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https://github.com/RGBCube/serenity
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LibCrypto: Move all elliptic curve private methods into .cpp
All the elliptic curve implementations had a long list of private methods which were all stored in a single .cpp file. Now we simply use static methods instead.
This commit is contained in:
Michiel Visser
Ali Mohammad Pur
parent
596391a4ee
commit
e07ec02470
6 changed files with 171 additions and 220 deletions
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@ -14,6 +14,14 @@
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namespace Crypto::Curves {
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static constexpr u256 REDUCE_PRIME { u128 { 0x0000000000000001ull, 0xffffffff00000000ull }, u128 { 0xffffffffffffffffull, 0x00000000fffffffe } };
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static constexpr u256 REDUCE_ORDER { u128 { 0x0c46353d039cdaafull, 0x4319055258e8617bull }, u128 { 0x0000000000000000ull, 0x00000000ffffffff } };
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static constexpr u256 PRIME_INVERSE_MOD_R { u128 { 0x0000000000000001ull, 0x0000000100000000ull }, u128 { 0x0000000000000000ull, 0xffffffff00000002ull } };
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static constexpr u256 PRIME { u128 { 0xffffffffffffffffull, 0x00000000ffffffffull }, u128 { 0x0000000000000000ull, 0xffffffff00000001ull } };
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static constexpr u256 R2_MOD_PRIME { u128 { 0x0000000000000003ull, 0xfffffffbffffffffull }, u128 { 0xfffffffffffffffeull, 0x00000004fffffffdull } };
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static constexpr u256 ONE { 1u };
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static constexpr u256 B_MONTGOMERY { u128 { 0xd89cdf6229c4bddfull, 0xacf005cd78843090ull }, u128 { 0xe5a220abf7212ed6ull, 0xdc30061d04874834ull } };
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static u256 import_big_endian(ReadonlyBytes data)
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{
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VERIFY(data.size() == 32);
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@ -53,7 +61,7 @@ static u512 multiply(u256 const& left, u256 const& right)
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return { result.low, result.high };
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}
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u256 SECP256r1::modular_reduce(u256 const& value)
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static u256 modular_reduce(u256 const& value)
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{
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// Add -prime % 2^256 = 2^224-2^192-2^96+1
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bool carry = false;
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@ -63,7 +71,7 @@ u256 SECP256r1::modular_reduce(u256 const& value)
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return select(value, other, carry);
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}
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u256 SECP256r1::modular_reduce_order(u256 const& value)
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static u256 modular_reduce_order(u256 const& value)
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{
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// Add -order % 2^256
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bool carry = false;
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@ -73,7 +81,7 @@ u256 SECP256r1::modular_reduce_order(u256 const& value)
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return select(value, other, carry);
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}
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u256 SECP256r1::modular_add(u256 const& left, u256 const& right, bool carry_in)
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static u256 modular_add(u256 const& left, u256 const& right, bool carry_in = false)
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{
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bool carry = carry_in;
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u256 output = left.addc(right, carry);
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@ -90,7 +98,7 @@ u256 SECP256r1::modular_add(u256 const& left, u256 const& right, bool carry_in)
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return output + addend;
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}
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u256 SECP256r1::modular_sub(u256 const& left, u256 const& right)
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static u256 modular_sub(u256 const& left, u256 const& right)
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{
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bool borrow = false;
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u256 output = left.subc(right, borrow);
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@ -107,7 +115,7 @@ u256 SECP256r1::modular_sub(u256 const& left, u256 const& right)
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return output - sub;
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}
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u256 SECP256r1::modular_multiply(u256 const& left, u256 const& right)
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static u256 modular_multiply(u256 const& left, u256 const& right)
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{
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// Modular multiplication using the Montgomery method: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication
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// This requires that the inputs to this function are in Montgomery form.
