LibCrypto: Add curve x25519

Tests/LibCrypto/CMakeLists.txt

@@ -2,6 +2,7 @@ set(TEST_SOURCES
     TestAES.cpp
     TestBigInteger.cpp
     TestChecksum.cpp
+    TestCurves.cpp
     TestHash.cpp
     TestHMAC.cpp
     TestRSA.cpp

Tests/LibCrypto/TestCurves.cpp

@@ -0,0 +1,76 @@
+/*
+ * Copyright (c) 2022, stelar7 <dudedbz@gmail.com>
+ *
+ * SPDX-License-Identifier: BSD-2-Clause
+ */
+
+#include <AK/ByteBuffer.h>
+#include <LibCrypto/Curves/X25519.h>
+#include <LibTest/TestCase.h>
+
+TEST_CASE(test_x25519)
+{
+    // https://datatracker.ietf.org/doc/html/rfc7748#section-6.1
+    u8 alice_private_key_data[32] {
+        0x77, 0x07, 0x6d, 0x0a, 0x73, 0x18, 0xa5, 0x7d,
+        0x3c, 0x16, 0xc1, 0x72, 0x51, 0xb2, 0x66, 0x45,
+        0xdf, 0x4c, 0x2f, 0x87, 0xeb, 0xc0, 0x99, 0x2a,
+        0xb1, 0x77, 0xfb, 0xa5, 0x1d, 0xb9, 0x2c, 0x2a
+    };
+
+    u8 alice_public_key_data[32] {
+        0x85, 0x20, 0xf0, 0x09, 0x89, 0x30, 0xa7, 0x54,
+        0x74, 0x8b, 0x7d, 0xdc, 0xb4, 0x3e, 0xf7, 0x5a,
+        0x0d, 0xbf, 0x3a, 0x0d, 0x26, 0x38, 0x1a, 0xf4,
+        0xeb, 0xa4, 0xa9, 0x8e, 0xaa, 0x9b, 0x4e, 0x6a
+    };
+
+    u8 bob_private_key_data[32] {
+        0x5d, 0xab, 0x08, 0x7e, 0x62, 0x4a, 0x8a, 0x4b,
+        0x79, 0xe1, 0x7f, 0x8b, 0x83, 0x80, 0x0e, 0xe6,
+        0x6f, 0x3b, 0xb1, 0x29, 0x26, 0x18, 0xb6, 0xfd,
+        0x1c, 0x2f, 0x8b, 0x27, 0xff, 0x88, 0xe0, 0xeb
+    };
+
+    u8 bob_public_key_data[32] {
+        0xde, 0x9e, 0xdb, 0x7d, 0x7b, 0x7d, 0xc1, 0xb4,
+        0xd3, 0x5b, 0x61, 0xc2, 0xec, 0xe4, 0x35, 0x37,
+        0x3f, 0x83, 0x43, 0xc8, 0x5b, 0x78, 0x67, 0x4d,
+        0xad, 0xfc, 0x7e, 0x14, 0x6f, 0x88, 0x2b, 0x4f
+    };
+
+    u8 shared_secret_data[32] {
+        0x4a, 0x5d, 0x9d, 0x5b, 0xa4, 0xce, 0x2d, 0xe1,
+        0x72, 0x8e, 0x3b, 0xf4, 0x80, 0x35, 0x0f, 0x25,
+        0xe0, 0x7e, 0x21, 0xc9, 0x47, 0xd1, 0x9e, 0x33,
+        0x76, 0xf0, 0x9b, 0x3c, 0x1e, 0x16, 0x17, 0x42
+    };
+
+    u8 coordinate_data[32] {
+        0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+    };
+
+    ReadonlyBytes coordinate { coordinate_data, 32 };
+    ReadonlyBytes alice_public_key { alice_public_key_data, 32 };
+    ReadonlyBytes alice_private_key { alice_private_key_data, 32 };
+    ReadonlyBytes bob_public_key { bob_public_key_data, 32 };
+    ReadonlyBytes bob_private_key { bob_private_key_data, 32 };
+    ReadonlyBytes shared_secret { shared_secret_data, 32 };
+
+    auto generated_alice_public = MUST(Crypto::Curves::X25519::compute_coordinate(alice_private_key, coordinate));
+    EXPECT_EQ(alice_public_key, generated_alice_public);
+
+    auto generated_bob_public = MUST(Crypto::Curves::X25519::compute_coordinate(bob_private_key, coordinate));
+    EXPECT_EQ(bob_public_key, generated_bob_public);
+
+    auto shared_alice = MUST(Crypto::Curves::X25519::compute_coordinate(alice_private_key, bob_public_key));
+    EXPECT_EQ(shared_alice, shared_secret);
+
+    auto shared_bob = MUST(Crypto::Curves::X25519::compute_coordinate(bob_private_key, alice_public_key));
+    EXPECT_EQ(shared_bob, shared_secret);
+
+    EXPECT_EQ(shared_alice, shared_bob);
+}

