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Merge branch 'jedisct1-25519'

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closes #6050
This commit is contained in:
Andrew Kelley 2020-08-16 22:35:39 -07:00
commit addeff889a
10 changed files with 1315 additions and 678 deletions
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15
lib/std/crypto.zig
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@ -34,12 +34,17 @@ pub const chaCha20IETF = import_chaCha20.chaCha20IETF;
pub const chaCha20With64BitNonce = import_chaCha20.chaCha20With64BitNonce;
pub const Poly1305 = @import("crypto/poly1305.zig").Poly1305;
pub const X25519 = @import("crypto/x25519.zig").X25519;
const import_aes = @import("crypto/aes.zig");
pub const AES128 = import_aes.AES128;
pub const AES256 = import_aes.AES256;
pub const Curve25519 = @import("crypto/25519/curve25519.zig").Curve25519;
pub const Ed25519 = @import("crypto/25519/ed25519.zig").Ed25519;
pub const Edwards25519 = @import("crypto/25519/edwards25519.zig").Edwards25519;
pub const X25519 = @import("crypto/25519/x25519.zig").X25519;
pub const Ristretto255 = @import("crypto/25519/ristretto255.zig").Ristretto255;
const std = @import("std.zig");
pub const randomBytes = std.os.getrandom;
@ -55,7 +60,13 @@ test "crypto" {
_ = @import("crypto/sha1.zig");
_ = @import("crypto/sha2.zig");
_ = @import("crypto/sha3.zig");
_ = @import("crypto/x25519.zig");
_ = @import("crypto/25519/curve25519.zig");
_ = @import("crypto/25519/ed25519.zig");
_ = @import("crypto/25519/edwards25519.zig");
_ = @import("crypto/25519/field.zig");
_ = @import("crypto/25519/scalar.zig");
_ = @import("crypto/25519/x25519.zig");
_ = @import("crypto/25519/ristretto255.zig");
}
test "issue #4532: no index out of bounds" {

144
lib/std/crypto/25519/curve25519.zig Normal file
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@ -0,0 +1,144 @@
const std = @import("std");
/// Group operations over Curve25519.
pub const Curve25519 = struct {
/// The underlying prime field.
pub const Fe = @import("field.zig").Fe;
/// Field arithmetic mod the order of the main subgroup.
pub const scalar = @import("scalar.zig");
x: Fe,
/// Decode a Curve25519 point from its compressed (X) coordinates.
pub inline fn fromBytes(s: [32]u8) Curve25519 {
return .{ .x = Fe.fromBytes(s) };
}
/// Encode a Curve25519 point.
pub inline fn toBytes(p: Curve25519) [32]u8 {
return p.x.toBytes();
}
/// The Curve25519 base point.
pub const basePoint = Curve25519{ .x = Fe.curve25519BasePoint };
/// Check that the encoding of a Curve25519 point is canonical.
pub fn rejectNonCanonical(s: [32]u8) !void {
return Fe.rejectNonCanonical(s, false);
}
/// Reject the neutral element.
pub fn rejectIdentity(p: Curve25519) !void {
if (p.x.isZero()) {
return error.IdentityElement;
}
}
fn ladder(p: Curve25519, s: [32]u8, comptime bits: usize) !Curve25519 {
var x1 = p.x;
var x2 = Fe.one;
var z2 = Fe.zero;
var x3 = x1;
var z3 = Fe.one;
var swap: u8 = 0;
var pos: usize = bits - 1;
while (true) : (pos -= 1) {
const bit = (s[pos >> 3] >> @truncate(u3, pos)) & 1;
swap ^= bit;
Fe.cSwap2(&x2, &x3, &z2, &z3, swap);
swap = bit;
const a = x2.add(z2);
const b = x2.sub(z2);
const aa = a.sq();
const bb = b.sq();
x2 = aa.mul(bb);
const e = aa.sub(bb);
const da = x3.sub(z3).mul(a);
const cb = x3.add(z3).mul(b);
x3 = da.add(cb).sq();
z3 = x1.mul(da.sub(cb).sq());
z2 = e.mul(bb.add(e.mul32(121666)));
if (pos == 0) break;
}
Fe.cSwap2(&x2, &x3, &z2, &z3, swap);
z2 = z2.invert();
x2 = x2.mul(z2);
if (x2.isZero()) {
return error.IdentityElement;
}
return Curve25519{ .x = x2 };
}
/// Multiply a Curve25519 point by a scalar after "clamping" it.
/// Clamping forces the scalar to be a multiple of the cofactor in
/// order to prevent small subgroups attacks. This is the standard
/// way to use Curve25519 for a DH operation.
/// Return error.IdentityElement if the resulting point is
/// the identity element.
pub fn clampedMul(p: Curve25519, s: [32]u8) !Curve25519 {
var t: [32]u8 = s;
scalar.clamp(&t);
return try ladder(p, t, 255);
}
/// Multiply a Curve25519 point by a scalar without clamping it.
/// Return error.IdentityElement if the resulting point is
/// the identity element or error.WeakPublicKey if the public
/// key is a low-order point.
pub fn mul(p: Curve25519, s: [32]u8) !Curve25519 {
const cofactor = [_]u8{8} ++ [_]u8{0} ** 31;
_ = ladder(p, cofactor, 4) catch |_| return error.WeakPublicKey;
return try ladder(p, s, 256);
}
};
test "curve25519" {
var s = [32]u8{ 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8 };
const p = try Curve25519.basePoint.clampedMul(s);
try p.rejectIdentity();
var buf: [128]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{p.toBytes()}), "E6F2A4D1C28EE5C7AD0329268255A468AD407D2672824C0C0EB30EA6EF450145");
const q = try p.clampedMul(s);
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{q.toBytes()}), "3614E119FFE55EC55B87D6B19971A9F4CBC78EFE80BEC55B96392BABCC712537");
try Curve25519.rejectNonCanonical(s);
s[31] |= 0x80;
std.testing.expectError(error.NonCanonical, Curve25519.rejectNonCanonical(s));
}
test "curve25519 small order check" {
var s: [32]u8 = [_]u8{1} ++ [_]u8{0} ** 31;
const small_order_ss: [7][32]u8 = .{
.{
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 0 (order 4)
},
.{
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 1 (order 1)
},
.{
0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, // 325606250916557431795983626356110631294008115727848805560023387167927233504 (order 8) */
},
.{
0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, // 39382357235489614581723060781553021112529911719440698176882885853963445705823 (order 8)
},
.{
0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p-1 (order 2)
},
.{
0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p (=0, order 4)
},
.{
0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p+1 (=1, order 1)
},
};
for (small_order_ss) |small_order_s| {
std.testing.expectError(error.WeakPublicKey, Curve25519.fromBytes(small_order_s).mul(s));
var extra = small_order_s;
extra[31] ^= 0x80;
std.testing.expectError(error.WeakPublicKey, Curve25519.fromBytes(extra).mul(s));
var valid = small_order_s;
valid[31] = 0x40;
s[0] = 0;
std.testing.expectError(error.IdentityElement, Curve25519.fromBytes(valid).mul(s));
}
}

134
lib/std/crypto/25519/ed25519.zig Normal file
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@ -0,0 +1,134 @@
const std = @import("std");
const fmt = std.fmt;
const mem = std.mem;
const Sha512 = std.crypto.Sha512;
/// Ed25519 (EdDSA) signatures.
pub const Ed25519 = struct {
/// The underlying elliptic curve.
pub const Curve = @import("edwards25519.zig").Edwards25519;
/// Length (in bytes) of a seed required to create a key pair.
pub const seed_length = 32;
/// Length (in bytes) of a compressed key pair.
pub const keypair_length = 64;
/// Length (in bytes) of a compressed public key.
pub const public_length = 32;
/// Length (in bytes) of a signature.
pub const signature_length = 64;
/// Length (in bytes) of optional random bytes, for non-deterministic signatures.
pub const noise_length = 32;
/// Derive a key pair from a secret seed.
///
/// As in RFC 8032, an Ed25519 public key is generated by hashing
/// the secret key using the SHA-512 function, and interpreting the
/// bit-swapped, clamped lower-half of the output as the secret scalar.
///
/// For this reason, an EdDSA secret key is commonly called a seed,
/// from which the actual secret is derived.
pub fn createKeyPair(seed: [seed_length]u8) ![keypair_length]u8 {
var az: [Sha512.digest_length]u8 = undefined;
var h = Sha512.init();
h.update(&seed);
h.final(&az);
const p = try Curve.basePoint.clampedMul(az[0..32].*);
var keypair: [keypair_length]u8 = undefined;
mem.copy(u8, &keypair, &seed);
mem.copy(u8, keypair[seed_length..], &p.toBytes());
return keypair;
}
/// Return the public key for a given key pair.
pub fn publicKey(key_pair: [keypair_length]u8) [public_length]u8 {
var public_key: [public_length]u8 = undefined;
mem.copy(u8, public_key[0..], key_pair[seed_length..]);
return public_key;
}
/// Sign a message using a key pair, and optional random noise.
/// Having noise creates non-standard, non-deterministic signatures,
/// but has been proven to increase resilience against fault attacks.
pub fn sign(msg: []const u8, key_pair: [keypair_length]u8, noise: ?[noise_length]u8) ![signature_length]u8 {
const public_key = key_pair[32..];
var az: [Sha512.digest_length]u8 = undefined;
var h = Sha512.init();
h.update(key_pair[0..seed_length]);
h.final(&az);
h = Sha512.init();
if (noise) |*z| {
h.update(z);
}
h.update(az[32..]);
h.update(msg);
var nonce64: [64]u8 = undefined;
h.final(&nonce64);
const nonce = Curve.scalar.reduce64(nonce64);
const r = try Curve.basePoint.mul(nonce);
var sig: [signature_length]u8 = undefined;
mem.copy(u8, sig[0..32], &r.toBytes());
mem.copy(u8, sig[32..], public_key);
h = Sha512.init();
h.update(&sig);
h.update(msg);
var hram64: [Sha512.digest_length]u8 = undefined;
h.final(&hram64);
const hram = Curve.scalar.reduce64(hram64);
var x = az[0..32];
Curve.scalar.clamp(x);
const s = Curve.scalar.mulAdd(hram, x.*, nonce);
mem.copy(u8, sig[32..], s[0..]);
return sig;
}
/// Verify an Ed25519 signature given a message and a public key.