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@ -129,22 +137,22 @@ u256 SECP256r1::modular_multiply(u256 const& left, u256 const& right)
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return modular_add(mult.high(), mp.high(), carry);
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}
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u256 SECP256r1::modular_square(u256 const& value)
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static u256 modular_square(u256 const& value)
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{
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return modular_multiply(value, value);
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}
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u256 SECP256r1::to_montgomery(u256 const& value)
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static u256 to_montgomery(u256 const& value)
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{
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return modular_multiply(value, R2_MOD_PRIME);
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}
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u256 SECP256r1::from_montgomery(u256 const& value)
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static u256 from_montgomery(u256 const& value)
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{
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return modular_multiply(value, ONE);
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}
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u256 SECP256r1::modular_inverse(u256 const& value)
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static u256 modular_inverse(u256 const& value)
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{
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// Modular inverse modulo the curve prime can be computed using Fermat's little theorem: a^(p-2) mod p = a^-1 mod p.
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// Calculating a^(p-2) mod p can be done using the square-and-multiply exponentiation method, as p-2 is constant.
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@ -193,7 +201,7 @@ u256 SECP256r1::modular_inverse(u256 const& value)
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return result;
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}
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void SECP256r1::point_double(JacobianPoint& output_point, JacobianPoint const& point)
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static void point_double(JacobianPoint& output_point, JacobianPoint const& point)
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{
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// Based on "Point Doubling" from http://point-at-infinity.org/ecc/Prime_Curve_Jacobian_Coordinates.html
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@ -247,7 +255,7 @@ void SECP256r1::point_double(JacobianPoint& output_point, JacobianPoint const& p
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output_point.z = zp;
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}
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void SECP256r1::point_add(JacobianPoint& output_point, JacobianPoint const& point_a, JacobianPoint const& point_b)
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static void point_add(JacobianPoint& output_point, JacobianPoint const& point_a, JacobianPoint const& point_b)
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{
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// Based on "Point Addition" from http://point-at-infinity.org/ecc/Prime_Curve_Jacobian_Coordinates.html
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if (point_a.x.is_zero_constant_time() && point_a.y.is_zero_constant_time() && point_a.z.is_zero_constant_time()) {
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@ -314,7 +322,7 @@ void SECP256r1::point_add(JacobianPoint& output_point, JacobianPoint const& poin
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output_point.z = z3;
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}
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void SECP256r1::convert_jacobian_to_affine(JacobianPoint& point)
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static void convert_jacobian_to_affine(JacobianPoint& point)
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{
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u256 temp;
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// X' = X/Z^2
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@ -328,7 +336,7 @@ void SECP256r1::convert_jacobian_to_affine(JacobianPoint& point)
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point.y = modular_multiply(point.y, temp);
