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LibCrypto: Add curve X448
This commit is contained in:
stelar7
Ali Mohammad Pur
parent
c8803afe3e
commit
0df7ad7493
Notes:
sideshowbarker
2024-07-17 17:41:28 +09:00
Author: https://github.com/stelar7 Commit: https://github.com/SerenityOS/serenity/commit/0df7ad7493 Pull-request: https://github.com/SerenityOS/serenity/pull/12627 Reviewed-by: https://github.com/alimpfard ✅
4 changed files with 483 additions and 0 deletions
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@ -6,6 +6,7 @@
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#include <AK/ByteBuffer.h>
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#include <LibCrypto/Curves/X25519.h>
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#include <LibCrypto/Curves/X448.h>
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#include <LibTest/TestCase.h>
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TEST_CASE(test_x25519)
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@ -74,3 +75,88 @@ TEST_CASE(test_x25519)
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EXPECT_EQ(shared_alice, shared_bob);
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}
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TEST_CASE(test_x448)
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{
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// https://datatracker.ietf.org/doc/html/rfc7748#section-6.1
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u8 alice_private_key_data[56] {
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0x9a, 0x8f, 0x49, 0x25, 0xd1, 0x51, 0x9f, 0x57,
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0x75, 0xcf, 0x46, 0xb0, 0x4b, 0x58, 0x00, 0xd4,
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0xee, 0x9e, 0xe8, 0xba, 0xe8, 0xbc, 0x55, 0x65,
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0xd4, 0x98, 0xc2, 0x8d, 0xd9, 0xc9, 0xba, 0xf5,
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0x74, 0xa9, 0x41, 0x97, 0x44, 0x89, 0x73, 0x91,
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0x00, 0x63, 0x82, 0xa6, 0xf1, 0x27, 0xab, 0x1d,
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0x9a, 0xc2, 0xd8, 0xc0, 0xa5, 0x98, 0x72, 0x6b
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};
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u8 alice_public_key_data[56] {
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0x9b, 0x08, 0xf7, 0xcc, 0x31, 0xb7, 0xe3, 0xe6,
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0x7d, 0x22, 0xd5, 0xae, 0xa1, 0x21, 0x07, 0x4a,
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0x27, 0x3b, 0xd2, 0xb8, 0x3d, 0xe0, 0x9c, 0x63,
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0xfa, 0xa7, 0x3d, 0x2c, 0x22, 0xc5, 0xd9, 0xbb,
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0xc8, 0x36, 0x64, 0x72, 0x41, 0xd9, 0x53, 0xd4,
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0x0c, 0x5b, 0x12, 0xda, 0x88, 0x12, 0x0d, 0x53,
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0x17, 0x7f, 0x80, 0xe5, 0x32, 0xc4, 0x1f, 0xa0
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};
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u8 bob_private_key_data[56] {
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0x1c, 0x30, 0x6a, 0x7a, 0xc2, 0xa0, 0xe2, 0xe0,
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0x99, 0x0b, 0x29, 0x44, 0x70, 0xcb, 0xa3, 0x39,
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0xe6, 0x45, 0x37, 0x72, 0xb0, 0x75, 0x81, 0x1d,
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0x8f, 0xad, 0x0d, 0x1d, 0x69, 0x27, 0xc1, 0x20,
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0xbb, 0x5e, 0xe8, 0x97, 0x2b, 0x0d, 0x3e, 0x21,
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0x37, 0x4c, 0x9c, 0x92, 0x1b, 0x09, 0xd1, 0xb0,
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0x36, 0x6f, 0x10, 0xb6, 0x51, 0x73, 0x99, 0x2d
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};
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u8 bob_public_key_data[56] {
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0x3e, 0xb7, 0xa8, 0x29, 0xb0, 0xcd, 0x20, 0xf5,
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0xbc, 0xfc, 0x0b, 0x59, 0x9b, 0x6f, 0xec, 0xcf,
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0x6d, 0xa4, 0x62, 0x71, 0x07, 0xbd, 0xb0, 0xd4,
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0xf3, 0x45, 0xb4, 0x30, 0x27, 0xd8, 0xb9, 0x72,
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0xfc, 0x3e, 0x34, 0xfb, 0x42, 0x32, 0xa1, 0x3c,
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0xa7, 0x06, 0xdc, 0xb5, 0x7a, 0xec, 0x3d, 0xae,
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0x07, 0xbd, 0xc1, 0xc6, 0x7b, 0xf3, 0x36, 0x09
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};
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u8 shared_secret_data[56] {
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0x07, 0xff, 0xf4, 0x18, 0x1a, 0xc6, 0xcc, 0x95,
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0xec, 0x1c, 0x16, 0xa9, 0x4a, 0x0f, 0x74, 0xd1,
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0x2d, 0xa2, 0x32, 0xce, 0x40, 0xa7, 0x75, 0x52,
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0x28, 0x1d, 0x28, 0x2b, 0xb6, 0x0c, 0x0b, 0x56,
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0xfd, 0x24, 0x64, 0xc3, 0x35, 0x54, 0x39, 0x36,
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0x52, 0x1c, 0x24, 0x40, 0x30, 0x85, 0xd5, 0x9a,
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0x44, 0x9a, 0x50, 0x37, 0x51, 0x4a, 0x87, 0x9d
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};
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u8 coordinate_data[56] {
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0x05, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
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};
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ReadonlyBytes coordinate { coordinate_data, 56 };
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ReadonlyBytes alice_public_key { alice_public_key_data, 56 };
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ReadonlyBytes alice_private_key { alice_private_key_data, 56 };
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ReadonlyBytes bob_public_key { bob_public_key_data, 56 };
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ReadonlyBytes bob_private_key { bob_private_key_data, 56 };
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ReadonlyBytes shared_secret { shared_secret_data, 56 };
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auto generated_alice_public = MUST(Crypto::Curves::X448::compute_coordinate(alice_private_key, coordinate));
