diff options
| -rw-r--r-- | Tests/LibCrypto/CMakeLists.txt | 1 | ||||
| -rw-r--r-- | Tests/LibCrypto/TestEd25519.cpp | 185 | ||||
| -rw-r--r-- | Userland/Libraries/LibCrypto/CMakeLists.txt | 1 | ||||
| -rw-r--r-- | Userland/Libraries/LibCrypto/Curves/Ed25519.cpp | 433 | ||||
| -rw-r--r-- | Userland/Libraries/LibCrypto/Curves/Ed25519.h | 75 |
5 files changed, 695 insertions, 0 deletions
diff --git a/Tests/LibCrypto/CMakeLists.txt b/Tests/LibCrypto/CMakeLists.txt index 41e62e1c9c..81e3176ba2 100644 --- a/Tests/LibCrypto/CMakeLists.txt +++ b/Tests/LibCrypto/CMakeLists.txt @@ -4,6 +4,7 @@ set(TEST_SOURCES TestChecksum.cpp TestChaCha20.cpp TestCurves.cpp + TestEd25519.cpp TestHash.cpp TestHMAC.cpp TestPoly1305.cpp diff --git a/Tests/LibCrypto/TestEd25519.cpp b/Tests/LibCrypto/TestEd25519.cpp new file mode 100644 index 0000000000..1b7751061b --- /dev/null +++ b/Tests/LibCrypto/TestEd25519.cpp @@ -0,0 +1,185 @@ +/* + * Copyright (c) 2022, stelar7 <dudedbz@gmail.com> + * + * SPDX-License-Identifier: BSD-2-Clause + */ + +#include <AK/ByteBuffer.h> +#include <LibCrypto/Curves/Ed25519.h> +#include <LibTest/TestCase.h> + +// https://datatracker.ietf.org/doc/html/rfc8032#section-7.1 +TEST_CASE(TEST_1) +{ + u8 private_bytes[32] = { + 0x9d, 0x61, 0xb1, 0x9d, 0xef, 0xfd, 0x5a, 0x60, + 0xba, 0x84, 0x4a, 0xf4, 0x92, 0xec, 0x2c, 0xc4, + 0x44, 0x49, 0xc5, 0x69, 0x7b, 0x32, 0x69, 0x19, + 0x70, 0x3b, 0xac, 0x03, 0x1c, 0xae, 0x7f, 0x60 + }; + + u8 public_bytes[32] = { + 0xd7, 0x5a, 0x98, 0x01, 0x82, 0xb1, 0x0a, 0xb7, + 0xd5, 0x4b, 0xfe, 0xd3, 0xc9, 0x64, 0x07, 0x3a, + 0x0e, 0xe1, 0x72, 0xf3, 0xda, 0xa6, 0x23, 0x25, + 0xaf, 0x02, 0x1a, 0x68, 0xf7, 0x07, 0x51, 0x1a + }; + + u8 message_bytes[0] = {}; + + u8 signature_bytes[64] = { + 0xe5, 0x56, 0x43, 0x00, 0xc3, 0x60, 0xac, 0x72, + 0x90, 0x86, 0xe2, 0xcc, 0x80, 0x6e, 0x82, 0x8a, + 0x84, 0x87, 0x7f, 0x1e, 0xb8, 0xe5, 0xd9, 0x74, + 0xd8, 0x73, 0xe0, 0x65, 0x22, 0x49, 0x01, 0x55, + 0x5f, 0xb8, 0x82, 0x15, 0x90, 0xa3, 0x3b, 0xac, + 0xc6, 0x1e, 0x39, 0x70, 0x1c, 0xf9, 0xb4, 0x6b, + 0xd2, 0x5b, 0xf5, 0xf0, 0x59, 0x5b, 0xbe, 0x24, + 0x65, 0x51, 0x41, 0x43, 0x8e, 0x7a, 0x10, 0x0b + }; + + ReadonlyBytes private_key { private_bytes, 32 }; + ReadonlyBytes public_key { public_bytes, 32 }; + ReadonlyBytes message { message_bytes, 0 }; + ReadonlyBytes expected_signature { signature_bytes, 64 }; + + Crypto::Curves::Ed25519 curve; + + auto generated_signature = MUST(curve.sign(public_key, private_key, message)); + EXPECT_EQ(generated_signature, expected_signature); + EXPECT_EQ(true, curve.verify(public_key, expected_signature, message)); +} + +TEST_CASE(TEST_2) +{ + u8 private_bytes[32] = { + 0x4c, 0xcd, 0x08, 0x9b, 0x28, 0xff, 0x96, 0xda, + 0x9d, 0xb6, 0xc3, 0x46, 0xec, 0x11, 0x4e, 0x0f, + 0x5b, 0x8a, 0x31, 0x9f, 0x35, 0xab, 0xa6, 0x24, + 0xda, 0x8c, 0xf6, 0xed, 0x4f, 0xb8, 0xa6, 0xfb + }; + + u8 public_bytes[32] = { + 0x3d, 0x40, 0x17, 0xc3, 0xe8, 0x43, 0x89, 0x5a, + 0x92, 0xb7, 0x0a, 0xa7, 0x4d, 0x1b, 0x7e, 0xbc, + 0x9c, 0x98, 0x2c, 0xcf, 0x2e, 0xc4, 0x96, 0x8c, + 0xc0, 0xcd, 0x55, 0xf1, 0x2a, 0xf4, 0x66, 0x0c + }; + + u8 message_bytes[1] = { 0x72 }; + + u8 