diff --git a/lib/std/crypto/25519/ed25519.zig b/lib/std/crypto/25519/ed25519.zig index 784ba62de0..6874d5a394 100644 --- a/lib/std/crypto/25519/ed25519.zig +++ b/lib/std/crypto/25519/ed25519.zig @@ -97,6 +97,7 @@ pub const Ed25519 = struct { try Curve.rejectNonCanonical(public_key); const a = try Curve.fromBytes(public_key); try a.rejectIdentity(); + try Curve.rejectNonCanonical(r.*); const expected_r = try Curve.fromBytes(r.*); var h = Sha512.init(.{}); @@ -113,6 +114,78 @@ pub const Ed25519 = struct { return error.InvalidSignature; } else |_| {} } + + /// A (signature, message, public_key) tuple for batch verification + pub const BatchElement = struct { + sig: [signature_length]u8, + msg: []const u8, + public_key: [public_length]u8, + }; + + /// Verify several signatures in a single operation, much faster than verifying signatures one-by-one + pub fn verifyBatch(comptime count: usize, signature_batch: [count]BatchElement) !void { + var r_batch: [count][32]u8 = undefined; + var s_batch: [count][32]u8 = undefined; + var a_batch: [count]Curve = undefined; + var expected_r_batch: [count]Curve = undefined; + + for (signature_batch) |signature, i| { + const r = signature.sig[0..32]; + const s = signature.sig[32..64]; + try Curve.scalar.rejectNonCanonical(s.*); + try Curve.rejectNonCanonical(signature.public_key); + const a = try Curve.fromBytes(signature.public_key); + try a.rejectIdentity(); + try Curve.rejectNonCanonical(r.*); + const expected_r = try Curve.fromBytes(r.*); + expected_r_batch[i] = expected_r; + r_batch[i] = r.*; + s_batch[i] = s.*; + a_batch[i] = a; + } + + var hram_batch: [count]Curve.scalar.Scalar = undefined; + for (signature_batch) |signature, i| { + var h = Sha512.init(.{}); + h.update(&r_batch[i]); + h.update(&signature.public_key); + h.update(signature.msg); + var hram64: [Sha512.digest_length]u8 = undefined; + h.final(&hram64); + hram_batch[i] = Curve.scalar.reduce64(hram64); + } + + var z_batch: [count]Curve.scalar.Scalar = undefined; + for (z_batch) |*z| { + try std.crypto.randomBytes(z[0..16]); + mem.set(u8, z[16..], 0); + } + + var zs_sum = Curve.scalar.zero; + for (z_batch) |z, i| { + const zs = Curve.scalar.mul(z, s_batch[i]); + zs_sum = Curve.scalar.add(zs_sum, zs); + } + zs_sum = Curve.scalar.mul8(zs_sum); + + var zr = Curve.neutralElement; + for (z_batch) |z, i| { + zr = zr.add(try expected_r_batch[i].mul(z)); + } + zr = zr.clearCofactor(); + + var zah = Curve.neutralElement; + for (z_batch) |z, i| { + const zh = Curve.scalar.mul(z, hram_batch[i]); + zah = zah.add(try a_batch[i].mul(zh)); + } + zah = zah.clearCofactor(); + + const zsb = try Curve.basePoint.mul(zs_sum); + if (zr.add(zah).sub(zsb).rejectIdentity()) |_| { + return error.InvalidSignature; + } else |_| {} + } }; test "ed25519 key pair creation" { @@ -138,3 +211,132 @@ test "ed25519 signature" { try Ed25519.verify(sig, "test", public_key); std.testing.expectError(error.InvalidSignature, Ed25519.verify(sig, "TEST", public_key)); } + +test "ed25519 batch verification" { + var i: usize = 0; + while (i < 100) : (i += 1) { + var seed: [32]u8 = undefined; + try std.crypto.randomBytes(&seed); + const key_pair = try Ed25519.createKeyPair(seed); + var msg1: [32]u8 = undefined; + var msg2: [32]u8 = undefined; + try std.crypto.randomBytes(&msg1); + try std.crypto.randomBytes(&msg2); + const sig1 = try Ed25519.sign(&msg1, key_pair, null); + const sig2 = try Ed25519.sign(&msg2, key_pair, null); + const public_key = Ed25519.publicKey(key_pair); + var signature_batch = [_]Ed25519.BatchElement{ + Ed25519.BatchElement{ + .sig = sig1, + .msg = &msg1, + .public_key = public_key, + }, + Ed25519.BatchElement{ + .sig = sig2, + .msg = &msg2, + .public_key = public_key, + }, + }; + try Ed25519.verifyBatch(2, signature_batch); + + signature_batch[1].sig = sig1; + std.testing.expectError(error.InvalidSignature, Ed25519.verifyBatch(signature_batch.len, signature_batch)); + } +} + +test "ed25519 test vectors" { + const