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}
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bool SECP256r1::is_point_on_curve(JacobianPoint const& point)
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static bool is_point_on_curve(JacobianPoint const& point)
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{
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// This check requires the point to be in Montgomery form, with Z=1
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u256 temp, temp2;
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@ -25,29 +25,6 @@ public:
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ErrorOr<ByteBuffer> generate_public_key(ReadonlyBytes a) override;
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ErrorOr<ByteBuffer> compute_coordinate(ReadonlyBytes scalar_bytes, ReadonlyBytes point_bytes) override;
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ErrorOr<ByteBuffer> derive_premaster_key(ReadonlyBytes shared_point) override;
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private:
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static u256 modular_reduce(u256 const& value);
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static u256 modular_reduce_order(u256 const& value);
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static u256 modular_add(u256 const& left, u256 const& right, bool carry_in = false);
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static u256 modular_sub(u256 const& left, u256 const& right);
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static u256 modular_multiply(u256 const& left, u256 const& right);
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static u256 modular_square(u256 const& value);
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static u256 to_montgomery(u256 const& value);
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static u256 from_montgomery(u256 const& value);
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static u256 modular_inverse(u256 const& value);
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static void point_double(JacobianPoint& output_point, JacobianPoint const& point);
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static void point_add(JacobianPoint& output_point, JacobianPoint const& point_a, JacobianPoint const& point_b);
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static void convert_jacobian_to_affine(JacobianPoint& point);
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static bool is_point_on_curve(JacobianPoint const& point);
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static constexpr u256 REDUCE_PRIME { u128 { 0x0000000000000001ull, 0xffffffff00000000ull }, u128 { 0xffffffffffffffffull, 0x00000000fffffffe } };
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static constexpr u256 REDUCE_ORDER { u128 { 0x0c46353d039cdaafull, 0x4319055258e8617bull }, u128 { 0x0000000000000000ull, 0x00000000ffffffff } };
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static constexpr u256 PRIME_INVERSE_MOD_R { u128 { 0x0000000000000001ull, 0x0000000100000000ull }, u128 { 0x0000000000000000ull, 0xffffffff00000002ull } };
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static constexpr u256 PRIME { u128 { 0xffffffffffffffffull, 0x00000000ffffffffull }, u128 { 0x0000000000000000ull, 0xffffffff00000001ull } };
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static constexpr u256 R2_MOD_PRIME { u128 { 0x0000000000000003ull, 0xfffffffbffffffffull }, u128 { 0xfffffffffffffffeull, 0x00000004fffffffdull } };
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static constexpr u256 ONE { 1u };
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static constexpr u256 B_MONTGOMERY { u128 { 0xd89cdf6229c4bddfull, 0xacf005cd78843090ull }, u128 { 0xe5a220abf7212ed6ull, 0xdc30061d04874834ull } };
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};
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}
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@ -11,19 +11,24 @@
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namespace Crypto::Curves {
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void X25519::import_state(u32* state, ReadonlyBytes data)
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static constexpr u8 BITS = 255;
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static constexpr u8 BYTES = 32;
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static constexpr u8 WORDS = 8;
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static constexpr u32 A24 = 121666;
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static void import_state(u32* state, ReadonlyBytes data)
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{