Userland/Libraries/LibCrypto/CMakeLists.txt

@@ -17,6 +17,7 @@ set(SOURCES
     Checksum/Adler32.cpp
     Checksum/CRC32.cpp
     Cipher/AES.cpp
+    Curves/X25519.cpp
     Hash/MD5.cpp
     Hash/SHA1.cpp
     Hash/SHA2.cpp

Userland/Libraries/LibCrypto/Curves/X25519.cpp

@@ -0,0 +1,337 @@
+/*
+ * Copyright (c) 2022, stelar7 <dudedbz@gmail.com>
+ *
+ * SPDX-License-Identifier: BSD-2-Clause
+ */
+
+#include <AK/ByteReader.h>
+#include <AK/Endian.h>
+#include <LibCrypto/Curves/X25519.h>
+
+namespace Crypto::Curves {
+
+void X25519::import_state(u32* state, ReadonlyBytes data)
+{
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        u32 value = ByteReader::load32(data.offset_pointer(sizeof(u32) * i));
+        state[i] = AK::convert_between_host_and_little_endian(value);
+    }
+}
+
+ErrorOr<ByteBuffer> X25519::export_state(u32* data)
+{
+    auto buffer = TRY(ByteBuffer::create_uninitialized(X25519::BYTES));
+
+    for (auto i = 0; i < X25519::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 X25519::select(u32* state, u32* a, u32* b, u32 condition)
+{
+    // If B < (2^255 - 19) then R = B, else R = A
+    u32 mask = condition - 1;
+
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        state[i] = (a[i] & mask) | (b[i] & ~mask);
+    }
+}
+
+void X25519::set(u32* state, u32 value)
+{
+    state[0] = value;
+
+    for (auto i = 1; i < X25519::WORDS; i++) {
+        state[i] = 0;
+    }
+}
+
+void X25519::copy(u32* state, u32* value)
+{
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        state[i] = value[i];
+    }
+}
+
+void X25519::conditional_swap(u32* first, u32* second, u32 condition)
+{
+    u32 mask = ~condition + 1;
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        u32 temp = mask & (first[i] ^ second[i]);
+        first[i] ^= temp;
+        second[i] ^= temp;
+    }
+}
+
+void X25519::modular_multiply_single(u32* state, u32* first, u32 second)
+{
+    // Compute R = (A * B) mod p
+    u64 temp = 0;
+    u32 output[X25519::WORDS];
+
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += (u64)first[i] * second;
+        output[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    // Reduce bit 256 (2^256 = 38 mod p)
+    temp *= 38;
+    // Reduce bit 255 (2^255 = 19 mod p)
+    temp += (output[7] >> 31) * 19;
+    // Mask the most significant bit
+    output[7] &= 0x7FFFFFFF;
+
+    // Fast modular reduction
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += output[i];
+        output[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    modular_reduce(state, output);
+}
+
+void X25519::modular_square(u32* state, u32* value)
+{
+    // Compute R = (A ^ 2) mod p
+    modular_multiply(state, value, value);
+}
+
+void X25519::modular_multiply(u32* state, u32* first, u32* second)
+{
+    // Compute R = (A * B) mod p
+    u64 temp = 0;
+    u64 carry = 0;
+    u32 output[X25519::WORDS * 2];
+
+    // Comba's method
+    for (auto i = 0; i < 16; i++) {
+        if (i < X25519::WORDS) {
+            for (auto j = 0; j <= i; j++) {
+                temp += (u64)first[j] * second[i - j];
+                carry += temp >> 32;
+                temp &= 0xFFFFFFFF;
+            }
+        } else {
+            for (auto j = i - 7; j < X25519::WORDS; j++) {
+                temp += (u64)first[j] * second[i - j];
+                carry += temp >> 32;
+                temp &= 0xFFFFFFFF;
+            }
+        }
+
+        output[i] = temp & 0xFFFFFFFF;
+        temp = carry & 0xFFFFFFFF;
+        carry >>= 32;
+    }
+
+    // Reduce bit 255 (2^255 = 19 mod p)
+    temp = (output[7] >> 31) * 19;
+    // Mask the most significant bit
+    output[7] &= 0x7FFFFFFF;
+
+    // Fast modular reduction 1st pass
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += output[i];
+        temp += (u64)output[i + 8] * 38;
+        output[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    // Reduce bit 256 (2^256 = 38 mod p)
+    temp *= 38;
+    // Reduce bit 255 (2^255 = 19 mod p)
+    temp += (output[7] >> 31) * 19;
+    // Mask the most significant bit
+    output[7] &= 0x7FFFFFFF;
+
+    // Fast modular reduction 2nd pass
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += output[i];