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EXPECT_EQ(alice_public_key, generated_alice_public);
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auto generated_bob_public = MUST(Crypto::Curves::X448::compute_coordinate(bob_private_key, coordinate));
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EXPECT_EQ(bob_public_key, generated_bob_public);
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auto shared_alice = MUST(Crypto::Curves::X448::compute_coordinate(alice_private_key, bob_public_key));
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EXPECT_EQ(shared_alice, shared_secret);
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auto shared_bob = MUST(Crypto::Curves::X448::compute_coordinate(bob_private_key, alice_public_key));
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EXPECT_EQ(shared_bob, shared_secret);
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EXPECT_EQ(shared_alice, shared_bob);
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}
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@ -18,6 +18,7 @@ set(SOURCES
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Checksum/CRC32.cpp
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Cipher/AES.cpp
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Curves/X25519.cpp
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Curves/X448.cpp
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Hash/MD5.cpp
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Hash/SHA1.cpp
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Hash/SHA2.cpp
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356
Userland/Libraries/LibCrypto/Curves/X448.cpp
Normal file
356
Userland/Libraries/LibCrypto/Curves/X448.cpp
Normal file
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@ -0,0 +1,356 @@
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/*
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* Copyright (c) 2022, stelar7 <dudedbz@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#include <AK/ByteReader.h>
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#include <AK/Endian.h>
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#include <LibCrypto/Curves/X448.h>
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namespace Crypto::Curves {
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void X448::import_state(u32* state, ReadonlyBytes data)
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{
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for (auto i = 0; i < X448::WORDS; i++) {
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u32 value = ByteReader::load32(data.offset_pointer(sizeof(u32) * i));
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state[i] = AK::convert_between_host_and_little_endian(value);
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}
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}
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ErrorOr<ByteBuffer> X448::export_state(u32* data)
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{
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auto buffer = TRY(ByteBuffer::create_uninitialized(X448::BYTES));
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for (auto i = 0; i < X448::WORDS; i++) {
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u32 value = AK::convert_between_host_and_little_endian(data[i]);
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ByteReader::store(buffer.offset_pointer(sizeof(u32) * i), value);
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}
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return buffer;
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}
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void X448::select(u32* state, u32* a, u32* b, u32 condition)
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{
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// If B < (2^448 - 2^224 + 1) then R = B, else R = A
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u32 mask = condition - 1;
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for (auto i = 0; i < X448::WORDS; i++) {
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state[i] = (a[i] & mask) | (b[i] & ~mask);
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}
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}
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void X448::set(u32* state, u32 value)
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{
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state[0] = value;
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for (auto i = 1; i < X448::WORDS; i++) {
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state[i] = 0;
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}
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}
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void X448::copy(u32* state, u32* value)
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{
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for (auto i = 0; i < X448::WORDS; i++) {
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state[i] = value[i];
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}
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}
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void X448::conditional_swap(u32* first, u32* second, u32 condition)
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{
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u32 mask = ~condition + 1;
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for (auto i = 0; i < X448::WORDS; i++) {
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u32 temp = mask & (first[i] ^ second[i]);
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first[i] ^= temp;
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second[i] ^= temp;
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}
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}
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void X448::modular_multiply_single(u32* state, u32* first, u32 second)
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{
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// Compute R = (A * B) mod p
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u64 temp = 0;
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u64 carry = 0;
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u32 output[X448::WORDS];
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for (auto i = 0; i < X448::WORDS; i++) {
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temp += (u64)first[i] * second;
