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