/// Returns error.InvalidSignature is the signature verification failed.
pub fn verify(sig: [signature_length]u8, msg: []const u8, public_key: [public_length]u8) !void {
const r = sig[0..32];
const s = sig[32..64];
try Curve.scalar.rejectNonCanonical(s.*);
try Curve.rejectNonCanonical(public_key);
const a = try Curve.fromBytes(public_key);
try a.rejectIdentity();
var h = Sha512.init();
h.update(r);
h.update(&public_key);
h.update(msg);
var hram64: [Sha512.digest_length]u8 = undefined;
h.final(&hram64);
const hram = Curve.scalar.reduce64(hram64);
const p = try a.neg().mul(hram);
const check = (try Curve.basePoint.mul(s.*)).add(p).toBytes();
if (mem.eql(u8, &check, r) == false) {
return error.InvalidSignature;
}
}
};
test "ed25519 key pair creation" {
var seed: [32]u8 = undefined;
try fmt.hexToBytes(seed[0..], "8052030376d47112be7f73ed7a019293dd12ad910b654455798b4667d73de166");
const key_pair = try Ed25519.createKeyPair(seed);
var buf: [256]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{key_pair}), "8052030376D47112BE7F73ED7A019293DD12AD910B654455798B4667D73DE1662D6F7455D97B4A3A10D7293909D1A4F2058CB9A370E43FA8154BB280DB839083");
const public_key = Ed25519.publicKey(key_pair);
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{public_key}), "2D6F7455D97B4A3A10D7293909D1A4F2058CB9A370E43FA8154BB280DB839083");
}
test "ed25519 signature" {
var seed: [32]u8 = undefined;
try fmt.hexToBytes(seed[0..], "8052030376d47112be7f73ed7a019293dd12ad910b654455798b4667d73de166");
const key_pair = try Ed25519.createKeyPair(seed);
const sig = try Ed25519.sign("test", key_pair, null);
var buf: [128]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{sig}), "10A442B4A80CC4225B154F43BEF28D2472CA80221951262EB8E0DF9091575E2687CC486E77263C3418C757522D54F84B0359236ABBBD4ACD20DC297FDCA66808");
const public_key = Ed25519.publicKey(key_pair);
try Ed25519.verify(sig, "test", public_key);
std.testing.expectError(error.InvalidSignature, Ed25519.verify(sig, "TEST", public_key));
}

214
lib/std/crypto/25519/edwards25519.zig Normal file
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@ -0,0 +1,214 @@
const std = @import("std");
const fmt = std.fmt;
/// Group operations over Edwards25519.
pub const Edwards25519 = struct {
/// The underlying prime field.
pub const Fe = @import("field.zig").Fe;
/// Field arithmetic mod the order of the main subgroup.
pub const scalar = @import("scalar.zig");
x: Fe,
y: Fe,
z: Fe,
t: Fe,
is_base: bool = false,
/// Decode an Edwards25519 point from its compressed (Y+sign) coordinates.
pub fn fromBytes(s: [32]u8) !Edwards25519 {
const z = Fe.one;
const y = Fe.fromBytes(s);
var u = y.sq();
var v = u.mul(Fe.edwards25519d);
u = u.sub(z);
v = v.add(z);
const v3 = v.sq().mul(v);
var x = v3.sq().mul(v).mul(u).pow2523().mul(v3).mul(u);
const vxx = x.sq().mul(v);
const has_m_root = vxx.sub(u).isZero();
const has_p_root = vxx.add(u).isZero();
if ((@boolToInt(has_m_root) | @boolToInt(has_p_root)) == 0) { // best-effort to avoid two conditional branches
return error.InvalidEncoding;
}
x.cMov(x.mul(Fe.sqrtm1), 1 - @boolToInt(has_m_root));
x.cMov(x.neg(), @boolToInt(x.isNegative()) ^ (s[31] >> 7));
const t = x.mul(y);
return Edwards25519{ .x = x, .y = y, .z = z, .t = t };
}
/// Encode an Edwards25519 point.
pub fn toBytes(p: Edwards25519) [32]u8 {
const zi = p.z.invert();
var s = p.y.mul(zi).toBytes();
s[31] ^= @as(u8, @boolToInt(p.x.mul(zi).isNegative())) << 7;
return s;
}
/// Check that the encoding of a point is canonical.
pub fn rejectNonCanonical(s: [32]u8) !void {
return Fe.rejectNonCanonical(s, true);
}
/// The edwards25519 base point.
pub const basePoint = Edwards25519{
.x = Fe{ .limbs = .{ 3990542415680775, 3398198340507945, 4322667446711068, 2814063955482877, 2839572215813860 } },
.y = Fe{ .limbs = .{ 1801439850948184, 1351079888211148, 450359962737049, 900719925474099, 1801439850948198 } },
.z = Fe.one,
.t = Fe{ .limbs = .{ 1841354044333475, 16398895984059, 755974180946558, 900171276175154, 1821297809914039 } },
.is_base = true,
};
const identityElement = Edwards25519{ .x = Fe.zero, .y = Fe.one, .z = Fe.one, .t = Fe.zero };
/// Reject the neutral element.
pub fn rejectIdentity(p: Edwards25519) !void {
if (p.x.isZero()) {
return error.IdentityElement;
}
}
/// Flip the sign of the X coordinate.
pub inline fn neg(p: Edwards25519) Edwards25519 {
return .{ .x = p.x.neg(), .y = p.y, .z = p.z, .t = p.t.neg() };
}
/// Double an Edwards25519 point.
pub fn dbl(p: Edwards25519) Edwards25519 {
const t0 = p.x.add(p.y).sq();
var x = p.x.sq();
var z = p.y.sq();
const y = z.add(x);
z = z.sub(x);
x = t0.sub(y);
const t = p.z.sq2().sub(z);
return .{
.x = x.mul(t),
.y = y.mul(z),
.z = z.mul(t),
.t = x.mul(y),
};
}
/// Add two Edwards25519 points.
pub fn add(p: Edwards25519, q: Edwards25519) Edwards25519 {
const a = p.y.sub(p.x).mul(q.y.sub(q.x));
const b = p.x.add(p.y).mul(q.x.add(q.y));
const c = p.t.mul(q.t).mul(Fe.edwards25519d2);
var d = p.z.mul(q.z);
d = d.add(d);
const x = b.sub(a);
const y = b.add(a);
const z = d.add(c);
const t = d.sub(c);
return .{
.x = x.mul(t),
.y = y.mul(z),
.z = z.mul(t),
.t = x.mul(y),
};
}
inline fn cMov(p: *Edwards25519, a: Edwards25519, c: u64) void {
p.x.cMov(a.x, c);
p.y.cMov(a.y, c);
p.z.cMov(a.z, c);
p.t.cMov(a.t, c);
}
inline fn pcSelect(pc: [16]Edwards25519, b: u8) Edwards25519 {
var t = Edwards25519.identityElement;
comptime var i: u8 = 0;
inline while (i < 16) : (i += 1) {
t.cMov(pc[i], ((@as(usize, b ^ i) -% 1) >> 8) & 1);
}
return t;
}
fn pcMul(pc: [16]Edwards25519, s: [32]u8) !Edwards25519 {
var q = Edwards25519.identityElement;
var pos: usize = 252;
while (true) : (pos -= 4) {
q = q.dbl().dbl().dbl().dbl();
const bit = (s[pos >> 3] >> @truncate(u3, pos)) & 0xf;
q = q.add(pcSelect(pc, bit));
if (pos == 0) break;
}
try q.rejectIdentity();
return q;
}
fn precompute(p: Edwards25519) [16]Edwards25519 {
var pc: [16]Edwards25519 = undefined;
pc[0] = Edwards25519.identityElement;
pc[1] = p;
var i: usize = 2;
while (i < 16) : (i += 1) {
pc[i] = pc[i - 1].add(p);
}
return pc;
}
/// Multiply an Edwards25519 point by a scalar without clamping it.
/// Return error.WeakPublicKey if the resulting point is
/// the identity element.
pub fn mul(p: Edwards25519, s: [32]u8) !Edwards25519 {
var pc: [16]Edwards25519 = undefined;
if (p.is_base) {
@setEvalBranchQuota(10000);
pc = comptime precompute(Edwards25519.basePoint);
} else {
pc = precompute(p);
pc[4].rejectIdentity() catch |_| return error.WeakPublicKey;
}
return pcMul(pc, s);
}
/// Multiply an Edwards25519 point by a scalar after "clamping" it.
/// Clamping forces the scalar to be a multiple of the cofactor in
/// order to prevent small subgroups attacks.
/// This is strongly recommended for DH operations.
/// Return error.WeakPublicKey if the resulting point is
/// the identity element.
