| /* |
| * Copyright 2017-2019 The OpenSSL Project Authors. All Rights Reserved. |
| * Copyright 2015-2016 Cryptography Research, Inc. |
| * |
| * Licensed under the OpenSSL license (the "License"). You may not use |
| * this file except in compliance with the License. You can obtain a copy |
| * in the file LICENSE in the source distribution or at |
| * https://www.openssl.org/source/license.html |
| * |
| * Originally written by Mike Hamburg |
| */ |
| |
| #ifndef HEADER_POINT_448_H |
| # define HEADER_POINT_448_H |
| |
| # include "curve448utils.h" |
| # include "field.h" |
| |
| /* Comb config: number of combs, n, t, s. */ |
| #define COMBS_N 5 |
| #define COMBS_T 5 |
| #define COMBS_S 18 |
| |
| /* Projective Niels coordinates */ |
| typedef struct { |
| gf a, b, c; |
| } niels_s, niels_t[1]; |
| typedef struct { |
| niels_t n; |
| gf z; |
| } pniels_t[1]; |
| |
| /* Precomputed base */ |
| struct curve448_precomputed_s { |
| niels_t table[COMBS_N << (COMBS_T - 1)]; |
| }; |
| |
| # define C448_SCALAR_LIMBS ((446-1)/C448_WORD_BITS+1) |
| |
| /* The number of bits in a scalar */ |
| # define C448_SCALAR_BITS 446 |
| |
| /* Number of bytes in a serialized scalar. */ |
| # define C448_SCALAR_BYTES 56 |
| |
| /* X448 encoding ratio. */ |
| # define X448_ENCODE_RATIO 2 |
| |
| /* Number of bytes in an x448 public key */ |
| # define X448_PUBLIC_BYTES 56 |
| |
| /* Number of bytes in an x448 private key */ |
| # define X448_PRIVATE_BYTES 56 |
| |
| /* Twisted Edwards extended homogeneous coordinates */ |
| typedef struct curve448_point_s { |
| gf x, y, z, t; |
| } curve448_point_t[1]; |
| |
| /* Precomputed table based on a point. Can be trivial implementation. */ |
| struct curve448_precomputed_s; |
| |
| /* Precomputed table based on a point. Can be trivial implementation. */ |
| typedef struct curve448_precomputed_s curve448_precomputed_s; |
| |
| /* Scalar is stored packed, because we don't need the speed. */ |
| typedef struct curve448_scalar_s { |
| c448_word_t limb[C448_SCALAR_LIMBS]; |
| } curve448_scalar_t[1]; |
| |
| /* A scalar equal to 1. */ |
| extern const curve448_scalar_t curve448_scalar_one; |
| |
| /* A scalar equal to 0. */ |
| extern const curve448_scalar_t curve448_scalar_zero; |
| |
| /* The identity point on the curve. */ |
| extern const curve448_point_t curve448_point_identity; |
| |
| /* Precomputed table for the base point on the curve. */ |
| extern const struct curve448_precomputed_s *curve448_precomputed_base; |
| extern const niels_t *curve448_wnaf_base; |
| |
| /* |
| * Read a scalar from wire format or from bytes. |
| * |
| * ser (in): Serialized form of a scalar. |
| * out (out): Deserialized form. |
| * |
| * Returns: |
| * C448_SUCCESS: The scalar was correctly encoded. |
| * C448_FAILURE: The scalar was greater than the modulus, and has been reduced |
| * modulo that modulus. |
| */ |
| c448_error_t curve448_scalar_decode(curve448_scalar_t out, |
| const unsigned char ser[C448_SCALAR_BYTES]); |
| |
| /* |
| * Read a scalar from wire format or from bytes. Reduces mod scalar prime. |
| * |
| * ser (in): Serialized form of a scalar. |
| * ser_len (in): Length of serialized form. |
| * out (out): Deserialized form. |
| */ |
| void curve448_scalar_decode_long(curve448_scalar_t out, |
| const unsigned char *ser, size_t ser_len); |
| |
| /* |
| * Serialize a scalar to wire format. |
| * |
| * ser (out): Serialized form of a scalar. |
| * s (in): Deserialized scalar. |
| */ |
| void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES], |
| const curve448_scalar_t s); |
| |
| /* |
| * Add two scalars. |a|, |b| and |out| may alias each other. |
| * |
| * a (in): One scalar. |
| * b (in): Another scalar. |
| * out (out): a+b. |
| */ |
| void curve448_scalar_add(curve448_scalar_t out, |
| const curve448_scalar_t a, const curve448_scalar_t b); |
| |
| /* |
| * Subtract two scalars. |a|, |b| and |out| may alias each other. |
| * a (in): One scalar. |
| * b (in): Another scalar. |
| * out (out): a-b. |
| */ |
| void curve448_scalar_sub(curve448_scalar_t out, |
| const curve448_scalar_t a, const curve448_scalar_t b); |
| |
| /* |
| * Multiply two scalars. |a|, |b| and |out| may alias each other. |
| * |
| * a (in): One scalar. |
| * b (in): Another scalar. |
| * out (out): a*b. |
| */ |
| void curve448_scalar_mul(curve448_scalar_t out, |
| const curve448_scalar_t a, const curve448_scalar_t b); |
| |
| /* |
| * Halve a scalar. |a| and |out| may alias each other. |
| * |
| * a (in): A scalar. |
| * out (out): a/2. |
| */ |
| void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a); |
| |
| /* |
| * Copy a scalar. The scalars may alias each other, in which case this |
| * function does nothing. |