Vec = struct { + msg_hex: *const [64:0]u8, + public_key_hex: *const [64:0]u8, + sig_hex: *const [128:0]u8, + expected: ?anyerror, + }; + + const entries = [_]Vec{ + Vec{ + .msg_hex = "8c93255d71dcab10e8f379c26200f3c7bd5f09d9bc3068d3ef4edeb4853022b6", + .public_key_hex = "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa", + .sig_hex = "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a0000000000000000000000000000000000000000000000000000000000000000", + .expected = error.WeakPublicKey, // 0 + }, + Vec{ + .msg_hex = "9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79", + .public_key_hex = "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa", + .sig_hex = "f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43a5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04", + .expected = error.WeakPublicKey, // 1 + }, + Vec{ + .msg_hex = "aebf3f2601a0c8c5d39cc7d8911642f740b78168218da8471772b35f9d35b9ab", + .public_key_hex = "f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43", + .sig_hex = "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa8c4bd45aecaca5b24fb97bc10ac27ac8751a7dfe1baff8b953ec9f5833ca260e", + .expected = null, // 2 - small order R is acceptable + }, + Vec{ + .msg_hex = "9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79", + .public_key_hex = "cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d", + .sig_hex = "9046a64750444938de19f227bb80485e92b83fdb4b6506c160484c016cc1852f87909e14428a7a1d62e9f22f3d3ad7802db02eb2e688b6c52fcd6648a98bd009", + .expected = null, // 3 - mixed orders + }, + Vec{ + .msg_hex = "e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c", + .public_key_hex = "cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d", + .sig_hex = "160a1cb0dc9c0258cd0a7d23e94d8fa878bcb1925f2c64246b2dee1796bed5125ec6bc982a269b723e0668e540911a9a6a58921d6925e434ab10aa7940551a09", + .expected = null, // 4 - cofactored verification + }, + Vec{ + .msg_hex = "e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c", + .public_key_hex = "cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d", + .sig_hex = "21122a84e0b5fca4052f5b1235c80a537878b38f3142356b2c2384ebad4668b7e40bc836dac0f71076f9abe3a53f9c03c1ceeeddb658d0030494ace586687405", + .expected = null, // 5 - cofactored verification + }, + Vec{ + .msg_hex = "85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40", + .public_key_hex = "442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623", + .sig_hex = "e96f66be976d82e60150baecff9906684aebb1ef181f67a7189ac78ea23b6c0e547f7690a0e2ddcd04d87dbc3490dc19b3b3052f7ff0538cb68afb369ba3a514", + .expected = error.NonCanonical, // 6 - S > L + }, + Vec{ + .msg_hex = "85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40", + .public_key_hex = "442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623", + .sig_hex = "8ce5b96c8f26d0ab6c47958c9e68b937104cd36e13c33566acd2fe8d38aa19427e71f98a4734e74f2f13f06f97c20d58cc3f54b8bd0d272f42b695dd7e89a8c2", + .expected = error.NonCanonical, // 7 - S >> L + }, + Vec{ + .msg_hex = "9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41", + .public_key_hex = "f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43", + .sig_hex = "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff03be9678ac102edcd92b0210bb34d7428d12ffc5df5f37e359941266a4e35f0f", + .expected = error.InvalidSignature, // 8 - non-canonical R + }, + Vec{ + .msg_hex = "9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41", + .public_key_hex = "f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43", + .sig_hex = "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffca8c5b64cd208982aa38d4936621a4775aa233aa0505711d8fdcfdaa943d4908", + .expected = null, // 9 - non-canonical R + }, + Vec{ + .msg_hex = "e96b7021eb39c1a163b6da4e3093dcd3f21387da4cc4572be588fafae23c155b", + .public_key_hex = "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + .sig_hex = "a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04", + .expected = error.IdentityElement, // 10 - small-order A + }, + Vec{ + .msg_hex = "39a591f5321bbe07fd5a23dc2f39d025d74526615746727ceefd6e82ae65c06f", + .public_key_hex = "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + .sig_hex = "a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04", + .expected = error.IdentityElement, // 11 - small-order A + }, + }; + for (entries) |entry, i| { + var msg: [entry.msg_hex.len / 2]u8 = undefined; + try fmt.hexToBytes(&msg, entry.msg_hex); + var public_key: [32]u8 = undefined; + try fmt.hexToBytes(&public_key, entry.public_key_hex); + var sig: [64]u8 = undefined; + try fmt.hexToBytes(&sig, entry.sig_hex); + if (entry.expected) |error_type| { + std.testing.expectError(error_type, Ed25519.verify(sig, &msg, public_key)); + } else { + try Ed25519.verify(sig, &msg, public_key); + } + } +} diff --git a/lib/std/crypto/25519/edwards25519.zig b/lib/std/crypto/25519/edwards25519.zig index f98774542f..7f85fc492a 100644 --- a/lib/std/crypto/25519/edwards25519.zig +++ b/lib/std/crypto/25519/edwards25519.zig @@ -64,6 +64,15 @@ pub const Edwards25519 = struct { .is_base = true, }; + /// The edwards25519 neutral element. + pub const neutralElement = Edwards25519{ + .x = Fe{ .limbs = .{ 2251799813685229, 2251799813685247, 2251799813685247, 2251799813685247, 2251799813685247 } }, + .y = Fe{ .limbs = .{ 1507481815385608, 2223447444246085, 1083941587175919, 2059929906842505, 1581435440146976 } }, + .z = Fe{ .limbs = .{ 1507481815385608, 2223447444246085, 1083941587175919, 2059929906842505, 1581435440146976 } }, + .t = Fe{ .limbs = .{ 2251799813685229, 2251799813685247, 2251799813685247, 2251799813685247, 2251799813685247 } }, + .is_base = false, + }; + const identityElement = Edwards25519{ .x = Fe.zero, .y = Fe.one, .z = Fe.one, .t = Fe.zero }; /// Reject the neutral element. diff --git a/lib/std/crypto/25519/scalar.zig b/lib/std/crypto/25519/scalar.zig index 2658126eeb..e9f46d68b9 100644 --- a/lib/std/crypto/25519/scalar.zig +++ b/lib/std/crypto/25519/scalar.zig @@ -6,10 +6,18 @@ const std = @import("std"); const mem = std.mem; -const field_size = [32]u8{ +/// A 32-byte representation of a scalar in 0 .. 2^252 + 27742317777372353535851937790883648493 +pub const Scalar = [32]u8; + +/// 2^252 + 27742317777372353535851937790883648493 +pub 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 }; +/// Zero +pub const zero = [_]u8{0} ** 32; + +/// Double-word scalar representation const ScalarExpanded = struct { limbs: [64]i64 = [_]i64{0} ** 64, @@ -62,6 +70,11 @@ const ScalarExpanded = struct { inline while (j < 32) : (j += 1) { limbs[j + 1] += limbs[j] >> 8; } + j = 0; + inline while (j < 32) : (j += 1) { + limbs[j] &= 0xff; + } + limbs[32] = 0; } fn toBytes(e: *ScalarExpanded) [32]u8 { @@ -150,11 +163,51 @@ pub inline fn clamp(s: *[32]u8) void { s[31] = (s[31] & 127) | 64; } +/// Return a*b (mod L) +pub fn mul(a: [32]u8, b: [32]u8) [32]u8 { + return ScalarExpanded.fromBytes(a).mul(ScalarExpanded.fromBytes(b)).toBytes(); +} + /// 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(); } +/// Return a*8 (mod L) +pub fn mul8(s: [32]u8) [32]u8 { + var x = ScalarExpanded.fromBytes(s); + x = x.add(x); + x = x.add(x); + x = x.add(x); + return x.toBytes(); +} + +/// Return a+b (mod L) +pub fn add(a: [32]u8, b: [32]u8) [32]u8 { + return ScalarExpanded.fromBytes(a).add(ScalarExpanded.fromBytes(b)).toBytes(); +} + +/// Return -s (mod L) +pub fn neg(s: [32]u8) [32]u8 { + const fs: [64]u8 = field_size ++ [_]u8{0} ** 32; + var sx: [64]u8 = undefined; + mem.copy(u8, sx[0..32], s[0..]); + mem.set(u8, sx[32..], 0); + var carry: u32 = 0; + var i: usize = 0; + while (i < 64) : (i += 1) { + carry = @as(u32, fs[i]) -% sx[i] -% @as(u32, carry); + sx[i] = @truncate(u8, carry); + carry = (carry >> 8) & 1; + } + return reduce64(sx); +} + +/// Return (a-b) (mod L) +pub fn sub(a: [32]u8, b: [32]u8) [32]u8 { + return add(a, neg(b)); +} + 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);