pub fn clampedMul(p: Edwards25519, s: [32]u8) !Edwards25519 {
var t: [32]u8 = s;
scalar.clamp(&t);
return mul(p, t);
}
};
test "edwards25519 packing/unpacking" {
const s = [_]u8{170} ++ [_]u8{0} ** 31;
var b = Edwards25519.basePoint;
const pk = try b.mul(s);
var buf: [128]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{pk.toBytes()}), "074BC7E0FCBD587FDBC0969444245FADC562809C8F6E97E949AF62484B5B81A6");
const small_order_ss: [7][32]u8 = .{
.{
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 0 (order 4)
},
.{
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // 1 (order 1)
},
.{
0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4, 0x89, 0xf2, 0xef, 0x98, 0xf0, 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6, 0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05, // 270738550114484064931822528722565878893680426757531351946374360975030340202(order 8)
},
.{
0xc7, 0x17, 0x6a, 0x70, 0x3d, 0x4d, 0xd8, 0x4f, 0xba, 0x3c, 0x0b, 0x76, 0x0d, 0x10, 0x67, 0x0f, 0x2a, 0x20, 0x53, 0xfa, 0x2c, 0x39, 0xcc, 0xc6, 0x4e, 0xc7, 0xfd, 0x77, 0x92, 0xac, 0x03, 0x7a, // 55188659117513257062467267217118295137698188065244968500265048394206261417927 (order 8)
},
.{
0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p-1 (order 2)
},
.{
0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p (=0, order 4)
},
.{
0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, // p+1 (=1, order 1)
},
};
for (small_order_ss) |small_order_s| {
const small_p = try Edwards25519.fromBytes(small_order_s);
std.testing.expectError(error.WeakPublicKey, small_p.mul(s));
}
}

312
lib/std/crypto/25519/field.zig Normal file
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const std = @import("std");
const readIntLittle = std.mem.readIntLittle;
const writeIntLittle = std.mem.writeIntLittle;
pub const Fe = struct {
limbs: [5]u64,
const MASK51: u64 = 0x7ffffffffffff;
pub const zero = Fe{ .limbs = .{ 0, 0, 0, 0, 0 } };
pub const one = Fe{ .limbs = .{ 1, 0, 0, 0, 0 } };
pub const sqrtm1 = Fe{ .limbs = .{ 1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133 } }; // sqrt(-1)
pub const curve25519BasePoint = Fe{ .limbs = .{ 9, 0, 0, 0, 0 } };
pub const edwards25519d = Fe{ .limbs = .{ 929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575 } }; // 37095705934669439343138083508754565189542113879843219016388785533085940283555
pub const edwards25519d2 = Fe{ .limbs = .{ 1859910466990425, 932731440258426, 1072319116312658, 1815898335770999, 633789495995903 } }; // 2d
pub const edwards25519sqrtamd = Fe{ .limbs = .{ 278908739862762, 821645201101625, 8113234426968, 1777959178193151, 2118520810568447 } }; // 1/sqrt(a-d)
pub inline fn isZero(fe: Fe) bool {
var reduced = fe;
reduced.reduce();
const limbs = reduced.limbs;
return (limbs[0] | limbs[1] | limbs[2] | limbs[3] | limbs[4]) == 0;
}
pub inline fn equivalent(a: Fe, b: Fe) bool {
return a.sub(b).isZero();
}
pub fn fromBytes(s: [32]u8) Fe {
var fe: Fe = undefined;
fe.limbs[0] = readIntLittle(u64, s[0..8]) & MASK51;
fe.limbs[1] = (readIntLittle(u64, s[6..14]) >> 3) & MASK51;
fe.limbs[2] = (readIntLittle(u64, s[12..20]) >> 6) & MASK51;
fe.limbs[3] = (readIntLittle(u64, s[19..27]) >> 1) & MASK51;
fe.limbs[4] = (readIntLittle(u64, s[24..32]) >> 12) & MASK51;
return fe;
}
pub fn toBytes(fe: Fe) [32]u8 {
var reduced = fe;
reduced.reduce();
var s: [32]u8 = undefined;
writeIntLittle(u64, s[0..8], reduced.limbs[0] | (reduced.limbs[1] << 51));
writeIntLittle(u64, s[8..16], (reduced.limbs[1] >> 13) | (reduced.limbs[2] << 38));
writeIntLittle(u64, s[16..24], (reduced.limbs[2] >> 26) | (reduced.limbs[3] << 25));
writeIntLittle(u64, s[24..32], (reduced.limbs[3] >> 39) | (reduced.limbs[4] << 12));
return s;
}
pub fn rejectNonCanonical(s: [32]u8, comptime ignore_extra_bit: bool) !void {
var c: u16 = (s[31] & 0x7f) ^ 0x7f;
comptime var i = 30;
inline while (i > 0) : (i -= 1) {
c |= s[i] ^ 0xff;
}
c = (c -% 1) >> 8;
const d = (@as(u16, 0xed - 1) -% @as(u16, s[0])) >> 8;
const x = if (ignore_extra_bit) 0 else s[31] >> 7;
if ((((c & d) | x) & 1) != 0) {
return error.NonCanonical;
}
}
fn reduce(fe: *Fe) void {
comptime var i = 0;
comptime var j = 0;
const limbs = &fe.limbs;
inline while (j < 2) : (j += 1) {
i = 0;
inline while (i < 4) : (i += 1) {
limbs[i + 1] += limbs[i] >> 51;
limbs[i] &= MASK51;
}
limbs[0] += 19 * (limbs[4] >> 51);
limbs[4] &= MASK51;
}
limbs[0] += 19;
i = 0;
inline while (i < 4) : (i += 1) {
limbs[i + 1] += limbs[i] >> 51;
limbs[i] &= MASK51;
}
limbs[0] += 19 * (limbs[4] >> 51);
limbs[4] &= MASK51;
limbs[0] += 0x8000000000000 - 19;
limbs[1] += 0x8000000000000 - 1;
limbs[2] += 0x8000000000000 - 1;
limbs[3] += 0x8000000000000 - 1;
limbs[4] += 0x8000000000000 - 1;
i = 0;
inline while (i < 4) : (i += 1) {
limbs[i + 1] += limbs[i] >> 51;
limbs[i] &= MASK51;
}
limbs[4] &= MASK51;
}
pub inline fn add(a: Fe, b: Fe) Fe {
var fe: Fe = undefined;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
fe.limbs[i] = a.limbs[i] + b.limbs[i];
}
return fe;
}
pub inline fn sub(a: Fe, b: Fe) Fe {
var fe = b;
comptime var i = 0;
inline while (i < 4) : (i += 1) {
fe.limbs[i + 1] += fe.limbs[i] >> 51;
fe.limbs[i] &= MASK51;
}
fe.limbs[0] += 19 * (fe.limbs[4] >> 51);
fe.limbs[4] &= MASK51;
fe.limbs[0] = (a.limbs[0] + 0xfffffffffffda) - fe.limbs[0];
fe.limbs[1] = (a.limbs[1] + 0xffffffffffffe) - fe.limbs[1];
fe.limbs[2] = (a.limbs[2] + 0xffffffffffffe) - fe.limbs[2];
fe.limbs[3] = (a.limbs[3] + 0xffffffffffffe) - fe.limbs[3];
fe.limbs[4] = (a.limbs[4] + 0xffffffffffffe) - fe.limbs[4];
return fe;
}
pub inline fn neg(a: Fe) Fe {
return zero.sub(a);
}
pub inline fn isNegative(a: Fe) bool {
return (a.toBytes()[0] & 1) != 0;
}
pub inline fn cMov(fe: *Fe, a: Fe, c: u64) void {
const mask: u64 = 0 -% c;
var x = fe.*;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
x.limbs[i] ^= a.limbs[i];
}
i = 0;
inline while (i < 5) : (i += 1) {
x.limbs[i] &= mask;
}
i = 0;
inline while (i < 5) : (i += 1) {
fe.limbs[i] ^= x.limbs[i];
}
}
pub fn cSwap2(a0: *Fe, b0: *Fe, a1: *Fe, b1: *Fe, c: u64) void {
const mask: u64 = 0 -% c;
var x0 = a0.*;
var x1 = a1.*;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
x0.limbs[i] ^= b0.limbs[i];
x1.limbs[i] ^= b1.limbs[i];
}
i = 0;
inline while (i < 5) : (i += 1) {
x0.limbs[i] &= mask;
x1.limbs[i] &= mask;
}
i = 0;
inline while (i < 5) : (i += 1) {
a0.limbs[i] ^= x0.limbs[i];
b0.limbs[i] ^= x0.limbs[i];
a1.limbs[i] ^= x1.limbs[i];
b1.limbs[i] ^= x1.limbs[i];
}
}
inline fn _carry128(r: *[5]u128) Fe {
var rs: [5]u64 = undefined;
comptime var i = 0;
inline while (i < 4) : (i += 1) {
rs[i] = @truncate(u64, r[i]) & MASK51;
r[i + 1] += @intCast(u64, r[i] >> 51);
}
rs[4] = @truncate(u64, r[4]) & MASK51;
var carry = @intCast(u64, r[4] >> 51);
rs[0] += 19 * carry;
carry = rs[0] >> 51;
rs[0] &= MASK51;
rs[1] += carry;
carry = rs[1] >> 51;
rs[1] &= MASK51;
rs[2] += carry;
return .{ .limbs = rs };
}
pub inline fn mul(a: Fe, b: Fe) Fe {
var ax: [5]u128 = undefined;
var bx: [5]u128 = undefined;
var a19: [5]u128 = undefined;
var r: [5]u128 = undefined;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
ax[i] = @intCast(u128, a.limbs[i]);
bx[i] = @intCast(u128, b.limbs[i]);
}
i = 1;
inline while (i < 5) : (i += 1) {
a19[i] = 19 * ax[i];
}
r[0] = ax[0] * bx[0] + a19[1] * bx[4] + a19[2] * bx[3] + a19[3] * bx[2] + a19[4] * bx[1];
r[1] = ax[0] * bx[1] + ax[1] * bx[0] + a19[2] * bx[4] + a19[3] * bx[3] + a19[4] * bx[2];
r[2] = ax[0] * bx[2] + ax[1] * bx[1] + ax[2] * bx[0] + a19[3] * bx[4] + a19[4] * bx[3];
r[3] = ax[0] * bx[3] + ax[1] * bx[2] + ax[2] * bx[1] + ax[3] * bx[0] + a19[4] * bx[4];
r[4] = ax[0] * bx[4] + ax[1] * bx[3] + ax[2] * bx[2] + ax[3] * bx[1] + ax[4] * bx[0];
return _carry128(&r);
}
inline fn _sq(a: Fe, double: comptime bool) Fe {
var ax: [5]u128 = undefined;
var r: [5]u128 = undefined;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
ax[i] = @intCast(u128, a.limbs[i]);
}
const a0_2 = 2 * ax[0];
const a1_2 = 2 * ax[1];
const a1_38 = 38 * ax[1];
const a2_38 = 38 * ax[2];
const a3_38 = 38 * ax[3];
const a3_19 = 19 * ax[3];
const a4_19 = 19 * ax[4];
r[0] = ax[0] * ax[0] + a1_38 * ax[4] + a2_38 * ax[3];
r[1] = a0_2 * ax[1] + a2_38 * ax[4] + a3_19 * ax[3];
r[2] = a0_2 * ax[2] + ax[1] * ax[1] + a3_38 * ax[4];
r[3] = a0_2 * ax[3] + a1_2 * ax[2] + a4_19 * ax[4];
r[4] = a0_2 * ax[4] + a1_2 * ax[3] + ax[2] * ax[2];
if (double) {
i = 0;
inline while (i < 5) : (i += 1) {
r[i] *= 2;
}
}
return _carry128(&r);
}
pub inline fn sq(a: Fe) Fe {
return _sq(a, false);
}
pub inline fn sq2(a: Fe) Fe {
return _sq(a, true);
}
pub inline fn mul32(a: Fe, comptime n: u32) Fe {
const sn = @intCast(u128, n);
var fe: Fe = undefined;
var x: u128 = 0;
comptime var i = 0;
inline while (i < 5) : (i += 1) {
x = a.limbs[i] * sn + (x >> 51);
fe.limbs[i] = @truncate(u64, x) & MASK51;
}
fe.limbs[0] += @intCast(u64, x >> 51) * 19;
return fe;
}
inline 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;
}
pub fn invert(a: Fe) Fe {
var t0 = a.sq();
var t1 = t0.sqn(2).mul(a);
t0 = t0.mul(t1);
t1 = t1.mul(t0.sq());
t1 = t1.mul(t1.sqn(5));
var t2 = t1.sqn(10).mul(t1);
t2 = t2.mul(t2.sqn(20)).sqn(10);
t1 = t1.mul(t2);
t2 = t1.sqn(50).mul(t1);
return t1.mul(t2.mul(t2.sqn(100)).sqn(50)).sqn(5).mul(t0);
}
pub fn pow2523(a: Fe) Fe {
var c = a;
var i: usize = 0;
while (i < 249) : (i += 1) {
c = c.sq().mul(a);
}
return c.sq().sq().mul(a);
}
pub fn abs(a: Fe) Fe {
var r = a;
r.cMov(a.neg(), @boolToInt(a.isNegative()));
return r;
}
};

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const std = @import("std");
const fmt = std.fmt;
/// Group operations over Edwards25519.