| * |
| * a (in): A scalar. |
| * out (out): Will become a copy of a. |
| */ |
| static ossl_inline void curve448_scalar_copy(curve448_scalar_t out, |
| const curve448_scalar_t a) |
| { |
| *out = *a; |
| } |
| |
| /* |
| * Copy a point. The input and output may alias, in which case this function |
| * does nothing. |
| * |
| * a (out): A copy of the point. |
| * b (in): Any point. |
| */ |
| static ossl_inline void curve448_point_copy(curve448_point_t a, |
| const curve448_point_t b) |
| { |
| *a = *b; |
| } |
| |
| /* |
| * Test whether two points are equal. If yes, return C448_TRUE, else return |
| * C448_FALSE. |
| * |
| * a (in): A point. |
| * b (in): Another point. |
| * |
| * Returns: |
| * C448_TRUE: The points are equal. |
| * C448_FALSE: The points are not equal. |
| */ |
| __owur c448_bool_t curve448_point_eq(const curve448_point_t a, |
| const curve448_point_t b); |
| |
| /* |
| * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially |
| * faster. |
| * |
| * two_a (out): The sum a+a. |
| * a (in): A point. |
| */ |
| void curve448_point_double(curve448_point_t two_a, const curve448_point_t a); |
| |
| /* |
| * RFC 7748 Diffie-Hellman scalarmul. This function uses a different |
| * (non-Decaf) encoding. |
| * |
| * out (out): The scaled point base*scalar |
| * base (in): The point to be scaled. |
| * scalar (in): The scalar to multiply by. |
| * |
| * Returns: |
| * C448_SUCCESS: The scalarmul succeeded. |
| * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a |
| * small subgroup. |
| */ |
| __owur c448_error_t x448_int(uint8_t out[X448_PUBLIC_BYTES], |
| const uint8_t base[X448_PUBLIC_BYTES], |
| const uint8_t scalar[X448_PRIVATE_BYTES]); |
| |
| /* |
| * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748. |
| * |
| * This function is mainly used internally, but is exported in case |
| * it will be useful. |
| * |
| * The ratio is necessary because the internal representation doesn't |
| * track the cofactor information, so on output we must clear the cofactor. |
| * This would multiply by the cofactor, but in fact internally points are always |
| * even, so it multiplies by half the cofactor instead. |
| * |
| * As it happens, this aligns with the base point definitions; that is, |
| * if you pass the Decaf/Ristretto base point to this function, the result |
| * will be X448_ENCODE_RATIO times the X448 |
| * base point. |
| * |
| * out (out): The scaled and encoded point. |
| * p (in): The point to be scaled and encoded. |
| */ |
| void curve448_point_mul_by_ratio_and_encode_like_x448( |
| uint8_t out[X448_PUBLIC_BYTES], |
| const curve448_point_t p); |
| |
| /* |
| * RFC 7748 Diffie-Hellman base point scalarmul. This function uses a different |
| * (non-Decaf) encoding. |
| * |
| * out (out): The scaled point base*scalar |
| * scalar (in): The scalar to multiply by. |
| */ |
| void x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES], |
| const uint8_t scalar[X448_PRIVATE_BYTES]); |
| |
| /* |
| * Multiply a precomputed base point by a scalar: out = scalar*base. |
| * |
| * scaled (out): The scaled point base*scalar |
| * base (in): The point to be scaled. |
| * scalar (in): The scalar to multiply by. |
| */ |
| void curve448_precomputed_scalarmul(curve448_point_t scaled, |
| const curve448_precomputed_s * base, |
| const curve448_scalar_t scalar); |
| |
| /* |
| * Multiply two base points by two scalars: |
| * combo = scalar1*curve448_point_base + scalar2*base2. |
| * |
| * Otherwise equivalent to curve448_point_double_scalarmul, but may be |
| * faster at the expense of being variable time. |
| * |
| * combo (out): The linear combination scalar1*base + scalar2*base2. |
| * scalar1 (in): A first scalar to multiply by. |
| * base2 (in): A second point to be scaled. |
| * scalar2 (in) A second scalar to multiply by. |
| * |
| * Warning: This function takes variable time, and may leak the scalars used. |
| * It is designed for signature verification. |
| */ |
| void curve448_base_double_scalarmul_non_secret(curve448_point_t combo, |
| const curve448_scalar_t scalar1, |
| const curve448_point_t base2, |
| const curve448_scalar_t scalar2); |
| |
| /* |
| * Test that a point is valid, for debugging purposes. |
| * |
| * to_test (in): The point to test. |
| * |
| * Returns: |
| * C448_TRUE The point is valid. |
| * C448_FALSE The point is invalid. |
| */ |
| __owur c448_bool_t curve448_point_valid(const curve448_point_t to_test); |
| |
| /* Overwrite scalar with zeros. */ |
| void curve448_scalar_destroy(curve448_scalar_t scalar); |
| |
| /* Overwrite point with zeros. */ |
| void curve448_point_destroy(curve448_point_t point); |
| |
| #endif /* HEADER_POINT_448_H */ |