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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// Fast modular reduction
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carry = temp;
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for (auto i = 0; i < X448::WORDS / 2; i++) {
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temp += output[i];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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temp += carry;
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for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
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temp += output[i];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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modular_reduce(state, output, (u32)temp);
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}
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void X448::modular_square(u32* state, u32* value)
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{
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// Compute R = (A ^ 2) mod p
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modular_multiply(state, value, value);
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}
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void X448::modular_multiply(u32* state, u32* first, u32* second)
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{
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// Compute R = (A * B) mod p
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u64 temp = 0;
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u64 carry = 0;
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u32 output[X448::WORDS * 2];
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// Comba's method
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for (auto i = 0; i < X448::WORDS * 2; i++) {
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if (i < 14) {
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for (auto j = 0; j <= i; j++) {
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temp += (u64)first[j] * second[i - j];
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carry += temp >> 32;
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temp &= 0xFFFFFFFF;
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}
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} else {
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for (auto j = i - 13; j < X448::WORDS; j++) {
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temp += (u64)first[j] * second[i - j];
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carry += temp >> 32;
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temp &= 0xFFFFFFFF;
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}
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}
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output[i] = temp & 0xFFFFFFFF;
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temp = carry & 0xFFFFFFFF;
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carry >>= 32;
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}
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// Fast modular reduction (first pass)
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temp = 0;
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for (auto i = 0; i < X448::WORDS / 2; i++) {
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temp += output[i];
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temp += output[i + 14];
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temp += output[i + 21];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
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temp += output[i];
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temp += output[i + 7];
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temp += output[i + 14];
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temp += output[i + 14];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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// Fast modular reduction (second pass)
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carry = temp;
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for (auto i = 0; i < X448::WORDS / 2; i++) {
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temp += output[i];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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temp += carry;
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for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
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temp += output[i];
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output[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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modular_reduce(state, output, (u32)temp);
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}
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void X448::modular_add(u32* state, u32* first, u32* second)
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{
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u64 temp = 0;
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// Compute R = A + B
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for (auto i = 0; i < X448::WORDS; i++) {
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temp += first[i];
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temp += second[i];
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state[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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modular_reduce(state, state, (u32)temp);
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}
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void X448::modular_subtract(u32* state, u32* first, u32* second)
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{
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i64 temp = -1;
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// Compute R = A + (2^448 - 2^224 - 1) - B
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for (auto i = 0; i < 7; i++) {
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temp += first[i];
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temp -= second[i];
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state[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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temp -= 1;
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for (auto i = 7; i < 14; i++) {
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temp += first[i];
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temp -= second[i];