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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> X25519::export_state(u32* data)
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static ErrorOr<ByteBuffer> export_state(u32* data)
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{
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auto buffer = TRY(ByteBuffer::create_uninitialized(X25519::BYTES));
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auto buffer = TRY(ByteBuffer::create_uninitialized(BYTES));
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -31,49 +36,68 @@ ErrorOr<ByteBuffer> X25519::export_state(u32* data)
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return buffer;
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}
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void X25519::select(u32* state, u32* a, u32* b, u32 condition)
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static void select(u32* state, u32* a, u32* b, u32 condition)
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{
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// If B < (2^255 - 19) then R = B, else R = A
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u32 mask = condition - 1;
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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 X25519::set(u32* state, u32 value)
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static void 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 < X25519::WORDS; i++) {
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for (auto i = 1; i < WORDS; i++) {
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state[i] = 0;
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}
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}
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void X25519::copy(u32* state, u32* value)
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static void copy(u32* state, u32* value)
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{
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < WORDS; i++) {
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state[i] = value[i];
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}
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}
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void X25519::conditional_swap(u32* first, u32* second, u32 condition)
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static void 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 < X25519::WORDS; i++) {
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for (auto i = 0; i < 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 X25519::modular_multiply_single(u32* state, u32* first, u32 second)
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static void modular_reduce(u32* state, u32* data)
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{
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// R = A mod p
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u64 temp = 19;
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u32 other[WORDS];
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for (auto i = 0; i < 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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// Compute B = A - (2^255 - 19)
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other[7] -= 0x80000000;
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u32 mask = (other[7] & 0x80000000) >> 31;
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select(state, other, data, mask);
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}
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static void 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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u32 output[X25519::WORDS];
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u32 output[WORDS];
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -87,7 +111,7 @@ void X25519::modular_multiply_single(u32* state, u32* first, u32 second)
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output[7] &= 0x7FFFFFFF;
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// Fast modular reduction
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -96,29 +120,23 @@ void X25519::modular_multiply_single(u32* state, u32* first, u32 second)
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modular_reduce(state, output);
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}
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void X25519::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 X25519::modular_multiply(u32* state, u32* first, u32* second)
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static void 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[X25519::WORDS * 2];
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u32 output[WORDS * 2];