pub const Ristretto255 = struct {
/// The underlying elliptic curve.
pub const Curve = @import("edwards25519.zig").Edwards25519;
/// The underlying prime field.
pub const Fe = Curve.Fe;
/// Field arithmetic mod the order of the main subgroup.
pub const scalar = Curve.scalar;
p: Curve,
fn sqrtRatioM1(u: Fe, v: Fe) !Fe {
const v3 = v.sq().mul(v); // v^3
var x = v3.sq().mul(u).mul(v).pow2523().mul(v3).mul(u); // uv^3(uv^7)^((q-5)/8)
const vxx = x.sq().mul(v); // vx^2
const m_root_check = vxx.sub(u); // vx^2-u
const p_root_check = vxx.add(u); // vx^2+u
const f_root_check = u.mul(Fe.sqrtm1).add(vxx); // vx^2+u*sqrt(-1)
const has_m_root = m_root_check.isZero();
const has_p_root = p_root_check.isZero();
const has_f_root = f_root_check.isZero();
const x_sqrtm1 = x.mul(Fe.sqrtm1); // x*sqrt(-1)
x.cMov(x_sqrtm1, @boolToInt(has_p_root) | @boolToInt(has_f_root));
const xa = x.abs();
if ((@boolToInt(has_m_root) | @boolToInt(has_p_root)) == 0) {
return error.NoRoot;
}
return xa;
}
fn rejectNonCanonical(s: [32]u8) !void {
if ((s[0] & 1) != 0) {
return error.NonCanonical;
}
try Fe.rejectNonCanonical(s, false);
}
/// Reject the neutral element.
pub inline fn rejectIdentity(p: Ristretto255) !void {
return p.p.rejectIdentity();
}
/// The base point (Ristretto is a curve in desguise).
pub const basePoint = Ristretto255{ .p = Curve.basePoint };
/// Decode a Ristretto255 representative.
pub fn fromBytes(s: [32]u8) !Ristretto255 {
try rejectNonCanonical(s);
const s_ = Fe.fromBytes(s);
const ss = s_.sq(); // s^2
const u1_ = Fe.one.sub(ss); // (1-s^2)
const u1u1 = u1_.sq(); // (1-s^2)^2
const u2_ = Fe.one.add(ss); // (1+s^2)
const u2u2 = u2_.sq(); // (1+s^2)^2
const v = Fe.edwards25519d.mul(u1u1).neg().sub(u2u2); // -(d*u1^2)-u2^2
const v_u2u2 = v.mul(u2u2); // v*u2^2
const inv_sqrt = sqrtRatioM1(Fe.one, v_u2u2) catch |e| {
return error.InvalidEncoding;
};
var x = inv_sqrt.mul(u2_);
const y = inv_sqrt.mul(x).mul(v).mul(u1_);
x = x.mul(s_);
x = x.add(x).abs();
const t = x.mul(y);
if ((@boolToInt(t.isNegative()) | @boolToInt(y.isZero())) != 0) {
return error.InvalidEncoding;
}
const p: Curve = .{
.x = x,
.y = y,
.z = Fe.one,
.t = t,
};
return Ristretto255{ .p = p };
}
/// Encode to a Ristretto255 representative.
pub fn toBytes(e: Ristretto255) [32]u8 {
const p = &e.p;
var u1_ = p.z.add(p.y); // Z+Y
const zmy = p.z.sub(p.y); // Z-Y
u1_ = u1_.mul(zmy); // (Z+Y)*(Z-Y)
const u2_ = p.x.mul(p.y); // X*Y
const u1_u2u2 = u2_.sq().mul(u1_); // u1*u2^2
const inv_sqrt = sqrtRatioM1(Fe.one, u1_u2u2) catch unreachable;
const den1 = inv_sqrt.mul(u1_);
const den2 = inv_sqrt.mul(u2_);
const z_inv = den1.mul(den2).mul(p.t); // den1*den2*T
const ix = p.x.mul(Fe.sqrtm1); // X*sqrt(-1)
const iy = p.y.mul(Fe.sqrtm1); // Y*sqrt(-1)
const eden = den1.mul(Fe.edwards25519sqrtamd); // den1/sqrt(a-d)
const t_z_inv = p.t.mul(z_inv); // T*z_inv
const rotate = @boolToInt(t_z_inv.isNegative());
var x = p.x;
var y = p.y;
var den_inv = den2;
x.cMov(iy, rotate);
y.cMov(ix, rotate);
den_inv.cMov(eden, rotate);
const x_z_inv = x.mul(z_inv);
const yneg = y.neg();
y.cMov(yneg, @boolToInt(x_z_inv.isNegative()));
return p.z.sub(y).mul(den_inv).abs().toBytes();
}
/// Double a Ristretto255 element.
pub inline fn dbl(p: Ristretto255) Ristretto255 {
return .{ .p = p.p.dbl() };
}
/// Add two Ristretto255 elements.
pub inline fn add(p: Ristretto255, q: Ristretto255) Ristretto255 {
return .{ .p = p.p.add(q.p) };
}
/// Multiply a Ristretto255 element with a scalar.
/// Return error.WeakPublicKey if the resulting element is
/// the identity element.
pub inline fn mul(p: Ristretto255, s: [32]u8) !Ristretto255 {
return Ristretto255{ .p = try p.p.mul(s) };
}
};
test "ristretto255" {
const p = Ristretto255.basePoint;
var buf: [256]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{p.toBytes()}), "E2F2AE0A6ABC4E71A884A961C500515F58E30B6AA582DD8DB6A65945E08D2D76");
var r: [32]u8 = undefined;
try fmt.hexToBytes(r[0..], "6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919");
var q = try Ristretto255.fromBytes(r);
q = q.dbl().add(p);
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{q.toBytes()}), "E882B131016B52C1D3337080187CF768423EFCCBB517BB495AB812C4160FF44E");
const s = [_]u8{15} ++ [_]u8{0} ** 31;
const w = try p.mul(s);
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{w.toBytes()}), "E0C418F7C8D9C4CDD7395B93EA124F3AD99021BB681DFC3302A9D99A2E53E64E");
}

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const std = @import("std");
const mem = std.mem;
const field_size = [32]u8{
0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, // 2^252+27742317777372353535851937790883648493
};
const ScalarExpanded = struct {
limbs: [64]i64 = [_]i64{0} ** 64,
fn fromBytes(s: [32]u8) ScalarExpanded {
var limbs: [64]i64 = undefined;
for (s) |x, idx| {
limbs[idx] = @as(i64, x);
}
mem.set(i64, limbs[32..], 0);
return .{ .limbs = limbs };
}
fn fromBytes64(s: [64]u8) ScalarExpanded {
var limbs: [64]i64 = undefined;
for (s) |x, idx| {
limbs[idx] = @as(i64, x);
}
return .{ .limbs = limbs };
}
fn reduce(e: *ScalarExpanded) void {
const limbs = &e.limbs;
var carry: i64 = undefined;
var i: usize = 63;
while (i >= 32) : (i -= 1) {
carry = 0;
const k = i - 12;
const xi = limbs[i];
var j = i - 32;
while (j < k) : (j += 1) {
const xj = limbs[j] + carry - 16 * xi * @as(i64, field_size[j - (i - 32)]);
carry = (xj + 128) >> 8;
limbs[j] = xj - carry * 256;
}
limbs[k] += carry;
limbs[i] = 0;
}
carry = 0;
comptime var j: usize = 0;
inline while (j < 32) : (j += 1) {
const xi = limbs[j] + carry - (limbs[31] >> 4) * @as(i64, field_size[j]);
carry = xi >> 8;
limbs[j] = xi & 255;
}
j = 0;
inline while (j < 32) : (j += 1) {
limbs[j] -= carry * @as(i64, field_size[j]);
}
j = 0;
inline while (j < 32) : (j += 1) {
limbs[j + 1] += limbs[j] >> 8;
}
}
fn toBytes(e: *ScalarExpanded) [32]u8 {
e.reduce();
var r: [32]u8 = undefined;
var i: usize = 0;
while (i < 32) : (i += 1) {
r[i] = @intCast(u8, e.limbs[i]);
}
return r;
}
fn add(a: ScalarExpanded, b: ScalarExpanded) ScalarExpanded {
var r = ScalarExpanded{};
comptime var i = 0;
inline while (i < 64) : (i += 1) {
r.limbs[i] = a.limbs[i] + b.limbs[i];
}
return r;
}
fn mul(a: ScalarExpanded, b: ScalarExpanded) ScalarExpanded {
var r = ScalarExpanded{};
var i: usize = 0;
while (i < 32) : (i += 1) {
const ai = a.limbs[i];
comptime var j = 0;
inline while (j < 32) : (j += 1) {
r.limbs[i + j] += ai * b.limbs[j];
}
}
r.reduce();
return r;
}
fn sq(a: ScalarExpanded) ScalarExpanded {
return a.mul(a);
}
fn mulAdd(a: ScalarExpanded, b: ScalarExpanded, c: ScalarExpanded) ScalarExpanded {
var r: ScalarExpanded = .{ .limbs = c.limbs };
var i: usize = 0;
while (i < 32) : (i += 1) {
const ai = a.limbs[i];
comptime var j = 0;
inline while (j < 32) : (j += 1) {
r.limbs[i + j] += ai * b.limbs[j];
}
}
r.reduce();
return r;
}
};
/// Reject a scalar whose encoding is not canonical.
