/* * Copyright (c) 2022, stelar7 * * SPDX-License-Identifier: BSD-2-Clause */ #include #include #include #include namespace Crypto::Curves { static constexpr u16 BITS = 448; static constexpr u8 BYTES = 56; static constexpr u8 WORDS = 14; static constexpr u32 A24 = 39082; static void import_state(u32* state, ReadonlyBytes data) { for (auto i = 0; i < WORDS; i++) { u32 value = ByteReader::load32(data.offset_pointer(sizeof(u32) * i)); state[i] = AK::convert_between_host_and_little_endian(value); } } static ErrorOr export_state(u32* data) { auto buffer = TRY(ByteBuffer::create_uninitialized(BYTES)); for (auto i = 0; i < WORDS; i++) { u32 value = AK::convert_between_host_and_little_endian(data[i]); ByteReader::store(buffer.offset_pointer(sizeof(u32) * i), value); } return buffer; } static void select(u32* state, u32* a, u32* b, u32 condition) { // If B < (2^448 - 2^224 + 1) then R = B, else R = A u32 mask = condition - 1; for (auto i = 0; i < WORDS; i++) { state[i] = (a[i] & mask) | (b[i] & ~mask); } } static void set(u32* state, u32 value) { state[0] = value; for (auto i = 1; i < WORDS; i++) { state[i] = 0; } } static void copy(u32* state, u32* value) { for (auto i = 0; i < WORDS; i++) { state[i] = value[i]; } } static void conditional_swap(u32* first, u32* second, u32 condition) { u32 mask = ~condition + 1; for (auto i = 0; i < WORDS; i++) { u32 temp = mask & (first[i] ^ second[i]); first[i] ^= temp; second[i] ^= temp; } } static void modular_reduce(u32* state, u32* data, u32 a_high) { u64 temp = 1; u32 other[WORDS]; // Compute B = A - (2^448 - 2^224 - 1) for (auto i = 0; i < WORDS / 2; i++) { temp += data[i]; other[i] = temp & 0xFFFFFFFF; temp >>= 32; } temp += 1; for (auto i = 7; i < WORDS; i++) { temp += data[i]; other[i] = temp & 0xFFFFFFFF; temp >>= 32; } auto condition = (a_high + (u32)temp - 1) & 1; select(state, other, data, condition); } static void modular_multiply_single(u32* state, u32* first, u32 second) { // Compute R = (A * B) mod p u64 temp = 0; u64 carry = 0; u32 output[WORDS]; for (auto i = 0; i < WORDS; i++) { temp += (u64)first[i] * second; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } // Fast modular reduction carry = temp; for (auto i = 0; i < WORDS / 2; i++) { temp += output[i]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } temp += carry; for (auto i = WORDS / 2; i < WORDS; i++) { temp += output[i]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } modular_reduce(state, output, (u32)temp); } static void modular_multiply(u32* state, u32* first, u32* second) { // Compute R = (A * B) mod p u64 temp = 0; u64 carry = 0; u32 output[WORDS * 2]; // Comba's method for (auto i = 0; i < WORDS * 2; i++) { if (i < 14) { for (auto j = 0; j <= i; j++) { temp += (u64)first[j] * second[i - j]; carry += temp >> 32; temp &= 0xFFFFFFFF; } } else { for (auto j = i - 13; j < WORDS; j++) { temp += (u64)first[j] * second[i - j]; carry += temp >> 32; temp &= 0xFFFFFFFF; } } output[i] = temp & 0xFFFFFFFF; temp = carry & 0xFFFFFFFF; carry >>= 32; } // Fast modular reduction (first pass) temp = 0; for (auto i = 0; i < WORDS / 2; i++) { temp += output[i]; temp += output[i + 14]; temp += output[i + 21]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } for (auto i = WORDS / 2; i < WORDS; i++) { temp += output[i]; temp += output[i + 7]; temp += output[i + 14]; temp += output[i + 14]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } // Fast modular reduction (second pass) carry = temp; for (auto i = 0; i < WORDS / 2; i++) { temp += output[i]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } temp += carry; for (auto i = WORDS / 2; i < WORDS; i++) { temp += output[i]; output[i] = temp & 0xFFFFFFFF; temp >>= 32; } modular_reduce(state, output, (u32)temp); } static void modular_square(u32* state, u32* value) { // Compute R = (A ^ 2) mod p modular_multiply(state, value, value); } static void modular_add(u32* state, u32* first, u32* second) { u64 temp = 0; // Compute R = A + B for (auto i = 0; i < WORDS; i++) { temp += first[i]; temp += second[i]; state[i] = temp & 0xFFFFFFFF; temp >>= 32; } modular_reduce(state, state, (u32)temp); } static void modular_subtract(u32* state, u32* first, u32* second) { i64 temp = -1; // Compute R = A + (2^448 - 2^224 - 1) - B for (auto i = 0; i < 7; i++) { temp += first[i]; temp -= second[i]; state[i] = temp & 0xFFFFFFFF; temp >>= 32; } temp -= 1; for (auto i = 7; i < 14; i++) { temp += first[i]; temp -= second[i]; state[i] = temp & 0xFFFFFFFF; temp >>= 32; } temp += 1; modular_reduce(state, state, (u32)temp); } static void to_power_of_2n(u32* state, u32* value, u8 n) { // Compute R = (A ^ (2^n)) mod p modular_square(state, value); for (auto i = 1; i < n; i++) { modular_square(state, state); } } static void modular_multiply_inverse(u32* state, u32* value) { // Compute R = A^-1 mod p u32 u[WORDS]; u32 v[WORDS]; modular_square(u, value); modular_multiply(u, u, value); modular_square(u, u); modular_multiply(v, u, value); to_power_of_2n(u, v, 3); modular_multiply(v, u, v); to_power_of_2n(u, v, 6); modular_multiply(u, u, v); modular_square(u, u); modular_multiply(v, u, value); to_power_of_2n(u, v, 13); modular_multiply(u, u, v); modular_square(u, u); modular_multiply(v, u, value); to_power_of_2n(u, v, 27); modular_multiply(u, u, v); modular_square(u, u); modular_multiply(v, u, value); to_power_of_2n(u, v, 55); modular_multiply(u, u, v); modular_square(u, u); modular_multiply(v, u, value); to_power_of_2n(u, v, 111); modular_multiply(v, u, v); modular_square(u, v); modular_multiply(u, u, value); to_power_of_2n(u, u, 223); modular_multiply(u, u, v); modular_square(u, u); modular_square(u, u); modular_multiply(state, u, value); } ErrorOr X448::generate_private_key() { auto buffer = TRY(ByteBuffer::create_uninitialized(BYTES)); fill_with_random(buffer.data(), buffer.size()); return buffer; } ErrorOr X448::generate_public_key(ReadonlyBytes a) { u8 generator[BYTES] { 5 }; return compute_coordinate(a, { generator, BYTES }); } // https://datatracker.ietf.org/doc/html/rfc7748#section-5 ErrorOr X448::compute_coordinate(ReadonlyBytes input_k, ReadonlyBytes input_u) { u32 k[WORDS] {}; u32 u[WORDS] {}; u32 x1[WORDS] {}; u32 x2[WORDS] {}; u32 z1[WORDS] {}; u32 z2[WORDS] {}; u32 t1[WORDS] {}; u32 t2[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 = 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); } ErrorOr X448::derive_premaster_key(ReadonlyBytes shared_point) { VERIFY(shared_point.size() == BYTES); ByteBuffer premaster_key = TRY(ByteBuffer::copy(shared_point)); return premaster_key; } }