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// Comba's method
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for (auto i = 0; i < 16; i++) {
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if (i < X25519::WORDS) {
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if (i < WORDS) {
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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 - 7; j < X25519::WORDS; j++) {
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for (auto j = i - 7; j < 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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@ -136,7 +154,7 @@ void X25519::modular_multiply(u32* state, u32* first, u32* second)
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output[7] &= 0x7FFFFFFF;
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// Fast modular reduction 1st pass
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < WORDS; i++) {
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temp += output[i];
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temp += (u64)output[i + 8] * 38;
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output[i] = temp & 0xFFFFFFFF;
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@ -151,7 +169,7 @@ void X25519::modular_multiply(u32* state, u32* first, u32* second)
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output[7] &= 0x7FFFFFFF;
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// Fast modular reduction 2nd pass
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -160,11 +178,17 @@ void X25519::modular_multiply(u32* state, u32* first, u32* second)
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modular_reduce(state, output);
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}
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void X25519::modular_add(u32* state, u32* first, u32* second)
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static void 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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static void modular_add(u32* state, u32* first, u32* second)
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{
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// R = (A + B) mod p
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u64 temp = 0;
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -174,11 +198,11 @@ void X25519::modular_add(u32* state, u32* first, u32* second)
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modular_reduce(state, state);
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}
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void X25519::modular_subtract(u32* state, u32* first, u32* second)
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static void modular_subtract(u32* state, u32* first, u32* second)
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{
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// R = (A - B) mod p
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i64 temp = -19;
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for (auto i = 0; i < X25519::WORDS; i++) {
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for (auto i = 0; i < 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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@ -191,26 +215,7 @@ void X25519::modular_subtract(u32* state, u32* first, u32* second)
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modular_reduce(state, state);
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}
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void X25519::modular_reduce(u32* state, u32* data)
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{
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// R = A mod p
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u64 temp = 19;
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u32 other[X25519::WORDS];
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for (auto i = 0; i < X25519::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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// Compute B = A - (2^255 - 19)
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other[7] -= 0x80000000;
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|
||||
u32 mask = (other[7] & 0x80000000) >> 31;
|
||||
select(state, other, data, mask);
|
||||
}
|
||||
|
||||
void X25519::to_power_of_2n(u32* state, u32* value, u8 n)
|
||||
static void to_power_of_2n(u32* state, u32* value, u8 n)
|
||||
{
|
||||
// compute R = (A ^ (2^n)) mod p
|
||||
modular_square(state, value);
|
||||
|
|
@ -219,11 +224,11 @@ void X25519::to_power_of_2n(u32* state, u32* value, u8 n)
|
|||
}
|
||||
}
|
||||
|
||||
void X25519::modular_multiply_inverse(u32* state, u32* value)
|
||||