signature_bytes[64] = { + 0x92, 0xa0, 0x09, 0xa9, 0xf0, 0xd4, 0xca, 0xb8, + 0x72, 0x0e, 0x82, 0x0b, 0x5f, 0x64, 0x25, 0x40, + 0xa2, 0xb2, 0x7b, 0x54, 0x16, 0x50, 0x3f, 0x8f, + 0xb3, 0x76, 0x22, 0x23, 0xeb, 0xdb, 0x69, 0xda, + 0x08, 0x5a, 0xc1, 0xe4, 0x3e, 0x15, 0x99, 0x6e, + 0x45, 0x8f, 0x36, 0x13, 0xd0, 0xf1, 0x1d, 0x8c, + 0x38, 0x7b, 0x2e, 0xae, 0xb4, 0x30, 0x2a, 0xee, + 0xb0, 0x0d, 0x29, 0x16, 0x12, 0xbb, 0x0c, 0x00 + }; + + ReadonlyBytes private_key { private_bytes, 32 }; + ReadonlyBytes public_key { public_bytes, 32 }; + ReadonlyBytes message { message_bytes, 1 }; + ReadonlyBytes expected_signature { signature_bytes, 64 }; + + Crypto::Curves::Ed25519 curve; + + auto generated_signature = MUST(curve.sign(public_key, private_key, message)); + EXPECT_EQ(generated_signature, expected_signature); + EXPECT_EQ(true, curve.verify(public_key, expected_signature, message)); +} + +TEST_CASE(TEST_3) +{ + // https://datatracker.ietf.org/doc/html/rfc8032#section-7.1 + u8 private_bytes[32] = { + 0xc5, 0xaa, 0x8d, 0xf4, 0x3f, 0x9f, 0x83, 0x7b, + 0xed, 0xb7, 0x44, 0x2f, 0x31, 0xdc, 0xb7, 0xb1, + 0x66, 0xd3, 0x85, 0x35, 0x07, 0x6f, 0x09, 0x4b, + 0x85, 0xce, 0x3a, 0x2e, 0x0b, 0x44, 0x58, 0xf7 + }; + + u8 public_bytes[32] = { + 0xfc, 0x51, 0xcd, 0x8e, 0x62, 0x18, 0xa1, 0xa3, + 0x8d, 0xa4, 0x7e, 0xd0, 0x02, 0x30, 0xf0, 0x58, + 0x08, 0x16, 0xed, 0x13, 0xba, 0x33, 0x03, 0xac, + 0x5d, 0xeb, 0x91, 0x15, 0x48, 0x90, 0x80, 0x25 + }; + + u8 message_bytes[2] = { 0xaf, 0x82 }; + + u8 signature_bytes[64] = { + 0x62, 0x91, 0xd6, 0x57, 0xde, 0xec, 0x24, 0x02, + 0x48, 0x27, 0xe6, 0x9c, 0x3a, 0xbe, 0x01, 0xa3, + 0x0c, 0xe5, 0x48, 0xa2, 0x84, 0x74, 0x3a, 0x44, + 0x5e, 0x36, 0x80, 0xd7, 0xdb, 0x5a, 0xc3, 0xac, + 0x18, 0xff, 0x9b, 0x53, 0x8d, 0x16, 0xf2, 0x90, + 0xae, 0x67, 0xf7, 0x60, 0x98, 0x4d, 0xc6, 0x59, + 0x4a, 0x7c, 0x15, 0xe9, 0x71, 0x6e, 0xd2, 0x8d, + 0xc0, 0x27, 0xbe, 0xce, 0xea, 0x1e, 0xc4, 0x0a + }; + + ReadonlyBytes private_key { private_bytes, 32 }; + ReadonlyBytes public_key { public_bytes, 32 }; + ReadonlyBytes message { message_bytes, 2 }; + ReadonlyBytes expected_signature { signature_bytes, 64 }; + + Crypto::Curves::Ed25519 curve; + + auto generated_signature = MUST(curve.sign(public_key, private_key, message)); + EXPECT_EQ(generated_signature, expected_signature); + EXPECT_EQ(true, curve.verify(public_key, expected_signature, message)); +} + +TEST_CASE(TEST_SHA_ABC) +{ + // https://datatracker.ietf.org/doc/html/rfc8032#section-7.1 + u8 private_bytes[32] = { + 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, + 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, + 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, + 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42 + }; + + u8 public_bytes[32] = { + 0xec, 0x17, 0x2b, 0x93, 0xad, 0x5e, 0x56, 0x3b, + 0xf4, 0x93, 0x2c, 0x70, 0xe1, 0x24, 0x50, 0x34, + 0xc3, 0x54, 0x67, 0xef, 0x2e, 0xfd, 0x4d, 0x64, + 0xeb, 0xf8, 0x19, 0x68, 0x34, 0x67, 0xe2, 0xbf + }; + + u8 message_bytes[64] = { + 0xdd, 0xaf, 0x35, 0xa1, 0x93, 0x61, 0x7a, 0xba, + 0xcc, 0x41, 0x73, 0x49, 0xae, 0x20, 0x41, 0x31, + 0x12, 0xe6, 0xfa, 0x4e, 0x89, 0xa9, 