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state[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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temp += 1;
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modular_reduce(state, state, (u32)temp);
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}
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void X448::modular_reduce(u32* state, u32* data, u32 a_high)
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{
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u64 temp = 1;
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u32 other[X448::WORDS];
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// Compute B = A - (2^448 - 2^224 - 1)
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for (auto i = 0; i < X448::WORDS / 2; i++) {
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temp += data[i];
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other[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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temp += 1;
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for (auto i = 7; i < X448::WORDS; i++) {
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temp += data[i];
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other[i] = temp & 0xFFFFFFFF;
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temp >>= 32;
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}
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auto condition = (a_high + (u32)temp - 1) & 1;
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select(state, other, data, condition);
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}
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void X448::to_power_of_2n(u32* state, u32* value, u8 n)
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{
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// Compute R = (A ^ (2^n)) mod p
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modular_square(state, value);
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for (auto i = 1; i < n; i++) {
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modular_square(state, state);
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}
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}
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void X448::modular_multiply_inverse(u32* state, u32* value)
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{
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// Compute R = A^-1 mod p
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u32 u[X448::WORDS];
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u32 v[X448::WORDS];
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modular_square(u, value);
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modular_multiply(u, u, value);
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modular_square(u, u);
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modular_multiply(v, u, value);
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to_power_of_2n(u, v, 3);
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modular_multiply(v, u, v);
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to_power_of_2n(u, v, 6);
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modular_multiply(u, u, v);
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modular_square(u, u);
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modular_multiply(v, u, value);
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to_power_of_2n(u, v, 13);
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modular_multiply(u, u, v);
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modular_square(u, u);
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modular_multiply(v, u, value);
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to_power_of_2n(u, v, 27);
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modular_multiply(u, u, v);
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modular_square(u, u);
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modular_multiply(v, u, value);
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to_power_of_2n(u, v, 55);
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modular_multiply(u, u, v);
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modular_square(u, u);
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modular_multiply(v, u, value);
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to_power_of_2n(u, v, 111);
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modular_multiply(v, u, v);
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modular_square(u, v);
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modular_multiply(u, u, value);
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to_power_of_2n(u, u, 223);
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modular_multiply(u, u, v);
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modular_square(u, u);
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modular_square(u, u);
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modular_multiply(state, u, value);
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}
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// https://datatracker.ietf.org/doc/html/rfc7748#section-5
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ErrorOr<ByteBuffer> X448::compute_coordinate(ReadonlyBytes input_k, ReadonlyBytes input_u)
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{
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u32 k[X448::WORDS] {};
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u32 u[X448::WORDS] {};
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u32 x1[X448::WORDS] {};
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u32 x2[X448::WORDS] {};
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u32 z1[X448::WORDS] {};
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u32 z2[X448::WORDS] {};
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u32 t1[X448::WORDS] {};
|
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u32 t2[X448::WORDS] {};
|
||||
|
||||
// Copy input to internal state
|
||||
import_state(k, input_k);
|
||||
|
||||
// Set the two least significant bits of the first byte to 0, and the most significant bit of the last byte to 1
|
||||
k[0] &= 0xFFFFFFFC;
|
||||
k[13] |= 0x80000000;
|
||||
|
||||
// Copy coordinate to internal state
|
||||
import_state(u, input_u);
|
||||
|
||||
// Implementations MUST accept non-canonical values and process them as
|
||||
// if they had been reduced modulo the field prime.