static void modular_multiply_inverse(u32* state, u32* value)
|
||||
{
|
||||
// Compute R = A^-1 mod p
|
||||
u32 u[X25519::WORDS];
|
||||
u32 v[X25519::WORDS];
|
||||
u32 u[WORDS];
|
||||
u32 v[WORDS];
|
||||
|
||||
// Fermat's little theorem
|
||||
modular_square(u, value);
|
||||
|
|
@ -276,14 +281,14 @@ ErrorOr<ByteBuffer> X25519::generate_public_key(ReadonlyBytes a)
|
|||
// 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] {};
|
||||
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);
|
||||
|
|
@ -310,8 +315,8 @@ ErrorOr<ByteBuffer> X25519::compute_coordinate(ReadonlyBytes input_k, ReadonlyBy
|
|||
|
||||
// Montgomery ladder
|
||||
u32 swap = 0;
|
||||
for (auto i = X25519::BITS - 1; i >= 0; i--) {
|
||||
u32 b = (k[i / X25519::BYTES] >> (i % X25519::BYTES)) & 1;
|
||||
for (auto i = BITS - 1; i >= 0; i--) {
|
||||
u32 b = (k[i / BYTES] >> (i % BYTES)) & 1;
|
||||
|
||||
conditional_swap(x1, x2, swap ^ b);
|
||||
conditional_swap(z1, z2, swap ^ b);
|
||||
|
|
|
|||
|
|
@ -12,34 +12,12 @@
|
|||
namespace Crypto::Curves {
|
||||
|
||||
class X25519 : public EllipticCurve {
|
||||
|
||||
static constexpr u8 BITS = 255;
|
||||
static constexpr u8 BYTES = 32;
|
||||
static constexpr u8 WORDS = 8;
|
||||
static constexpr u32 A24 = 121666;
|
||||
|
||||
public:
|
||||
size_t key_size() override { return BYTES; }
|
||||
size_t key_size() override { return 32; }
|
||||
ErrorOr<ByteBuffer> generate_private_key() override;
|
||||
ErrorOr<ByteBuffer> generate_public_key(ReadonlyBytes a) override;
|
||||
ErrorOr<ByteBuffer> compute_coordinate(ReadonlyBytes a, ReadonlyBytes b) override;
|
||||
ErrorOr<ByteBuffer> derive_premaster_key(ReadonlyBytes shared_point) override;
|
||||
|
||||
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);
|
||||
};
|
||||
|
||||
}
|
||||
|
|
|
|||
|
|
@ -11,19 +11,24 @@
|
|||
|
||||
namespace Crypto::Curves {
|
||||
|
||||
void X448::import_state(u32* state, ReadonlyBytes data)
|
||||
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 < X448::WORDS; i++) {
|
||||
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);
|
||||
}
|
||||
}
|
||||
|
||||
ErrorOr<ByteBuffer> X448::export_state(u32* data)
|
||||
static ErrorOr<ByteBuffer> export_state(u32* data)
|
||||
{
|
||||
auto buffer = TRY(ByteBuffer::create_uninitialized(X448::BYTES));
|
||||
auto buffer = TRY(ByteBuffer::create_uninitialized(BYTES));
|
||||
|
||||
for (auto i = 0; i < X448::WORDS; i++) {
|
||||
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);
|
||||
}
|
||||
|
|
@ -31,50 +36,74 @@ ErrorOr<ByteBuffer> X448::export_state(u32* data)
|
|||
return buffer;
|
||||
}
|
||||
|
||||
void X448::select(u32* state, u32* a, u32* b, u32 condition)
|
||||
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 < X448::WORDS; i++) {
|
||||
for (auto i = 0; i < WORDS; i++) {
|
||||
state[i] = (a[i] & mask) | (b[i] & ~mask);
|
||||
}
|
||||
}
|
||||
|
||||
void X448::set(u32* state, u32 value)
|
||||
static void set(u32* state, u32 value)
|
||||
{
|
||||
state[0] = value;
|
||||
|
||||
for (auto i = 1; i < X448::WORDS; i++) {
|
||||
for (auto i = 1; i < WORDS; i++) {
|
||||
state[i] = 0;
|
||||
}
|
||||
}
|
||||
|
||||
void X448::copy(u32* state, u32* value)
|
||||
static void copy(u32* state, u32* value)
|
||||
{
|
||||
for (auto i = 0; i < X448::WORDS; i++) {
|
||||
for (auto i = 0; i < WORDS; i++) {
|
||||
state[i] = value[i];
|
||||
}
|
||||
}
|
||||
|
||||
void X448::conditional_swap(u32* first, u32* second, u32 condition)
|
||||
static void conditional_swap(u32* first, u32* second, u32 condition)
|
||||
{
|
||||
u32 mask = ~condition + 1;
|
||||
for (auto i = 0; i < X448::WORDS; i++) {
|
||||
for (auto i = 0; i < 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)
|
||||
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[X448::WORDS];
|
||||
u32 output[WORDS];
|
||||
|
||||
for (auto i = 0; i < X448::WORDS; i++) {
|
||||
for (auto i = 0; i < WORDS; i++) {
|
||||
temp += (u64)first[i] * second;
|
||||
output[i] = temp & 0xFFFFFFFF;
|
||||
temp >>= 32;
|
||||
|
|
@ -82,14 +111,14 @@ void X448::modular_multiply_single(u32* state, u32* first, u32 second)
|
|||
|
||||
// Fast modular reduction
|
||||
carry = temp;
|
||||
for (auto i = 0; i < X448::WORDS / 2; i++) {
|
||||
for (auto i = 0; i < WORDS / 2; i++) {
|
||||
temp += output[i];
|
||||
output[i] = temp & 0xFFFFFFFF;
|
||||
temp >>= 32;
|
||||
}
|
||||
|
||||
temp += carry;
|
||||
for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
|
||||
for (auto i = WORDS / 2; i < WORDS; i++) {
|
||||
temp += output[i];
|
||||
output[i] = temp & 0xFFFFFFFF;
|
||||
temp >>= 32;
|
||||
|
|
@ -98,22 +127,16 @@ void X448::modular_multiply_single(u32* state, u32* first, u32 second)
|
|||
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)
|
||||