0x7e, 0xa2, + 0x0a, 0x9e, 0xee, 0xe6, 0x4b, 0x55, 0xd3, 0x9a, + 0x21, 0x92, 0x99, 0x2a, 0x27, 0x4f, 0xc1, 0xa8, + 0x36, 0xba, 0x3c, 0x23, 0xa3, 0xfe, 0xeb, 0xbd, + 0x45, 0x4d, 0x44, 0x23, 0x64, 0x3c, 0xe8, 0x0e, + 0x2a, 0x9a, 0xc9, 0x4f, 0xa5, 0x4c, 0xa4, 0x9f + }; + + u8 signature_bytes[64] = { + 0xdc, 0x2a, 0x44, 0x59, 0xe7, 0x36, 0x96, 0x33, + 0xa5, 0x2b, 0x1b, 0xf2, 0x77, 0x83, 0x9a, 0x00, + 0x20, 0x10, 0x09, 0xa3, 0xef, 0xbf, 0x3e, 0xcb, + 0x69, 0xbe, 0xa2, 0x18, 0x6c, 0x26, 0xb5, 0x89, + 0x09, 0x35, 0x1f, 0xc9, 0xac, 0x90, 0xb3, 0xec, + 0xfd, 0xfb, 0xc7, 0xc6, 0x64, 0x31, 0xe0, 0x30, + 0x3d, 0xca, 0x17, 0x9c, 0x13, 0x8a, 0xc1, 0x7a, + 0xd9, 0xbe, 0xf1, 0x17, 0x73, 0x31, 0xa7, 0x04 + }; + + ReadonlyBytes private_key { private_bytes, 32 }; + ReadonlyBytes public_key { public_bytes, 32 }; + ReadonlyBytes message { message_bytes, 64 }; + ReadonlyBytes expected_signature { signature_bytes, 64 }; + + Crypto::Curves::Ed25519 curve; + + auto generated_signature = MUST(curve.sign(public_key, private_key, message)); + EXPECT_EQ(generated_signature, expected_signature); + EXPECT_EQ(true, curve.verify(public_key, expected_signature, message)); +} diff --git a/Userland/Libraries/LibCrypto/CMakeLists.txt b/Userland/Libraries/LibCrypto/CMakeLists.txt index a119f4474f..b9b3312d30 100644 --- a/Userland/Libraries/LibCrypto/CMakeLists.txt +++ b/Userland/Libraries/LibCrypto/CMakeLists.txt @@ -20,6 +20,7 @@ set(SOURCES Cipher/AES.cpp Cipher/ChaCha20.cpp Curves/Curve25519.cpp + Curves/Ed25519.cpp Curves/SECP256r1.cpp Curves/X25519.cpp Curves/X448.cpp diff --git a/Userland/Libraries/LibCrypto/Curves/Ed25519.cpp b/Userland/Libraries/LibCrypto/Curves/Ed25519.cpp new file mode 100644 index 0000000000..79a743bed6 --- /dev/null +++ b/Userland/Libraries/LibCrypto/Curves/Ed25519.cpp @@ -0,0 +1,433 @@ +/* + * Copyright (c) 2022, stelar7 <dudedbz@gmail.com> + * + * SPDX-License-Identifier: BSD-2-Clause + */ + +#include <AK/Random.h> +#include <LibCrypto/Curves/Curve25519.h> +#include <LibCrypto/Curves/Ed25519.h> +#include <LibCrypto/Hash/SHA2.h> + +namespace Crypto::Curves { + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.5 +ErrorOr<ByteBuffer> Ed25519::generate_private_key() +{ + // The private key is 32 octets (256 bits, corresponding to b) of + // cryptographically secure random data. See [RFC4086] for a discussion + // about randomness. + + auto buffer = TRY(ByteBuffer::create_uninitialized(key_size())); + fill_with_random(buffer.data(), buffer.size()); + return buffer; +}; + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.5 +ErrorOr<ByteBuffer> Ed25519::generate_public_key(ReadonlyBytes private_key) +{ + // The 32-byte public key is generated by the following steps. + + // 1. Hash the 32-byte private key using SHA-512, storing the digest in a 64-octet large buffer, denoted h. + // Only the lower 32 bytes are used for generating the public key. + auto digest = Crypto::Hash::SHA512::hash(private_key); + + // NOTE: we do these steps in the opposite order (since its easier to modify s) + // 3. Interpret the buffer as the little-endian integer, forming a secret scalar s. + memcpy(s, digest.data, 