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LibCrypto: Add curve X448
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stelar7
Ali Mohammad Pur
parent
c8803afe3e
commit
0df7ad7493
4 changed files with 483 additions and 0 deletions
356
Userland/Libraries/LibCrypto/Curves/X448.cpp
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356
Userland/Libraries/LibCrypto/Curves/X448.cpp
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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] {};
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// Copy input to internal state
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import_state(k, input_k);
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// Set the two least significant bits of the first byte to 0, and the most significant bit of the last byte to 1
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k[0] &= 0xFFFFFFFC;
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k[13] |= 0x80000000;
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// Copy coordinate to internal state
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import_state(u, input_u);
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// Implementations MUST accept non-canonical values and process them as
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// if they had been reduced modulo the field prime.
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modular_reduce(u, u, 0);
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set(x1, 1);
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set(z1, 0);
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copy(x2, u);
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set(z2, 1);
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// Montgomery ladder
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u32 swap = 0;
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for (auto i = X448::BITS - 1; i >= 0; i--) {
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u32 b = (k[i / 32] >> (i % 32)) & 1;
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conditional_swap(x1, x2, swap ^ b);
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conditional_swap(z1, z2, swap ^ b);
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swap = b;
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modular_add(t1, x2, z2);
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modular_subtract(x2, x2, z2);
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modular_add(z2, x1, z1);
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modular_subtract(x1, x1, z1);
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modular_multiply(t1, t1, x1);
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modular_multiply(x2, x2, z2);
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modular_square(z2, z2);
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modular_square(x1, x1);
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modular_subtract(t2, z2, x1);
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modular_multiply_single(z1, t2, A24);
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modular_add(z1, z1, x1);
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modular_multiply(z1, z1, t2);
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modular_multiply(x1, x1, z2);
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modular_subtract(z2, t1, x2);
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modular_square(z2, z2);
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modular_multiply(z2, z2, u);
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modular_add(x2, x2, t1);
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modular_square(x2, x2);
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}
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conditional_swap(x1, x2, swap);
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conditional_swap(z1, z2, swap);
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// Retrieve affine representation
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modular_multiply_inverse(u, z1);
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modular_multiply(u, u, x1);
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// Encode state for export
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return export_state(u);
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}
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}
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