static void 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];
|
||||
u32 output[WORDS * 2];
|
||||
|
||||
// Comba's method
|
||||
for (auto i = 0; i < X448::WORDS * 2; i++) {
|
||||
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];
|
||||
|
|
@ -121,7 +144,7 @@ void X448::modular_multiply(u32* state, u32* first, u32* second)
|
|||
temp &= 0xFFFFFFFF;
|
||||
}
|
||||
} else {
|
||||
for (auto j = i - 13; j < X448::WORDS; j++) {
|
||||
for (auto j = i - 13; j < WORDS; j++) {
|
||||
temp += (u64)first[j] * second[i - j];
|
||||
carry += temp >> 32;
|
||||
temp &= 0xFFFFFFFF;
|
||||
|
|
@ -135,7 +158,7 @@ void X448::modular_multiply(u32* state, u32* first, u32* second)
|
|||
|
||||
// Fast modular reduction (first pass)
|
||||
temp = 0;
|
||||
for (auto i = 0; i < X448::WORDS / 2; i++) {
|
||||
for (auto i = 0; i < WORDS / 2; i++) {
|
||||
temp += output[i];
|
||||
temp += output[i + 14];
|
||||
temp += output[i + 21];
|
||||
|
|
@ -143,7 +166,7 @@ void X448::modular_multiply(u32* state, u32* first, u32* second)
|
|||
temp >>= 32;
|
||||
}
|
||||
|
||||
for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
|
||||
for (auto i = WORDS / 2; i < WORDS; i++) {
|
||||
temp += output[i];
|
||||
temp += output[i + 7];
|
||||
temp += output[i + 14];
|
||||
|
|
@ -154,14 +177,14 @@ void X448::modular_multiply(u32* state, u32* first, u32* second)
|
|||
|
||||
// Fast modular reduction (second pass)
|
||||
carry = temp;
|
||||
for (auto i = 0; i < X448::WORDS / 2; i++) {
|
||||
for (auto i = 0; i < WORDS / 2; i++) {
|
||||
temp += output[i];
|
||||
output[i] = temp & 0xFFFFFFFF;
|
||||
temp >>= 32;
|
||||
}
|
||||
|
||||
temp += carry;
|
||||
for (auto i = X448::WORDS / 2; i < X448::WORDS; i++) {
|
||||
for (auto i = WORDS / 2; i < WORDS; i++) {
|
||||
temp += output[i];
|
||||
output[i] = temp & 0xFFFFFFFF;
|
||||
temp >>= 32;
|
||||
|
|
@ -170,12 +193,18 @@ void X448::modular_multiply(u32* state, u32* first, u32* second)
|
|||
modular_reduce(state, output, (u32)temp);
|
||||
}
|
||||
|
||||
void X448::modular_add(u32* state, u32* first, u32* second)
|
||||
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 < X448::WORDS; i++) {
|
||||
for (auto i = 0; i < WORDS; i++) {
|
||||
temp += first[i];
|
||||
temp += second[i];
|
||||
state[i] = temp & 0xFFFFFFFF;
|
||||
|
|
@ -185,7 +214,7 @@ void X448::modular_add(u32* state, u32* first, u32* second)
|
|||
modular_reduce(state, state, (u32)temp);
|
||||
}
|
||||
|
||||
void X448::modular_subtract(u32* state, u32* first, u32* second)
|
||||
static void modular_subtract(u32* state, u32* first, u32* second)
|
||||
{
|
||||
i64 temp = -1;
|
||||
|
||||
|
|
@ -211,31 +240,7 @@ void X448::modular_subtract(u32* state, u32* first, u32* second)
|
|||
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)
|
||||
static void to_power_of_2n(u32* state, u32* value, u8 n)
|
||||
{
|
||||
// Compute R = (A ^ (2^n)) mod p
|
||||
modular_square(state, value);
|
||||
|
|
@ -244,11 +249,11 @@ void X448::to_power_of_2n(u32* state, u32* value, u8 n)
|
|||
}
|
||||
}
|
||||
|
||||
void X448::modular_multiply_inverse(u32* state, u32* value)
|
||||
static void modular_multiply_inverse(u32* state, u32* value)
|
||||
{
|
||||
// Compute R = A^-1 mod p
|
||||
u32 u[X448::WORDS];
|
||||
u32 v[X448::WORDS];
|
||||
u32 u[WORDS];
|
||||
u32 v[WORDS];
|
||||
|
||||
modular_square(u, value);
|
||||
modular_multiply(u, u, value);
|
||||
|
|
@ -299,14 +304,14 @@ ErrorOr<ByteBuffer> X448::generate_public_key(ReadonlyBytes a)
|
|||
// 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] {};
|
||||
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);
|
||||
|
|
@ -329,7 +334,7 @@ ErrorOr<ByteBuffer> X448::compute_coordinate(ReadonlyBytes input_k, ReadonlyByte
|
|||
|
||||
// Montgomery ladder
|
||||
u32 swap = 0;
|
||||
for (auto i = X448::BITS - 1; i >= 0; i--) {
|
||||
for (auto i = BITS - 1; i >= 0; i--) {
|
||||
u32 b = (k[i / 32] >> (i % 32)) & 1;
|
||||
|
||||
conditional_swap(x1, x2, swap ^ b);
|
||||
|
|
|
|||
|
|
@ -12,34 +12,12 @@
|
|||
namespace Crypto::Curves {
|
||||
|
||||
class X448 : public EllipticCurve {
|
||||
|
||||
static constexpr u16 BITS = 448;
|
||||
static constexpr u8 BYTES = 56;
|
||||
static constexpr u8 WORDS = 14;
|
||||
static constexpr u32 A24 = 39082;
|
||||
|
||||
public:
|
||||
size_t key_size() override { return BYTES; }
|
||||
size_t key_size() override { return 56; }
|
||||
ErrorOr<ByteBuffer> generate_private_key() override;
|
||||
ErrorOr<ByteBuffer> generate_public_key(ReadonlyBytes a) override;
|
||||
ErrorOr<ByteBuffer> compute_coordinate(ReadonlyBytes a, ReadonlyBytes b) override;
|
||||
ErrorOr<ByteBuffer> derive_premaster_key(ReadonlyBytes shared_point) override;
|
||||
|
||||
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…
Add table
Add a link
Reference in a new issue