32); + + // 2. Prune the buffer: + // The lowest three bits of the first octet are cleared, + s[0] &= 0xF8; + // the highest bit of the last octet is cleared, + s[31] &= 0x7F; + // and the second highest bit of the last octet is set. + s[31] |= 0x40; + + // Perform a fixed-base scalar multiplication [s]B. + point_multiply_scalar(&sb, s, &BASE_POINT); + + // 4. The public key A is the encoding of the point [s]B. + // First, encode the y-coordinate (in the range 0 <= y < p) as a little-endian string of 32 octets. + // The most significant bit of the final octet is always zero. + // To form the encoding of the point [s]B, copy the least significant bit of the x coordinate + // to the most significant bit of the final octet. The result is the public key. + auto public_key = TRY(ByteBuffer::create_uninitialized(key_size())); + encode_point(&sb, public_key.data()); + + return public_key; +} + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.6 +ErrorOr<ByteBuffer> Ed25519::sign(ReadonlyBytes public_key, ReadonlyBytes private_key, ReadonlyBytes message) +{ + // 1. Hash the private key, 32 octets, using SHA-512. + // Let h denote the resulting digest. + auto h = Crypto::Hash::SHA512::hash(private_key); + + // Construct the secret scalar s from the first half of the digest, + memcpy(s, h.data, 32); + // NOTE: This is done later in step 4, but we can also do it here. + s[0] &= 0xF8; + s[31] &= 0x7F; + s[31] |= 0x40; + + // and the corresponding public key A, as described in the previous section. + // NOTE: The public key A is taken as input to this function. + + // Let prefix denote the second half of the hash digest, h[32],...,h[63]. + memcpy(p, h.data + 32, 32); + + // 2. Compute SHA-512(dom2(F, C) || p || PH(M)), where M is the message to be signed. + Crypto::Hash::SHA512 hash; + // NOTE: dom2(F, C) is a blank octet string when signing or verifying Ed25519 + hash.update(p, 32); + // NOTE: PH(M) = M + hash.update(message.data(), message.size()); + + // Interpret the 64-octet digest as a little-endian integer r. + // For efficiency, do this by first reducing r modulo L, the group order of B. + auto digest = hash.digest(); + barrett_reduce(r, digest.data); + + // 3. Compute the point [r]B. + point_multiply_scalar(&rb, r, &BASE_POINT); + + auto R = TRY(ByteBuffer::create_uninitialized(32)); + // Let the string R be the encoding of this point + encode_point(&rb, R.data()); + + // 4. Compute SHA512(dom2(F, C) || R || A || PH(M)), + // NOTE: We can reuse hash here, since digest() calls reset() + // NOTE: dom2(F, C) is a blank octet string when signing or verifying Ed25519 + hash.update(R.data(), R.size()); + // NOTE: A == public_key + hash.update(public_key.data(), public_key.size()); + // NOTE: PH(M) = M + hash.update(message.data(), message.size()); + + digest = hash.digest(); + // and interpret the 64-octet digest as a little-endian integer k. + memcpy(k, digest.data, 64); + + // 5. Compute S = (r + k * s) mod L. For efficiency, again reduce k modulo L first. + barrett_reduce(p, k); + multiply(k, k + 32, p, s, 32); + barrett_reduce(p, k); + add(s, p, r, 