pub fn rejectNonCanonical(s: [32]u8) !void {
var c: u8 = 0;
var n: u8 = 1;
var i: usize = 31;
while (true) : (i -= 1) {
const xs = @as(u16, s[i]);
const xfield_size = @as(u16, field_size[i]);
c |= @intCast(u8, ((xs -% xfield_size) >> 8) & n);
n &= @intCast(u8, ((xs ^ xfield_size) -% 1) >> 8);
if (i == 0) break;
}
if (c == 0) {
return error.NonCanonical;
}
}
/// Reduce a scalar to the field size.
pub fn reduce(s: [32]u8) [32]u8 {
return ScalarExpanded.fromBytes(s).toBytes();
}
/// Reduce a 64-bytes scalar to the field size.
pub fn reduce64(s: [64]u8) [32]u8 {
return ScalarExpanded.fromBytes64(s).toBytes();
}
/// Perform the X25519 "clamping" operation.
/// The scalar is then guaranteed to be a multiple of the cofactor.
pub inline fn clamp(s: *[32]u8) void {
s[0] &= 248;
s[31] = (s[31] & 127) | 64;
}
/// Return a*b+c (mod L)
pub fn mulAdd(a: [32]u8, b: [32]u8, c: [32]u8) [32]u8 {
return ScalarExpanded.fromBytes(a).mulAdd(ScalarExpanded.fromBytes(b), ScalarExpanded.fromBytes(c)).toBytes();
}
test "scalar25519" {
const bytes: [32]u8 = .{ 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 255 };
var x = ScalarExpanded.fromBytes(bytes);
var y = x.toBytes();
try rejectNonCanonical(y);
var buf: [128]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{y}), "1E979B917937F3DE71D18077F961F6CEFF01030405060708010203040506070F");
const reduced = reduce(field_size);
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{reduced}), "0000000000000000000000000000000000000000000000000000000000000000");
}
test "non-canonical scalar25519" {
const too_targe: [32]u8 = .{ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 };
std.testing.expectError(error.NonCanonical, rejectNonCanonical(too_targe));
}
test "mulAdd overflow check" {
const a: [32]u8 = [_]u8{0xff} ** 32;
const b: [32]u8 = [_]u8{0xff} ** 32;
const c: [32]u8 = [_]u8{0xff} ** 32;
const x = mulAdd(a, b, c);
var buf: [128]u8 = undefined;
std.testing.expectEqualStrings(try std.fmt.bufPrint(&buf, "{X}", .{x}), "D14DF91389432C25AD60FF9791B9FD1D67BEF517D273ECCE3D9A307C1B419903");
}

146
lib/std/crypto/25519/x25519.zig Normal file
View File

@ -0,0 +1,146 @@
const std = @import("std");
const mem = std.mem;
const fmt = std.fmt;
/// X25519 DH function.
pub const X25519 = struct {
/// The underlying elliptic curve.
pub const Curve = @import("curve25519.zig").Curve25519;
/// Length (in bytes) of a secret key.
pub const secret_length = 32;
/// Length (in bytes) of the output of the DH function.
pub const minimum_key_length = 32;
/// Compute the public key for a given private key.
pub fn createPublicKey(public_key: []u8, private_key: []const u8) bool {
std.debug.assert(private_key.len >= minimum_key_length);
std.debug.assert(public_key.len >= minimum_key_length);
var s: [32]u8 = undefined;
mem.copy(u8, &s, private_key[0..32]);
if (Curve.basePoint.clampedMul(s)) |q| {
mem.copy(u8, public_key, q.toBytes()[0..]);
return true;
} else |_| {
return false;
}
}
/// Compute the scalar product of a public key and a secret scalar.
/// Note that the output should not be used as a shared secret without
/// hashing it first.
pub fn create(out: []u8, private_key: []const u8, public_key: []const u8) bool {
std.debug.assert(out.len >= secret_length);
std.debug.assert(private_key.len >= minimum_key_length);
std.debug.assert(public_key.len >= minimum_key_length);
var s: [32]u8 = undefined;
var b: [32]u8 = undefined;
mem.copy(u8, &s, private_key[0..32]);
mem.copy(u8, &b, public_key[0..32]);
if (Curve.fromBytes(b).clampedMul(s)) |q| {
mem.copy(u8, out, q.toBytes()[0..]);
return true;
} else |_| {
return false;
}
}
};
test "x25519 public key calculation from secret key" {
var sk: [32]u8 = undefined;
var pk_expected: [32]u8 = undefined;
var pk_calculated: [32]u8 = undefined;
try fmt.hexToBytes(sk[0..], "8052030376d47112be7f73ed7a019293dd12ad910b654455798b4667d73de166");
try fmt.hexToBytes(pk_expected[0..], "f1814f0e8ff1043d8a44d25babff3cedcae6c22c3edaa48f857ae70de2baae50");
std.testing.expect(X25519.createPublicKey(pk_calculated[0..], &sk));
std.testing.expectEqual(pk_calculated, pk_expected);
}
test "x25519 rfc7748 vector1" {
const secret_key = [32]u8{ 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d, 0x3b, 0x16, 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd, 0x62, 0x14, 0x4c, 0x0a, 0xc1, 0xfc, 0x5a, 0x18, 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44, 0x9a, 0xc4 };
const public_key = [32]u8{ 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb, 0x35, 0x94, 0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c, 0x72, 0x66, 0x24, 0xec, 0x26, 0xb3, 0x35, 0x3b, 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab, 0x1c, 0x4c };
const expected_output = [32]u8{ 0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90, 0x8e, 0x94, 0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f, 0x32, 0xec, 0xcf, 0x03, 0x49, 0x1c, 0x71, 0xf7, 0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2, 0x85, 0x52 };
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], secret_key[0..], public_key[0..]));
std.testing.expectEqual(output, expected_output);
}
test "x25519 rfc7748 vector2" {
const secret_key = [32]u8{ 0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c, 0x5a, 0xd2, 0x26, 0x91, 0x95, 0x7d, 0x6a, 0xf5, 0xc1, 0x1b, 0x64, 0x21, 0xe0, 0xea, 0x01, 0xd4, 0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18, 0xba, 0x0d };
const public_key = [32]u8{ 0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3, 0xf4, 0xb7, 0x95, 0x9d, 0x05, 0x38, 0xae, 0x2c, 0x31, 0xdb, 0xe7, 0x10, 0x6f, 0xc0, 0x3c, 0x3e, 0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15, 0xa4, 0x93 };
const expected_output = [32]u8{ 0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d, 0x7a, 0xad, 0xe4, 0x5c, 0xb4, 0xb8, 0x73, 0xf8, 0x8b, 0x59, 0x5a, 0x68, 0x79, 0x9f, 0xa1, 0x52, 0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac, 0x79, 0x57 };
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], secret_key[0..], public_key[0..]));
std.testing.expectEqual(output, expected_output);
}
test "x25519 rfc7748 one iteration" {
const initial_value = [32]u8{ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
const expected_output = [32]u8{ 0x42, 0x2c, 0x8e, 0x7a, 0x62, 0x27, 0xd7, 0xbc, 0xa1, 0x35, 0x0b, 0x3e, 0x2b, 0xb7, 0x27, 0x9f, 0x78, 0x97, 0xb8, 0x7b, 0xb6, 0x85, 0x4b, 0x78, 0x3c, 0x60, 0xe8, 0x03, 0x11, 0xae, 0x30, 0x79 };
var k: [32]u8 = initial_value;
var u: [32]u8 = initial_value;
var i: usize = 0;
while (i < 1) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
mem.copy(u8, u[0..], k[0..]);
mem.copy(u8, k[0..], output[0..]);
}
std.testing.expectEqual(k, expected_output);
}
test "x25519 rfc7748 1,000 iterations" {
// These iteration tests are slow so we always skip them. Results have been verified.