+        output[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    modular_reduce(state, output);
+}
+
+void X25519::modular_add(u32* state, u32* first, u32* second)
+{
+    // R = (A + B) mod p
+    u64 temp = 0;
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += first[i];
+        temp += second[i];
+        state[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    modular_reduce(state, state);
+}
+
+void X25519::modular_subtract(u32* state, u32* first, u32* second)
+{
+    // R = (A - B) mod p
+    i64 temp = -19;
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += first[i];
+        temp -= second[i];
+        state[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    // Compute R = A + (2^255 - 19) - B
+    state[7] += 0x80000000;
+
+    modular_reduce(state, state);
+}
+
+void X25519::modular_reduce(u32* state, u32* data)
+{
+    // R = A mod p
+    u64 temp = 19;
+    u32 other[X25519::WORDS];
+
+    for (auto i = 0; i < X25519::WORDS; i++) {
+        temp += data[i];
+        other[i] = temp & 0xFFFFFFFF;
+        temp >>= 32;
+    }
+
+    // Compute B = A - (2^255 - 19)
+    other[7] -= 0x80000000;
+
+    u32 mask = (other[7] & 0x80000000) >> 31;
+    select(state, other, data, mask);
+}
+
+void X25519::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 X25519::modular_multiply_inverse(u32* state, u32* value)
+{
+    // Compute R = A^-1 mod p
+    u32 u[X25519::WORDS];
+    u32 v[X25519::WORDS];
+
+    // Fermat's little theorem
+    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(u, u, v);
+    modular_square(u, u);
+    modular_multiply(v, u, value);
+    to_power_of_2n(u, v, 7);
+    modular_multiply(u, u, v);
+    modular_square(u, u);
+    modular_multiply(v, u, value);
+    to_power_of_2n(u, v, 15);
+    modular_multiply(u, u, v);
+    modular_square(u, u);
+    modular_multiply(v, u, value);
+    to_power_of_2n(u, v, 31);
+    modular_multiply(v, u, v);
+    to_power_of_2n(u, v, 62);
+    modular_multiply(u, u, v);
+    modular_square(u, u);
+    modular_multiply(v, u, value);
+    to_power_of_2n(u, v, 125);
+    modular_multiply(u, u, v);
+    modular_square(u, u);
+    modular_square(u, u);
+    modular_multiply(u, u, value);
+    modular_square(u, u);
+    modular_square(u, u);
+    modular_multiply(u, u, value);
+    modular_square(u, u);
+    modular_multiply(state, u, value);
+}
+
+// https://datatracker.ietf.org/doc/html/rfc7748#section-5
+ErrorOr<ByteBuffer> X25519::compute_coordinate(ReadonlyBytes input_k, ReadonlyBytes input_u)
+{
+    u32 k[X25519::WORDS] {};
+    u32 u[X25519::WORDS] {};
+    u32 x1[X25519::WORDS] {};
+    u32 x2[X25519::WORDS] {};
+    u32 z1[X25519::WORDS] {};
+    u32 z2[X25519::WORDS] {};
+    u32 t1[X25519::WORDS] {};
+    u32 t2[X25519::WORDS] {};
+
+    // Copy input to internal state
+    import_state(k, input_k);
+
+    // Set the three least significant bits of the first byte and the most significant bit of the last to zero,
+    // set the second most significant bit of the last byte to 1
+    k[0] &= 0xFFFFFFF8;
+    k[7] &= 0x7FFFFFFF;
+    k[7] |= 0x40000000;
+
+    // Copy coordinate to internal state
+    import_state(u, input_u);
+    // mask the most significant bit in the final byte.
+    u[7] &= 0x7FFFFFFF;
+
+    // Implementations MUST accept non-canonical values and process them as
+    // if they had been reduced modulo the field prime.
+    modular_reduce(u, u);
+
+    set(x1, 1);
+    set(z1, 0);
+    copy(x2, u);
+    set(z2, 1);
+
+    // Montgomery ladder
+    u32 swap = 0;
+    for (auto i = X25519::BITS - 1; i >= 0; i--) {
+        u32 b = (k[i / X25519::BYTES] >> (i % X25519::BYTES)) & 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);
+}
+}

Userland/Libraries/LibCrypto/Curves/X25519.h

@@ -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 X25519 {
+
+    static constexpr u8 BITS = 255;
+    static constexpr u8 BYTES = 32;
+    static constexpr u8 WORDS = 8;
+    static constexpr u32 A24 = 121666;
+
+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);
+    static void to_power_of_2n(u32* state, u32* value, u8 n);
+    static void modular_multiply_inverse(u32* state, u32* value);
+};
+
+}