32); + + // modular reduction + auto reduced_s = TRY(ByteBuffer::create_uninitialized(32)); + auto is_negative = subtract(p, s, Curve25519::BASE_POINT_L_ORDER, 32); + select(reduced_s.data(), p, s, is_negative, 32); + + // 6. Form the signature of the concatenation of R (32 octets) and the little-endian encoding of S + // (32 octets; the three most significant bits of the final octet are always zero). + auto signature = TRY(ByteBuffer::copy(R)); + signature.append(reduced_s); + + return signature; +} + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.7 +bool Ed25519::verify(ReadonlyBytes public_key, ReadonlyBytes signature, ReadonlyBytes message) +{ + auto not_valid = false; + + // 1. To verify a signature on a message M using public key A, + // with F being 0 for Ed25519ctx, 1 for Ed25519ph, and if Ed25519ctx or Ed25519ph is being used, C being the context + // first split the signature into two 32-octet halves. + // If any of the decodings fail (including S being out of range), the signature is invalid. + + // NOTE: We dont care about F, since we dont implement Ed25519ctx or Ed25519PH + // NOTE: C is the internal state, so its not a parameter + + auto half_signature_size = signature_size() / 2; + + // Decode the first half as a point R + memcpy(r, signature.data(), half_signature_size); + + // and the second half as an integer S, in the range 0 <= s < L. + memcpy(s, signature.data() + half_signature_size, half_signature_size); + + // NOTE: Ed25519 and Ed448 signatures are not malleable due to the verification check that decoded S is smaller than l. + // Without this check, one can add a multiple of l into a scalar part and still pass signature verification, + // resulting in malleable signatures. + auto is_negative = subtract(p, s, Curve25519::BASE_POINT_L_ORDER, half_signature_size); + not_valid |= 1 ^ is_negative; + + // Decode the public key A as point A'. + not_valid |= decode_point(&ka, public_key.data()); + + // 2. Compute SHA512(dom2(F, C) || R || A || PH(M)), and interpret the 64-octet digest as a little-endian integer k. + Crypto::Hash::SHA512 hash; + // NOTE: dom2(F, C) is a blank octet string when signing or verifying Ed25519 + hash.update(r, half_signature_size); + // NOTE: A == public_key + hash.update(public_key.data(), key_size()); + // NOTE: PH(M) = M + hash.update(message.data(), message.size()); + + auto digest = hash.digest(); + auto k = digest.data; + + // 3. Check the group equation [8][S]B = [8]R + [8][k]A'. + // It's sufficient, but not required, to instead check [S]B = R + [k]A'. + // NOTE: For efficiency, do this by first reducing k modulo L. + barrett_reduce(k, k); + + // NOTE: We check [S]B - [k]A' == R + Curve25519::modular_subtract(ka.x, Curve25519::ZERO, ka.x); + Curve25519::modular_subtract(ka.t, Curve25519::ZERO, ka.t); + point_multiply_scalar(&sb, s, &BASE_POINT); + point_multiply_scalar(&ka, k, &ka); + point_add(&ka, &sb, &ka); + encode_point(&ka, p); + + not_valid |= compare(p, r, half_signature_size); + + return !not_valid; +} + +void Ed25519::point_double(Ed25519Point* result, Ed25519Point const* point) +{ + Curve25519::modular_square(a, point->x); + Curve25519::modular_square(b, point->y); + Curve25519::modular_square(c, point->z); + Curve25519::modular_add(c, c, c); + Curve25519::modular_add(e, a, b); + Curve25519::modular_add(f, point->x, point->y); + Curve25519::modular_square(f, f); + Curve25519::modular_subtract(f, e, f); + Curve25519::modular_subtract(g, a, b); + Curve25519::modular_add(h, c, g); + Curve25519::modular_multiply(result->x, f, h); + Curve25519::modular_multiply(result->y, e, g); + Curve25519::modular_multiply(result->z, g, h); + Curve25519::modular_multiply(result->t, e, f); +} + +void Ed25519::point_multiply_scalar(Ed25519Point* result, u8 const* scalar, Ed25519Point const* point) +{ + // Set U to the neutral element (0, 1, 1, 0) + Curve25519::set(u.x, 0); + Curve25519::set(u.y, 1); + Curve25519::set(u.z, 1); + Curve25519::set(u.t, 0); + + for (i32 i = Curve25519::BITS - 1; i >= 0; i--) { + u8 b = (scalar[i / 8] >> (i % 8)) & 1; + + // Compute U = 2 * U + point_double(&u, &u); + // Compute V = U + P + point_add(&v, &u, point); + + // If b is set, then U = V + Curve25519::select(u.x, u.x, v.x, b); + Curve25519::select(u.y, u.y, v.y, b); + Curve25519::select(u.z, u.z, v.z, b); + Curve25519::select(u.t, u.t, v.t, b); + } + + Curve25519::copy(result->x, u.x); + Curve25519::copy(result->y, u.y); + Curve25519::copy(result->z, u.z); + Curve25519::copy(result->t, u.t); +} + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.2 +void Ed25519::encode_point(Ed25519Point* point, u8* data) +{ + // Retrieve affine representation + Curve25519::modular_multiply_inverse(point->z, point->z); + Curve25519::modular_multiply(point->x, point->x, point->z); + Curve25519::modular_multiply(point->y, point->y, point->z); + Curve25519::set(point->z, 1); + Curve25519::modular_multiply(point->t, point->x, point->y); + + // First, encode the y-coordinate (in the range 0 <= y < p) as a little-endian string of 32 octets. + // The most significant bit of the final octet is always zero. + Curve25519::export_state(point->y, data); + + // To form the encoding of the point [s]B, + // copy the least significant bit of the x coordinate to the most significant bit of the final octet. + data[31] |= (point->x[0] & 1) << 7; +} + +void Ed25519::barrett_reduce(u8* result, u8 const* input) +{ + // Barrett reduction b = 2^8 && k = 32 + u8 is_negative; + u8 u[33]; + u8 v[33]; + + multiply(NULL, u, input + 31, Curve25519::BARRETT_REDUCTION_QUOTIENT, 33); + multiply(v, NULL, u, Curve25519::BASE_POINT_L_ORDER, 33); + + subtract(u, input, v, 33); + + is_negative = subtract(v, u, Curve25519::BASE_POINT_L_ORDER, 33); + select(u, v, u, is_negative, 33); + is_negative = subtract(v, u, Curve25519::BASE_POINT_L_ORDER, 33); + select(u, v, u, is_negative, 33); + + copy(result, u, 32); +} + +void Ed25519::multiply(u8* result_low, u8* result_high, u8 const* a, u8 const* b, u8 n) +{ + // Comba's algorithm + u32 temp = 0; + for (u32 i = 0; i < n; i++) { + for (u32 j = 0; j <= i; j++) { + temp += (uint16_t)a[j] * b[i - j]; + } + + if (result_low != NULL) { + result_low[i] = temp & 0xFF; + } + + temp >>= 8; + } + + if (result_high != NULL) { + for (u32 i = n; i < (2 * n); i++) { + for (u32 j = i + 1 - n; j < n; j++) { + temp += (uint16_t)a[j] * b[i - j]; + } + + result_high[i - n] = temp & 0xFF; + temp >>= 8; + } + } +} + +void Ed25519::add(u8* result, u8 const* a, u8 const* b, u8 n) +{ + // Compute R = A + B + u16 temp = 0; + for (u8 i = 0; i < n; i++) { + temp += a[i]; + temp += b[i]; + result[i] = temp & 0xFF; + temp >>= 8; + } +} + +u8 Ed25519::subtract(u8* result, u8 const* a, u8 const* b, u8 n) +{ + i16 temp = 0; + + // Compute R = A - B + for (i8 i = 0; i < n; i++) { + temp += a[i]; + temp -= b[i]; + result[i] = temp & 0xFF; + temp >>= 8; + } + + // Return 1 if the result of the subtraction is negative + return temp & 1; +} + +void Ed25519::select(u8* r, u8 const* a, u8 const* b, u8 c, u8 n) +{ + u8 mask = c - 1; + for (u8 i = 0; i < n; i++) { + r[i] = (a[i] & mask) | (b[i] & ~mask); + } +} + +// https://datatracker.ietf.org/doc/html/rfc8032#section-5.1.3 +u32 Ed25519::decode_point(Ed25519Point* point, u8 const* data) +{ + u32 u[8]; + u32 v[8]; + u32 ret; + u64 temp = 19; + + // 1. First, interpret the string as an integer in little-endian representation. + // Bit 255 of this number is the least significant bit of the x-coordinate and denote this value x_0. + u8 x0 = data[31] >> 7; + + // The y-coordinate is recovered simply by clearing this bit. + Curve25519::import_state(point->y, data); + point->y[7] &= 0x7FFFFFFF; + + // Compute U = Y + 19 + for (u32 i = 0; i < 8; i++) { + temp += point->y[i]; + u[i] = temp & 0xFFFFFFFF; + temp >>= 32; + } + + // If the resulting value is >= p, decoding fails. + ret = (u[7] >> 31) & 1; + + // 2. To recover the x-coordinate, the curve equation implies x^2 = (y^2 - 1) / (d y^2 + 1) (mod p). + // The denominator is always non-zero mod p. + // Let u = y^2 - 1 and v = d * y^2 + 1 + Curve25519::modular_square(v, point->y); + Curve25519::modular_subtract_single(u, v, 1); + Curve25519::modular_multiply(v, v, Curve25519::CURVE_D); + Curve25519::modular_add_single(v, v, 1); + + // 3. Compute u = sqrt(u / v) + ret |= Curve25519::modular_square_root(u, u, v); + + // If x = 0, and x_0 = 1, decoding fails. + ret |= (Curve25519::compare(u, Curve25519::ZERO) ^ 1) & x0; + + // 4. Finally, use the x_0 bit to select the right square root. + Curve25519::modular_subtract(v, Curve25519::ZERO, u); + Curve25519::select(point->x, u, v, (x0 ^ u[0]) & 1); + Curve25519::set(point->z, 1); + Curve25519::modular_multiply(point->t, point->x, point->y); + + // Return 0 if the point has been successfully decoded, else 1 + return ret; +} + +void Ed25519::point_add(Ed25519Point* result, Ed25519Point const* p, Ed25519Point const* q) +{ + // Compute R = P + Q + Curve25519::modular_add(c, p->y, p->x); + Curve25519::modular_add(d, q->y, q->x); + Curve25519::modular_multiply(a, c, d); + Curve25519::modular_subtract(c, p->y, p->x); + Curve25519::modular_subtract(d, q->y, q->x); + Curve25519::modular_multiply(b, c, d); + Curve25519::modular_multiply(c, p->z, q->z); + Curve25519::modular_add(c, c, c); + Curve25519::modular_multiply(d, p->t, q->t); + Curve25519::modular_multiply(d, d, Curve25519::CURVE_D_2); + Curve25519::modular_add(e, a, b); + Curve25519::modular_subtract(f, a, b); + Curve25519::modular_add(g, c, d); + Curve25519::modular_subtract(h, c, d); + Curve25519::modular_multiply(result->x, f, h); + Curve25519::modular_multiply(result->y, e, g); + Curve25519::modular_multiply(result->z, g, h); + Curve25519::modular_multiply(result->t, e, f); +} + +u8 