if (true) {
return error.SkipZigTest;
}
const initial_value = [32]u8{ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
const expected_output = [32]u8{ 0x68, 0x4c, 0xf5, 0x9b, 0xa8, 0x33, 0x09, 0x55, 0x28, 0x00, 0xef, 0x56, 0x6f, 0x2f, 0x4d, 0x3c, 0x1c, 0x38, 0x87, 0xc4, 0x93, 0x60, 0xe3, 0x87, 0x5f, 0x2e, 0xb9, 0x4d, 0x99, 0x53, 0x2c, 0x51 };
var k: [32]u8 = initial_value.*;
var u: [32]u8 = initial_value.*;
var i: usize = 0;
while (i < 1000) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
mem.copy(u8, u[0..], k[0..]);
mem.copy(u8, k[0..], output[0..]);
}
std.testing.expectEqual(k, expected_output);
}
test "x25519 rfc7748 1,000,000 iterations" {
if (true) {
return error.SkipZigTest;
}
const initial_value = [32]u8{ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
const expected_output = [32]u8{ 0x7c, 0x39, 0x11, 0xe0, 0xab, 0x25, 0x86, 0xfd, 0x86, 0x44, 0x97, 0x29, 0x7e, 0x57, 0x5e, 0x6f, 0x3b, 0xc6, 0x01, 0xc0, 0x88, 0x3c, 0x30, 0xdf, 0x5f, 0x4d, 0xd2, 0xd2, 0x4f, 0x66, 0x54, 0x24 };
var k: [32]u8 = initial_value.*;
var u: [32]u8 = initial_value.*;
var i: usize = 0;
while (i < 1000000) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
mem.copy(u8, u[0..], k[0..]);
mem.copy(u8, k[0..], output[0..]);
}
std.testing.expectEqual(k[0..], expected_output);
}

32
lib/std/crypto/benchmark.zig
View File

@ -90,7 +90,6 @@ pub fn benchmarkKeyExchange(comptime DhKeyExchange: anytype, comptime exchange_c
var out: [DhKeyExchange.minimum_key_length]u8 = undefined;
prng.random.bytes(out[0..]);
var offset: usize = 0;
var timer = try Timer.start();
const start = timer.lap();
{
@ -107,6 +106,30 @@ pub fn benchmarkKeyExchange(comptime DhKeyExchange: anytype, comptime exchange_c
return throughput;
}
const signatures = [_]Crypto{Crypto{ .ty = crypto.Ed25519, .name = "ed25519" }};
pub fn benchmarkSignatures(comptime Signature: anytype, comptime signatures_count: comptime_int) !u64 {
var seed: [Signature.seed_length]u8 = undefined;
prng.random.bytes(seed[0..]);
const msg = [_]u8{0} ** 64;
const key_pair = try Signature.createKeyPair(seed);
var timer = try Timer.start();
const start = timer.lap();
{
var i: usize = 0;
while (i < signatures_count) : (i += 1) {
_ = try Signature.sign(&msg, key_pair, null);
}
}
const end = timer.read();
const elapsed_s = @intToFloat(f64, end - start) / time.ns_per_s;
const throughput = @floatToInt(u64, signatures_count / elapsed_s);
return throughput;
}
fn usage() void {
std.debug.warn(
\\throughput_test [options]
@ -183,4 +206,11 @@ pub fn main() !void {
try stdout.print("{:>11}: {:5} exchanges/s\n", .{ E.name, throughput });
}
}
inline for (signatures) |E| {
if (filter == null or std.mem.indexOf(u8, E.name, filter.?) != null) {
const throughput = try benchmarkSignatures(E.ty, mode(1000));
try stdout.print("{:>11}: {:5} signatures/s\n", .{ E.name, throughput });
}
}
}

675
lib/std/crypto/x25519.zig
View File

@ -1,675 +0,0 @@
// Translated from monocypher which is licensed under CC-0/BSD-3.
//
// https://monocypher.org/
const std = @import("../std.zig");
const builtin = @import("builtin");
const fmt = std.fmt;
const Endian = builtin.Endian;
const readIntLittle = std.mem.readIntLittle;
const writeIntLittle = std.mem.writeIntLittle;
// Based on Supercop's ref10 implementation.
pub const X25519 = struct {
pub const secret_length = 32;
pub const minimum_key_length = 32;
fn trimScalar(s: []u8) void {
s[0] &= 248;
s[31] &= 127;
s[31] |= 64;
}
fn scalarBit(s: []const u8, i: usize) i32 {
return (s[i >> 3] >> @intCast(u3, i & 7)) & 1;
}
pub fn create(out: []u8, private_key: []const u8, public_key: []const u8) bool {
std.debug.assert(out.len >= secret_length);
std.debug.assert(private_key.len >= minimum_key_length);
std.debug.assert(public_key.len >= minimum_key_length);
var storage: [7]Fe = undefined;
var x1 = &storage[0];
var x2 = &storage[1];
var z2 = &storage[2];
var x3 = &storage[3];
var z3 = &storage[4];
var t0 = &storage[5];
var t1 = &storage[6];
// computes the scalar product
Fe.fromBytes(x1, public_key);
// restrict the possible scalar values
var e: [32]u8 = undefined;
for (e[0..]) |_, i| {
e[i] = private_key[i];
}
trimScalar(e[0..]);
// computes the actual scalar product (the result is in x2 and z2)
// Montgomery ladder
// In projective coordinates, to avoid divisions: x = X / Z
// We don't care about the y coordinate, it's only 1 bit of information
Fe.init1(x2);
Fe.init0(z2); // "zero" point
Fe.copy(x3, x1);
Fe.init1(z3);
var swap: i32 = 0;
var pos: isize = 254;
while (pos >= 0) : (pos -= 1) {
// constant time conditional swap before ladder step
const b = scalarBit(&e, @intCast(usize, pos));
swap ^= b; // xor trick avoids swapping at the end of the loop
Fe.cswap(x2, x3, swap);
Fe.cswap(z2, z3, swap);
swap = b; // anticipates one last swap after the loop
// Montgomery ladder step: replaces (P2, P3) by (P2*2, P2+P3)
// with differential addition
Fe.sub(t0, x3, z3);
Fe.sub(t1, x2, z2);
Fe.add(x2, x2, z2);
Fe.add(z2, x3, z3);
Fe.mul(z3, t0, x2);
Fe.mul(z2, z2, t1);
Fe.sq(t0, t1);
Fe.sq(t1, x2);
Fe.add(x3, z3, z2);
Fe.sub(z2, z3, z2);
Fe.mul(x2, t1, t0);
Fe.sub(t1, t1, t0);
Fe.sq(z2, z2);
Fe.mulSmall(z3, t1, 121666);
Fe.sq(x3, x3);
Fe.add(t0, t0, z3);
Fe.mul(z3, x1, z2);
Fe.mul(z2, t1, t0);
}
// last swap is necessary to compensate for the xor trick
// Note: after this swap, P3 == P2 + P1.
Fe.cswap(x2, x3, swap);
Fe.cswap(z2, z3, swap);
// normalises the coordinates: x == X / Z
Fe.invert(z2, z2);
Fe.mul(x2, x2, z2);
Fe.toBytes(out, x2);
x1.secureZero();
x2.secureZero();
x3.secureZero();
t0.secureZero();
t1.secureZero();
z2.secureZero();
z3.secureZero();
std.mem.secureZero(u8, e[0..]);
// Returns false if the output is all zero
// (happens with some malicious public keys)
return !zerocmp(u8, out);
}
pub fn createPublicKey(public_key: []u8, private_key: []const u8) bool {
var base_point = [_]u8{9} ++ [_]u8{0} ** 31;
return create(public_key, private_key, &base_point);
}
};
// Constant time compare to zero.
fn zerocmp(comptime T: type, a: []const T) bool {
var s: T = 0;
for (a) |b| {
s |= b;
}
return s == 0;
}
////////////////////////////////////
/// Arithmetic modulo 2^255 - 19 ///
////////////////////////////////////
// Taken from Supercop's ref10 implementation.
// A bit bigger than TweetNaCl, over 4 times faster.
// field element
const Fe = struct {
b: [10]i32,
fn secureZero(self: *Fe) void {
std.mem.secureZero(u8, @ptrCast([*]u8, self)[0..@sizeOf(Fe)]);
}
fn init0(h: *Fe) void {
for (h.b) |*e| {
e.* = 0;
}
}
fn init1(h: *Fe) void {
for (h.b[1..]) |*e| {
e.* = 0;
}
h.b[0] = 1;
}
fn copy(h: *Fe, f: *const Fe) void {
for (h.b) |_, i| {
h.b[i] = f.b[i];
}
}
fn neg(h: *Fe, f: *const Fe) void {
for (h.b) |_, i| {
h.b[i] = -f.b[i];
}
}
fn add(h: *Fe, f: *const Fe, g: *const Fe) void {
for (h.b) |_, i| {
h.b[i] = f.b[i] + g.b[i];
}
}
fn sub(h: *Fe, f: *const Fe, g: *const Fe) void {
for (h.b) |_, i| {
h.b[i] = f.b[i] - g.b[i];
}
}
fn cswap(f: *Fe, g: *Fe, b: i32) void {
for (f.b) |_, i| {
const x = (f.b[i] ^ g.b[i]) & -b;
f.b[i] ^= x;
g.b[i] ^= x;
}
}
fn ccopy(f: *Fe, g: *const Fe, b: i32) void {
for (f.b) |_, i| {
const x = (f.b[i] ^ g.b[i]) & -b;
f.b[i] ^= x;
}
}
inline fn carryRound(c: []i64, t: []i64, comptime i: comptime_int, comptime shift: comptime_int, comptime mult: comptime_int) void {
const j = (i + 1) % 10;
