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-rw-r--r--Userland/Libraries/LibCrypto/Curves/X448.cpp356
1 files changed, 356 insertions, 0 deletions
diff --git a/Userland/Libraries/LibCrypto/Curves/X448.cpp b/Userland/Libraries/LibCrypto/Curves/X448.cpp
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+++ b/Userland/Libraries/LibCrypto/Curves/X448.cpp
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+/*
+ * Copyright (c) 2022, stelar7 <dudedbz@gmail.com>
+ *
+ * SPDX-License-Identifier: BSD-2-Clause
+ */
+
+#include <AK/ByteReader.h>
+#include <AK/Endian.h>
+#include <LibCrypto/Curves/X448.h>
+
+namespace Crypto::Curves {
+
+void X448::import_state(u32* state, ReadonlyBytes data)
+{
+ for (auto i = 0; i < X448::WORDS; i++) {
+ u32 value = ByteReader::load32(data.offset_pointer(sizeof(u32) * i));
+ state[i] = AK::convert_between_host_and_little_endian(value);
+ }
+}
+
+ErrorOr<ByteBuffer> X448::export_state(u32* data)
+{
+ auto buffer = TRY(ByteBuffer::create_uninitialized(X448::BYTES));
+
+ for (auto i = 0; i < X448::WORDS; i++) {
+ u32 value = AK::convert_between_host_and_little_endian(data[i]);
+ ByteReader::store(buffer.offset_pointer(sizeof(u32) * i), value);
+ }
+
+ return buffer;
+}
+
+void X448::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 < X448::WORDS; i++) {
+ state[i] = (a[i] & mask) | (b[i] & ~mask);
+ }
+}
+
+void X448::set(u32* state, u32 value)
+{
+ state[0] = value;
+
+ for (auto i = 1; i < X448::WORDS; i++) {
+ state[i] = 0;
+ }
+}
+
+void X448::copy(u32* state, u32* value)
+{
+ for (auto i = 0; i < X448::WORDS; i++) {
+ state[i] = value[i];
+ }
+}
+
+void X448::conditional_swap(u32* first, u32* second, u32 condition)
+{
+ u32 mask = ~condition + 1;
+ for (auto i = 0; i < X448::WORDS; i++) {
+ u32 temp = mask & (first[i] ^ second[i]);
+ first[i] ^= temp;
+ second[i] ^= temp;
+ }
+}
+
+void X448::modular_multiply_single(u32* state, u32* first, u32 second)
+{
+ // Compute R = (A * B) mod p
+ u64 temp = 0;
+ u64 carry = 0;
+ u32 output[X448::WORDS];
+
+ for (auto i = 0; i < X448::WORDS; i++) {
+ temp += (u64)first[i] * second;
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ // Fast modular reduction
+ carry = temp;
+ for (auto i = 0; i < X448::WORDS / 2; i++) {
+ temp += output[i];
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ temp += carry;
+ for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
+ temp += output[i];
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ modular_reduce(state, output, (u32)temp);
+}
+
+void X448::modular_square(u32* state, u32* value)
+{
+ // Compute R = (A ^ 2) mod p
+ modular_multiply(state, value, value);
+}
+
+void X448::modular_multiply(u32* state, u32* first, u32* second)
+{
+ // Compute R = (A * B) mod p
+
+ u64 temp = 0;
+ u64 carry = 0;
+ u32 output[X448::WORDS * 2];
+
+ // Comba's method
+ for (auto i = 0; i < X448::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 < X448::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 < X448::WORDS / 2; i++) {
+ temp += output[i];
+ temp += output[i + 14];
+ temp += output[i + 21];
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ for (auto i = X448::WORDS / 2; i < X448::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 < X448::WORDS / 2; i++) {
+ temp += output[i];
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ temp += carry;
+ for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
+ temp += output[i];
+ output[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ modular_reduce(state, output, (u32)temp);
+}
+
+void X448::modular_add(u32* state, u32* first, u32* second)
+{
+ u64 temp = 0;
+
+ // Compute R = A + B
+ for (auto i = 0; i < X448::WORDS; i++) {
+ temp += first[i];
+ temp += second[i];
+ state[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ modular_reduce(state, state, (u32)temp);
+}
+
+void X448::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);
+}
+
+void X448::modular_reduce(u32* state, u32* data, u32 a_high)
+{
+ u64 temp = 1;
+ u32 other[X448::WORDS];
+
+ // Compute B = A - (2^448 - 2^224 - 1)
+ for (auto i = 0; i < X448::WORDS / 2; i++) {
+ temp += data[i];
+ other[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ temp += 1;
+
+ for (auto i = 7; i < X448::WORDS; i++) {
+ temp += data[i];
+ other[i] = temp & 0xFFFFFFFF;
+ temp >>= 32;
+ }
+
+ auto condition = (a_high + (u32)temp - 1) & 1;
+ select(state, other, data, condition);
+}
+
+void X448::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);
+ }
+}
+
+void X448::modular_multiply_inverse(u32* state, u32* value)
+{
+ // Compute R = A^-1 mod p
+ u32 u[X448::WORDS];
+ u32 v[X448::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);
+}
+
+// https://datatracker.ietf.org/doc/html/rfc7748#section-5
+ErrorOr<ByteBuffer> X448::compute_coordinate(ReadonlyBytes input_k, ReadonlyBytes input_u)
+{
+ u32 k[X448::WORDS] {};
+ u32 u[X448::WORDS] {};
+ u32 x1[X448::WORDS] {};
+ u32 x2[X448::WORDS] {};
+ u32 z1[X448::WORDS] {};
+ u32 z2[X448::WORDS] {};
+ u32 t1[X448::WORDS] {};
+ 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);
+}
+}
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