Ed25519::compare(u8 const* a, u8 const* b, u8 n) +{ + u8 mask = 0; + for (u32 i = 0; i < n; i++) { + mask |= a[i] ^ b[i]; + } + + // Return 0 if A = B, else 1 + return ((u8)(mask | (~mask + 1))) >> 7; +} + +void Ed25519::copy(u8* a, u8 const* b, u32 n) +{ + for (u32 i = 0; i < n; i++) { + a[i] = b[i]; + } +} + +} diff --git a/Userland/Libraries/LibCrypto/Curves/Ed25519.h b/Userland/Libraries/LibCrypto/Curves/Ed25519.h new file mode 100644 index 0000000000..81b1a42b59 --- /dev/null +++ b/Userland/Libraries/LibCrypto/Curves/Ed25519.h @@ -0,0 +1,75 @@ +/* + * Copyright (c) 2022, stelar7 <dudedbz@gmail.com> + * + * SPDX-License-Identifier: BSD-2-Clause + */ + +#pragma once + +#include <AK/ByteBuffer.h> +#include <LibCrypto/Curves/EllipticCurve.h> + +namespace Crypto::Curves { + +struct Ed25519Point { + u32 x[8] {}; + u32 y[8] {}; + u32 z[8] {}; + u32 t[8] {}; +}; + +class Ed25519 { +public: + static constexpr Ed25519Point BASE_POINT = { + { 0x8F25D51A, 0xC9562D60, 0x9525A7B2, 0x692CC760, 0xFDD6DC5C, 0xC0A4E231, 0xCD6E53FE, 0x216936D3 }, + { 0x66666658, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666 }, + { 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 }, + { 0xA5B7DDA3, 0x6DDE8AB3, 0x775152F5, 0x20F09F80, 0x64ABE37D, 0x66EA4E8E, 0xD78B7665, 0x67875F0F } + }; + + size_t key_size() { return 32; } + size_t signature_size() { return 64; } + ErrorOr<ByteBuffer> generate_private_key(); + ErrorOr<ByteBuffer> generate_public_key(ReadonlyBytes private_key); + + ErrorOr<ByteBuffer> sign(ReadonlyBytes public_key, ReadonlyBytes private_key, ReadonlyBytes message); + bool verify(ReadonlyBytes public_key, ReadonlyBytes signature, ReadonlyBytes message); + +private: + void encode_point(Ed25519Point* point, u8* data); + u32 decode_point(Ed25519Point* point, u8 const* data); + + void point_add(Ed25519Point* result, Ed25519Point const* p, Ed25519Point const* q); + void point_double(Ed25519Point* result, Ed25519Point const* point); + void point_multiply_scalar(Ed25519Point* result, u8 const* scalar, Ed25519Point const* point); + + void barrett_reduce(u8* result, u8 const* input); + + void add(u8* result, u8 const* a, u8 const* b, u8 n); + u8 subtract(u8* result, u8 const* a, u8 const* b, u8 n); + void multiply(u8* result_low, u8* result_high, u8 const* a, u8 const* b, u8 n); + + void select(u8* result, u8 const* a, u8 const* b, u8 c, u8 n); + u8 compare(u8 const* a, u8 const* b, u8 n); + void copy(u8* a, u8 const* b, u32 n); + + u8 k[64] {}; + u8 p[32] {}; + u8 r[32] {}; + u8 s[32] {}; + Ed25519Point ka {}; + Ed25519Point rb {}; + Ed25519Point sb {}; + Ed25519Point u {}; + Ed25519Point v {}; + u32 a[8] {}; + u32 b[8] {}; + u32 c[8] {}; + u32 d[8] {}; + u32 e[8] {}; + u32 f[8] {}; + u32 g[8] {}; + u32 h[8] {}; +}; + +} |