c[i] = (t[i] + (@as(i64, 1) << shift)) >> (shift + 1);
t[j] += c[i] * mult;
t[i] -= c[i] * (@as(i64, 1) << (shift + 1));
}
fn carry1(h: *Fe, t: []i64) void {
var c: [10]i64 = undefined;
var sc = c[0..];
var st = t[0..];
carryRound(sc, st, 9, 24, 19);
carryRound(sc, st, 1, 24, 1);
carryRound(sc, st, 3, 24, 1);
carryRound(sc, st, 5, 24, 1);
carryRound(sc, st, 7, 24, 1);
carryRound(sc, st, 0, 25, 1);
carryRound(sc, st, 2, 25, 1);
carryRound(sc, st, 4, 25, 1);
carryRound(sc, st, 6, 25, 1);
carryRound(sc, st, 8, 25, 1);
for (h.b) |_, i| {
h.b[i] = @intCast(i32, t[i]);
}
}
fn carry2(h: *Fe, t: []i64) void {
var c: [10]i64 = undefined;
var sc = c[0..];
var st = t[0..];
carryRound(sc, st, 0, 25, 1);
carryRound(sc, st, 4, 25, 1);
carryRound(sc, st, 1, 24, 1);
carryRound(sc, st, 5, 24, 1);
carryRound(sc, st, 2, 25, 1);
carryRound(sc, st, 6, 25, 1);
carryRound(sc, st, 3, 24, 1);
carryRound(sc, st, 7, 24, 1);
carryRound(sc, st, 4, 25, 1);
carryRound(sc, st, 8, 25, 1);
carryRound(sc, st, 9, 24, 19);
carryRound(sc, st, 0, 25, 1);
for (h.b) |_, i| {
h.b[i] = @intCast(i32, t[i]);
}
}
fn fromBytes(h: *Fe, s: []const u8) void {
std.debug.assert(s.len >= 32);
var t: [10]i64 = undefined;
t[0] = readIntLittle(u32, s[0..4]);
t[1] = @as(u32, readIntLittle(u24, s[4..7])) << 6;
t[2] = @as(u32, readIntLittle(u24, s[7..10])) << 5;
t[3] = @as(u32, readIntLittle(u24, s[10..13])) << 3;
t[4] = @as(u32, readIntLittle(u24, s[13..16])) << 2;
t[5] = readIntLittle(u32, s[16..20]);
t[6] = @as(u32, readIntLittle(u24, s[20..23])) << 7;
t[7] = @as(u32, readIntLittle(u24, s[23..26])) << 5;
t[8] = @as(u32, readIntLittle(u24, s[26..29])) << 4;
t[9] = (@as(u32, readIntLittle(u24, s[29..32])) & 0x7fffff) << 2;
carry1(h, t[0..]);
}
fn mulSmall(h: *Fe, f: *const Fe, comptime g: comptime_int) void {
var t: [10]i64 = undefined;
for (t[0..]) |_, i| {
t[i] = @as(i64, f.b[i]) * g;
}
carry1(h, t[0..]);
}
fn mul(h: *Fe, f1: *const Fe, g1: *const Fe) void {
const f = f1.b;
const g = g1.b;
var F: [10]i32 = undefined;
var G: [10]i32 = undefined;
F[1] = f[1] * 2;
F[3] = f[3] * 2;
F[5] = f[5] * 2;
F[7] = f[7] * 2;
F[9] = f[9] * 2;
G[1] = g[1] * 19;
G[2] = g[2] * 19;
G[3] = g[3] * 19;
G[4] = g[4] * 19;
G[5] = g[5] * 19;
G[6] = g[6] * 19;
G[7] = g[7] * 19;
G[8] = g[8] * 19;
G[9] = g[9] * 19;
// t's become h
var t: [10]i64 = undefined;
t[0] = f[0] * @as(i64, g[0]) + F[1] * @as(i64, G[9]) + f[2] * @as(i64, G[8]) + F[3] * @as(i64, G[7]) + f[4] * @as(i64, G[6]) + F[5] * @as(i64, G[5]) + f[6] * @as(i64, G[4]) + F[7] * @as(i64, G[3]) + f[8] * @as(i64, G[2]) + F[9] * @as(i64, G[1]);
t[1] = f[0] * @as(i64, g[1]) + f[1] * @as(i64, g[0]) + f[2] * @as(i64, G[9]) + f[3] * @as(i64, G[8]) + f[4] * @as(i64, G[7]) + f[5] * @as(i64, G[6]) + f[6] * @as(i64, G[5]) + f[7] * @as(i64, G[4]) + f[8] * @as(i64, G[3]) + f[9] * @as(i64, G[2]);
t[2] = f[0] * @as(i64, g[2]) + F[1] * @as(i64, g[1]) + f[2] * @as(i64, g[0]) + F[3] * @as(i64, G[9]) + f[4] * @as(i64, G[8]) + F[5] * @as(i64, G[7]) + f[6] * @as(i64, G[6]) + F[7] * @as(i64, G[5]) + f[8] * @as(i64, G[4]) + F[9] * @as(i64, G[3]);
t[3] = f[0] * @as(i64, g[3]) + f[1] * @as(i64, g[2]) + f[2] * @as(i64, g[1]) + f[3] * @as(i64, g[0]) + f[4] * @as(i64, G[9]) + f[5] * @as(i64, G[8]) + f[6] * @as(i64, G[7]) + f[7] * @as(i64, G[6]) + f[8] * @as(i64, G[5]) + f[9] * @as(i64, G[4]);
t[4] = f[0] * @as(i64, g[4]) + F[1] * @as(i64, g[3]) + f[2] * @as(i64, g[2]) + F[3] * @as(i64, g[1]) + f[4] * @as(i64, g[0]) + F[5] * @as(i64, G[9]) + f[6] * @as(i64, G[8]) + F[7] * @as(i64, G[7]) + f[8] * @as(i64, G[6]) + F[9] * @as(i64, G[5]);
t[5] = f[0] * @as(i64, g[5]) + f[1] * @as(i64, g[4]) + f[2] * @as(i64, g[3]) + f[3] * @as(i64, g[2]) + f[4] * @as(i64, g[1]) + f[5] * @as(i64, g[0]) + f[6] * @as(i64, G[9]) + f[7] * @as(i64, G[8]) + f[8] * @as(i64, G[7]) + f[9] * @as(i64, G[6]);
t[6] = f[0] * @as(i64, g[6]) + F[1] * @as(i64, g[5]) + f[2] * @as(i64, g[4]) + F[3] * @as(i64, g[3]) + f[4] * @as(i64, g[2]) + F[5] * @as(i64, g[1]) + f[6] * @as(i64, g[0]) + F[7] * @as(i64, G[9]) + f[8] * @as(i64, G[8]) + F[9] * @as(i64, G[7]);
t[7] = f[0] * @as(i64, g[7]) + f[1] * @as(i64, g[6]) + f[2] * @as(i64, g[5]) + f[3] * @as(i64, g[4]) + f[4] * @as(i64, g[3]) + f[5] * @as(i64, g[2]) + f[6] * @as(i64, g[1]) + f[7] * @as(i64, g[0]) + f[8] * @as(i64, G[9]) + f[9] * @as(i64, G[8]);
t[8] = f[0] * @as(i64, g[8]) + F[1] * @as(i64, g[7]) + f[2] * @as(i64, g[6]) + F[3] * @as(i64, g[5]) + f[4] * @as(i64, g[4]) + F[5] * @as(i64, g[3]) + f[6] * @as(i64, g[2]) + F[7] * @as(i64, g[1]) + f[8] * @as(i64, g[0]) + F[9] * @as(i64, G[9]);
t[9] = f[0] * @as(i64, g[9]) + f[1] * @as(i64, g[8]) + f[2] * @as(i64, g[7]) + f[3] * @as(i64, g[6]) + f[4] * @as(i64, g[5]) + f[5] * @as(i64, g[4]) + f[6] * @as(i64, g[3]) + f[7] * @as(i64, g[2]) + f[8] * @as(i64, g[1]) + f[9] * @as(i64, g[0]);
carry2(h, t[0..]);
}
// we could use Fe.mul() for this, but this is significantly faster
fn sq(h: *Fe, fz: *const Fe) void {
const f0 = fz.b[0];
const f1 = fz.b[1];
const f2 = fz.b[2];
const f3 = fz.b[3];
const f4 = fz.b[4];
const f5 = fz.b[5];
const f6 = fz.b[6];
const f7 = fz.b[7];
const f8 = fz.b[8];
const f9 = fz.b[9];
const f0_2 = f0 * 2;
const f1_2 = f1 * 2;
const f2_2 = f2 * 2;
const f3_2 = f3 * 2;
const f4_2 = f4 * 2;
const f5_2 = f5 * 2;
const f6_2 = f6 * 2;
const f7_2 = f7 * 2;
const f5_38 = f5 * 38;
const f6_19 = f6 * 19;
const f7_38 = f7 * 38;
const f8_19 = f8 * 19;
const f9_38 = f9 * 38;
var t: [10]i64 = undefined;
t[0] = f0 * @as(i64, f0) + f1_2 * @as(i64, f9_38) + f2_2 * @as(i64, f8_19) + f3_2 * @as(i64, f7_38) + f4_2 * @as(i64, f6_19) + f5 * @as(i64, f5_38);
t[1] = f0_2 * @as(i64, f1) + f2 * @as(i64, f9_38) + f3_2 * @as(i64, f8_19) + f4 * @as(i64, f7_38) + f5_2 * @as(i64, f6_19);
t[2] = f0_2 * @as(i64, f2) + f1_2 * @as(i64, f1) + f3_2 * @as(i64, f9_38) + f4_2 * @as(i64, f8_19) + f5_2 * @as(i64, f7_38) + f6 * @as(i64, f6_19);
t[3] = f0_2 * @as(i64, f3) + f1_2 * @as(i64, f2) + f4 * @as(i64, f9_38) + f5_2 * @as(i64, f8_19) + f6 * @as(i64, f7_38);
t[4] = f0_2 * @as(i64, f4) + f1_2 * @as(i64, f3_2) + f2 * @as(i64, f2) + f5_2 * @as(i64, f9_38) + f6_2 * @as(i64, f8_19) + f7 * @as(i64, f7_38);
t[5] = f0_2 * @as(i64, f5) + f1_2 * @as(i64, f4) + f2_2 * @as(i64, f3) + f6 * @as(i64, f9_38) + f7_2 * @as(i64, f8_19);
t[6] = f0_2 * @as(i64, f6) + f1_2 * @as(i64, f5_2) + f2_2 * @as(i64, f4) + f3_2 * @as(i64, f3) + f7_2 * @as(i64, f9_38) + f8 * @as(i64, f8_19);
t[7] = f0_2 * @as(i64, f7) + f1_2 * @as(i64, f6) + f2_2 * @as(i64, f5) + f3_2 * @as(i64, f4) + f8 * @as(i64, f9_38);
t[8] = f0_2 * @as(i64, f8) + f1_2 * @as(i64, f7_2) + f2_2 * @as(i64, f6) + f3_2 * @as(i64, f5_2) + f4 * @as(i64, f4) + f9 * @as(i64, f9_38);
t[9] = f0_2 * @as(i64, f9) + f1_2 * @as(i64, f8) + f2_2 * @as(i64, f7) + f3_2 * @as(i64, f6) + f4 * @as(i64, f5_2);
carry2(h, t[0..]);
}
fn sq2(h: *Fe, f: *const Fe) void {
Fe.sq(h, f);
Fe.mul_small(h, h, 2);
}
// This could be simplified, but it would be slower
fn invert(out: *Fe, z: *const Fe) void {
var i: usize = undefined;
var t: [4]Fe = undefined;
var t0 = &t[0];
var t1 = &t[1];
var t2 = &t[2];
var t3 = &t[3];
Fe.sq(t0, z);
Fe.sq(t1, t0);
Fe.sq(t1, t1);
Fe.mul(t1, z, t1);
Fe.mul(t0, t0, t1);
Fe.sq(t2, t0);
Fe.mul(t1, t1, t2);
Fe.sq(t2, t1);
i = 1;
while (i < 5) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t1, t2, t1);
Fe.sq(t2, t1);
i = 1;
