undefined; + p256CmovznzU64(&x121, x48, x43, x35); + var x122: u64 = undefined; + p256CmovznzU64(&x122, x48, x45, x37); + var x123: u64 = undefined; + p256CmovznzU64(&x123, x111, x102, x94); + var x124: u64 = undefined; + p256CmovznzU64(&x124, x111, x104, x96); + var x125: u64 = undefined; + p256CmovznzU64(&x125, x111, x106, x98); + var x126: u64 = undefined; + p256CmovznzU64(&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 p256DivstepPrecomp 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 +/// +/// Input Bounds: +/// Output Bounds: +/// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +pub fn p256DivstepPrecomp(out1: *Limbs) void { + out1[0] = 0x67ffffffb8000000; + out1[1] = 0xc000000038000000; + out1[2] = 0xd80000007fffffff; + out1[3] = 0x2fffffffffffffff; +} diff --git a/lib/std/crypto/pcurves/p256/scalar.zig b/lib/std/crypto/pcurves/p256/scalar.zig new file mode 100644 index 0000000000..e047f6a8d6 --- /dev/null +++ b/lib/std/crypto/pcurves/p256/scalar.zig @@ -0,0 +1,219 @@ +// SPDX-License-Identifier: MIT +// Copyright (c) 2015-2021 Zig Contributors +// This file is part of [zig](https://ziglang.org/), which is MIT licensed. +// The MIT license requires this copyright notice to be included in all copies +// and substantial portions of the software. + +const std = @import("std"); +const builtin = std.builtin; +const crypto = std.crypto; +const debug = std.debug; +const math = std.math; +const mem = std.mem; + +const Fe = @import("field.zig").Fe; + +const NonCanonicalError = std.crypto.errors.NonCanonicalError; +const NotSquareError = std.crypto.errors.NotSquareError; + +/// A compressed scalar, in canonical form. +pub const CompressedScalar = [32]u8; + +/// Reject a scalar whose encoding is not canonical. +pub fn rejectNonCanonical(s: CompressedScalar) NonCanonicalError!void { + return Fe.rejectNonCanonical(s); +} + +/// Reduce a 48-bytes scalar to the field size. +pub fn reduce48(s: [48]u8) CompressedScalar { + return Scalar.fromBytes48(s).toBytes(); +} + +/// Reduce a 64-bytes scalar to the field size. +pub fn reduce64(s: [64]u8) CompressedScalar { + return ScalarDouble.fromBytes64(s).toBytes(); +} + +/// Return a*b (mod L) +pub fn mul(a: CompressedScalar, b: CompressedScalar, endian: 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: 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: 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: builtin.Endian) NonCanonicalError!CompressedScalar { + return (try Scalar.fromBytes(a, endian)).neg().toBytes(endian); +} + +/// Return (a-b) (mod L) +pub fn sub(a: CompressedScalar, b: CompressedScalar, endian: 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: 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: 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: 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: 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: 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: 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} ** 32; + 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} ** 32; + 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} ** 32; + 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/tests.zig b/lib/std/crypto/pcurves/tests.zig new file mode 100644 index 0000000000..4e8e08a7fe --- /dev/null +++ b/lib/std/crypto/pcurves/tests.zig @@ -0,0 +1,103 @@ +// SPDX-License-Identifier: MIT +// Copyright (c) 2015-2021 Zig Contributors +// This file is part of [zig](https://ziglang.org/), which is MIT licensed. +// The MIT license requires this copyright notice to be included in all copies +// and substantial portions of the software. + +const std = @import("std"); +const fmt = std.fmt; +const testing = std.testing; + +const P256 = @import("p256.zig").P256; + +test "p256 ECDH key exchange" { + const dha = P256.scalar.random(.Little); + const dhb = P256.scalar.random(.Little); + const dhA = try P256.basePoint.mul(dha, .Little); + const dhB = try P256.basePoint.mul(dhb, .Little); + const shareda = try dhA.mul(dhb, .Little); + const sharedb = try dhB.mul(dha, .Little); + testing.expect(shareda.equivalent(sharedb)); +} + +test "p256 point from affine coordinates" { + const xh = "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"; + const yh = "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"; + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + var ys: [32]u8 = undefined; + _ = try fmt.hexToBytes(&ys, yh); + var p = try P256.fromSerializedAffineCoordinates(xs, ys, .Big); + testing.expect(p.equivalent(P256.basePoint)); +} + +test "p256 test vectors" { + const expected = [_][]const u8{ + "0000000000000000000000000000000000000000000000000000000000000000", + "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", + "7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978", + "5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c", + "e2534a3532d08fbba02dde659ee62bd0031fe2db785596ef509302446b030852", + "51590b7a515140d2d784c85608668fdfef8c82fd1f5be52421554a0dc3d033ed", + "b01a172a76a4602c92d3242cb897dde3024c740debb215b4c6b0aae93c2291a9", + "8e533b6fa0bf7b4625bb30667c01fb607ef9f8b8a80fef5b300628703187b2a3", + "62d9779dbee9b0534042742d3ab54cadc1d238980fce97dbb4dd9dc1db6fb393", + "ea68d7b6fedf0b71878938d51d71f8729e0acb8c2c6df8b3d79e8a4b90949ee0", + }; + var p = P256.identityElement; + for (expected) |xh| { + const x = p.affineCoordinates().x; + p = p.add(P256.basePoint); + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + testing.expectEqualSlices(u8, &x.toBytes(.Big), &xs); + } +} + +test "p256 test vectors - doubling" { + const expected = [_][]const u8{ + "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", + "7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978", + "e2534a3532d08fbba02dde659ee62bd0031fe2db785596ef509302446b030852", + "62d9779dbee9b0534042742d3ab54cadc1d238980fce97dbb4dd9dc1db6fb393", + }; + var p = P256.basePoint; + for (expected) |xh| { + const x = p.affineCoordinates().x; + p = p.dbl(); + var xs: [32]u8 = undefined; + _ = try fmt.hexToBytes(&xs, xh); + testing.expectEqualSlices(u8, &x.toBytes(.Big), &xs); + } +} + +test "p256 compressed sec1 encoding/decoding" { + const p = P256.random(); + const s = p.toCompressedSec1(); + const q = try P256.fromSec1(&s); + testing.expect(p.equivalent(q)); +} + +test "p256 uncompressed sec1 encoding/decoding" { + const p = P256.random(); + const s = p.toUncompressedSec1(); + const q = try P256.fromSec1(&s); + testing.expect(p.equivalent(q)); +} + +test "p256 public key is the neutral element" { + const n = P256.scalar.Scalar.zero.toBytes(.Little); + const p = P256.random(); + testing.expectError(error.IdentityElement, p.mul(n, .Little)); +} + +test "p256 public key is the neutral element (public verification)" { + const n = P256.scalar.Scalar.zero.toBytes(.Little); + const p = P256.random(); + testing.expectError(error.IdentityElement, p.mulPublic(n, .Little)); +} + +test "p256 field element non-canonical encoding" { + const s = [_]u8{0xff} ** 32; + testing.expectError(error.NonCanonical, P256.Fe.fromBytes(s, .Little)); +}