|
||||
modular_reduce(u, u, 0);
|
||||
|
||||
set(x1, 1);
|
||||
set(z1, 0);
|
||||
copy(x2, u);
|
||||
set(z2, 1);
|
||||
|
||||
// Montgomery ladder
|
||||
u32 swap = 0;
|
||||
for (auto i = X448::BITS - 1; i >= 0; i--) {
|
||||
u32 b = (k[i / 32] >> (i % 32)) & 1;
|
||||
|
||||
conditional_swap(x1, x2, swap ^ b);
|
||||
conditional_swap(z1, z2, swap ^ b);
|
||||
|
||||
swap = b;
|
||||
|
||||
modular_add(t1, x2, z2);
|
||||
modular_subtract(x2, x2, z2);
|
||||
modular_add(z2, x1, z1);
|
||||
modular_subtract(x1, x1, z1);
|
||||
modular_multiply(t1, t1, x1);
|
||||
modular_multiply(x2, x2, z2);
|
||||
modular_square(z2, z2);
|
||||
modular_square(x1, x1);
|
||||
modular_subtract(t2, z2, x1);
|
||||
modular_multiply_single(z1, t2, A24);
|
||||
modular_add(z1, z1, x1);
|
||||
modular_multiply(z1, z1, t2);
|
||||
modular_multiply(x1, x1, z2);
|
||||
modular_subtract(z2, t1, x2);
|
||||
modular_square(z2, z2);
|
||||
modular_multiply(z2, z2, u);
|
||||
modular_add(x2, x2, t1);
|
||||
modular_square(x2, x2);
|
||||
}
|
||||
|
||||
conditional_swap(x1, x2, swap);
|
||||
conditional_swap(z1, z2, swap);
|
||||
|
||||
// Retrieve affine representation
|
||||
modular_multiply_inverse(u, z1);
|
||||
modular_multiply(u, u, x1);
|
||||
|
||||
// Encode state for export
|
||||
return export_state(u);
|
||||
}
|
||||
}
|
||||
40
Userland/Libraries/LibCrypto/Curves/X448.h
Normal file
40
Userland/Libraries/LibCrypto/Curves/X448.h
Normal file
|
|
@ -0,0 +1,40 @@
|
|||
/*
|
||||
* Copyright (c) 2022, stelar7 <dudedbz@gmail.com>
|
||||
*
|
||||
* SPDX-License-Identifier: BSD-2-Clause
|
||||
*/
|
||||
|
||||
#pragma once
|
||||
|
||||
#include <AK/ByteBuffer.h>
|
||||
|
||||
namespace Crypto::Curves {
|
||||
|
||||
class X448 {
|
||||
|
||||
static constexpr u16 BITS = 448;
|
||||
static constexpr u8 BYTES = 56;
|
||||
static constexpr u8 WORDS = 14;
|
||||
static constexpr u32 A24 = 39082;
|
||||
|
||||
public:
|
||||
static ErrorOr<ByteBuffer> compute_coordinate(ReadonlyBytes a, ReadonlyBytes b);
|
||||
|
||||
private:
|
||||
static void import_state(u32* state, ReadonlyBytes data);
|
||||
static ErrorOr<ByteBuffer> export_state(u32* data);
|
||||
static void select(u32* state, u32* a, u32* b, u32 condition);
|
||||
static void set(u32* state, u32 value);
|
||||
static void copy(u32* state, u32* value);
|
||||
static void conditional_swap(u32* first, u32* second, u32 condition);
|
||||
static void modular_multiply_single(u32* state, u32* first, u32 second);
|
||||
static void modular_square(u32* state, u32* value);
|
||||
static void modular_multiply(u32* state, u32* first, u32* second);
|
||||
static void modular_add(u32* state, u32* first, u32* second);
|
||||
static void modular_subtract(u32* state, u32* first, u32* second);
|
||||
static void modular_reduce(u32* state, u32* data, u32 data_high);
|
||||
static void to_power_of_2n(u32* state, u32* value, u8 n);
|
||||
static void modular_multiply_inverse(u32* state, u32* value);
|
||||
};
|
||||
|
||||
}
|
||||
Loading…
Reference in a new issue