while (i < 10) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t2, t2, t1);
Fe.sq(t3, t2);
i = 1;
while (i < 20) : (i += 1) Fe.sq(t3, t3);
Fe.mul(t2, t3, t2);
Fe.sq(t2, t2);
i = 1;
while (i < 10) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t1, t2, t1);
Fe.sq(t2, t1);
i = 1;
while (i < 50) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t2, t2, t1);
Fe.sq(t3, t2);
i = 1;
while (i < 100) : (i += 1) Fe.sq(t3, t3);
Fe.mul(t2, t3, t2);
Fe.sq(t2, t2);
i = 1;
while (i < 50) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t1, t2, t1);
Fe.sq(t1, t1);
i = 1;
while (i < 5) : (i += 1) Fe.sq(t1, t1);
Fe.mul(out, t1, t0);
t0.secureZero();
t1.secureZero();
t2.secureZero();
t3.secureZero();
}
// This could be simplified, but it would be slower
fn pow22523(out: *Fe, z: *const Fe) void {
var i: usize = undefined;
var t: [3]Fe = undefined;
var t0 = &t[0];
var t1 = &t[1];
var t2 = &t[2];
Fe.sq(t0, z);
Fe.sq(t1, t0);
Fe.sq(t1, t1);
Fe.mul(t1, z, t1);
Fe.mul(t0, t0, t1);
Fe.sq(t0, t0);
Fe.mul(t0, t1, t0);
Fe.sq(t1, t0);
i = 1;
while (i < 5) : (i += 1) Fe.sq(t1, t1);
Fe.mul(t0, t1, t0);
Fe.sq(t1, t0);
i = 1;
while (i < 10) : (i += 1) Fe.sq(t1, t1);
Fe.mul(t1, t1, t0);
Fe.sq(t2, t1);
i = 1;
while (i < 20) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t1, t2, t1);
Fe.sq(t1, t1);
i = 1;
while (i < 10) : (i += 1) Fe.sq(t1, t1);
Fe.mul(t0, t1, t0);
Fe.sq(t1, t0);
i = 1;
while (i < 50) : (i += 1) Fe.sq(t1, t1);
Fe.mul(t1, t1, t0);
Fe.sq(t2, t1);
i = 1;
while (i < 100) : (i += 1) Fe.sq(t2, t2);
Fe.mul(t1, t2, t1);
Fe.sq(t1, t1);
i = 1;
while (i < 50) : (i += 1) Fe.sq(t1, t1);
Fe.mul(t0, t1, t0);
Fe.sq(t0, t0);
i = 1;
while (i < 2) : (i += 1) Fe.sq(t0, t0);
Fe.mul(out, t0, z);
t0.secureZero();
t1.secureZero();
t2.secureZero();
}
inline fn toBytesRound(c: []i64, t: []i64, comptime i: comptime_int, comptime shift: comptime_int) void {
c[i] = t[i] >> shift;
if (i + 1 < 10) {
t[i + 1] += c[i];
}
t[i] -= c[i] * (@as(i32, 1) << shift);
}
fn toBytes(s: []u8, h: *const Fe) void {
std.debug.assert(s.len >= 32);
var t: [10]i64 = undefined;
for (h.b[0..]) |_, i| {
t[i] = h.b[i];
}
var q = (19 * t[9] + ((@as(i32, 1) << 24))) >> 25;
{
var i: usize = 0;
while (i < 5) : (i += 1) {
q += t[2 * i];
q >>= 26;
q += t[2 * i + 1];
q >>= 25;
}
}
t[0] += 19 * q;
var c: [10]i64 = undefined;
var st = t[0..];
var sc = c[0..];
toBytesRound(sc, st, 0, 26);
toBytesRound(sc, st, 1, 25);
toBytesRound(sc, st, 2, 26);
toBytesRound(sc, st, 3, 25);
toBytesRound(sc, st, 4, 26);
toBytesRound(sc, st, 5, 25);
toBytesRound(sc, st, 6, 26);
toBytesRound(sc, st, 7, 25);
toBytesRound(sc, st, 8, 26);
toBytesRound(sc, st, 9, 25);
var ut: [10]u32 = undefined;
for (ut[0..]) |_, i| {
ut[i] = @bitCast(u32, @intCast(i32, t[i]));
}
writeIntLittle(u32, s[0..4], (ut[0] >> 0) | (ut[1] << 26));
writeIntLittle(u32, s[4..8], (ut[1] >> 6) | (ut[2] << 19));
writeIntLittle(u32, s[8..12], (ut[2] >> 13) | (ut[3] << 13));
writeIntLittle(u32, s[12..16], (ut[3] >> 19) | (ut[4] << 6));
writeIntLittle(u32, s[16..20], (ut[5] >> 0) | (ut[6] << 25));
writeIntLittle(u32, s[20..24], (ut[6] >> 7) | (ut[7] << 19));
writeIntLittle(u32, s[24..28], (ut[7] >> 13) | (ut[8] << 12));
writeIntLittle(u32, s[28..32], (ut[8] >> 20) | (ut[9] << 6));
std.mem.secureZero(i64, t[0..]);
}
// Parity check. Returns 0 if even, 1 if odd
fn isNegative(f: *const Fe) bool {
var s: [32]u8 = undefined;
Fe.toBytes(s[0..], f);
const isneg = s[0] & 1;
s.secureZero();
return isneg;
}
fn isNonZero(f: *const Fe) bool {
var s: [32]u8 = undefined;
Fe.toBytes(s[0..], f);
const isnonzero = zerocmp(u8, s[0..]);
s.secureZero();
return isneg;
}
};
test "x25519 public key calculation from secret key" {
var sk: [32]u8 = undefined;
var pk_expected: [32]u8 = undefined;
var pk_calculated: [32]u8 = undefined;
try fmt.hexToBytes(sk[0..], "8052030376d47112be7f73ed7a019293dd12ad910b654455798b4667d73de166");
try fmt.hexToBytes(pk_expected[0..], "f1814f0e8ff1043d8a44d25babff3cedcae6c22c3edaa48f857ae70de2baae50");
std.testing.expect(X25519.createPublicKey(pk_calculated[0..], &sk));
std.testing.expect(std.mem.eql(u8, &pk_calculated, &pk_expected));
}
test "x25519 rfc7748 vector1" {
const secret_key = "\xa5\x46\xe3\x6b\xf0\x52\x7c\x9d\x3b\x16\x15\x4b\x82\x46\x5e\xdd\x62\x14\x4c\x0a\xc1\xfc\x5a\x18\x50\x6a\x22\x44\xba\x44\x9a\xc4";
const public_key = "\xe6\xdb\x68\x67\x58\x30\x30\xdb\x35\x94\xc1\xa4\x24\xb1\x5f\x7c\x72\x66\x24\xec\x26\xb3\x35\x3b\x10\xa9\x03\xa6\xd0\xab\x1c\x4c";
const expected_output = "\xc3\xda\x55\x37\x9d\xe9\xc6\x90\x8e\x94\xea\x4d\xf2\x8d\x08\x4f\x32\xec\xcf\x03\x49\x1c\x71\xf7\x54\xb4\x07\x55\x77\xa2\x85\x52";
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], secret_key, public_key));
std.testing.expect(std.mem.eql(u8, &output, expected_output));
}
test "x25519 rfc7748 vector2" {
const secret_key = "\x4b\x66\xe9\xd4\xd1\xb4\x67\x3c\x5a\xd2\x26\x91\x95\x7d\x6a\xf5\xc1\x1b\x64\x21\xe0\xea\x01\xd4\x2c\xa4\x16\x9e\x79\x18\xba\x0d";
const public_key = "\xe5\x21\x0f\x12\x78\x68\x11\xd3\xf4\xb7\x95\x9d\x05\x38\xae\x2c\x31\xdb\xe7\x10\x6f\xc0\x3c\x3e\xfc\x4c\xd5\x49\xc7\x15\xa4\x93";
const expected_output = "\x95\xcb\xde\x94\x76\xe8\x90\x7d\x7a\xad\xe4\x5c\xb4\xb8\x73\xf8\x8b\x59\x5a\x68\x79\x9f\xa1\x52\xe6\xf8\xf7\x64\x7a\xac\x79\x57";
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], secret_key, public_key));
std.testing.expect(std.mem.eql(u8, &output, expected_output));
}
test "x25519 rfc7748 one iteration" {
const initial_value = "\x09\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00".*;
const expected_output = "\x42\x2c\x8e\x7a\x62\x27\xd7\xbc\xa1\x35\x0b\x3e\x2b\xb7\x27\x9f\x78\x97\xb8\x7b\xb6\x85\x4b\x78\x3c\x60\xe8\x03\x11\xae\x30\x79";
var k: [32]u8 = initial_value;
var u: [32]u8 = initial_value;
var i: usize = 0;
while (i < 1) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
std.mem.copy(u8, u[0..], k[0..]);
std.mem.copy(u8, k[0..], output[0..]);
}
std.testing.expect(std.mem.eql(u8, k[0..], expected_output));
}
test "x25519 rfc7748 1,000 iterations" {
// These iteration tests are slow so we always skip them. Results have been verified.
if (true) {
return error.SkipZigTest;
}
const initial_value = "\x09\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00";
const expected_output = "\x68\x4c\xf5\x9b\xa8\x33\x09\x55\x28\x00\xef\x56\x6f\x2f\x4d\x3c\x1c\x38\x87\xc4\x93\x60\xe3\x87\x5f\x2e\xb9\x4d\x99\x53\x2c\x51";
var k: [32]u8 = initial_value.*;
var u: [32]u8 = initial_value.*;
var i: usize = 0;
while (i < 1000) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
std.mem.copy(u8, u[0..], k[0..]);
std.mem.copy(u8, k[0..], output[0..]);
}
std.testing.expect(std.mem.eql(u8, k[0..], expected_output));
}
test "x25519 rfc7748 1,000,000 iterations" {
if (true) {
return error.SkipZigTest;
}
const initial_value = "\x09\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00";
const expected_output = "\x7c\x39\x11\xe0\xab\x25\x86\xfd\x86\x44\x97\x29\x7e\x57\x5e\x6f\x3b\xc6\x01\xc0\x88\x3c\x30\xdf\x5f\x4d\xd2\xd2\x4f\x66\x54\x24";
var k: [32]u8 = initial_value.*;
var u: [32]u8 = initial_value.*;
var i: usize = 0;
while (i < 1000000) : (i += 1) {
var output: [32]u8 = undefined;
std.testing.expect(X25519.create(output[0..], &k, &u));
std.mem.copy(u8, u[0..], k[0..]);
std.mem.copy(u8, k[0..], output[0..]);
}
std.testing.expect(std.mem.eql(u8, k[0..], expected_output));
}