e777257746
Reviewed-by: Bernd Edlinger <bernd.edlinger@hotmail.de> (Merged from https://github.com/openssl/openssl/pull/5105)
535 lines
16 KiB
C
535 lines
16 KiB
C
/**
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* @file decaf/point_448.h
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* @author Mike Hamburg
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*
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* @copyright
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* Copyright (c) 2015-2016 Cryptography Research, Inc. \n
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* Released under the MIT License. See LICENSE.txt for license information.
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*
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* @brief A group of prime order p, based on Ed448-Goldilocks.
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*
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* @warning This file was automatically generated in Python.
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* Please do not edit it.
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*/
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#ifndef __DECAF_POINT_448_H__
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#define __DECAF_POINT_448_H__ 1
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#include "curve448utils.h"
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#include "field.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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/** @cond internal */
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#define DECAF_448_SCALAR_LIMBS ((446-1)/DECAF_WORD_BITS+1)
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/** @endcond */
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/** The number of bits in a scalar */
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#define DECAF_448_SCALAR_BITS 446
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/** Number of bytes in a serialized point. */
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#define DECAF_448_SER_BYTES 56
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/** Number of bytes in an elligated point. For now set the same as SER_BYTES
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* but could be different for other curves.
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*/
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#define DECAF_448_HASH_BYTES 56
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/** Number of bytes in a serialized scalar. */
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#define DECAF_448_SCALAR_BYTES 56
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/** Number of bits in the "which" field of an elligator inverse */
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#define DECAF_448_INVERT_ELLIGATOR_WHICH_BITS 3
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/** The cofactor the curve would have, if we hadn't removed it */
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#define DECAF_448_REMOVED_COFACTOR 4
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/** X448 encoding ratio. */
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#define DECAF_X448_ENCODE_RATIO 2
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/** Number of bytes in an x448 public key */
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#define DECAF_X448_PUBLIC_BYTES 56
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/** Number of bytes in an x448 private key */
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#define DECAF_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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/** @cond internal */
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gf_448_t x,y,z,t;
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/** @endcond */
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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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/** @cond internal */
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decaf_word_t limb[DECAF_448_SCALAR_LIMBS];
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/** @endcond */
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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 DECAF_API_VIS;
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/** A scalar equal to 0. */
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extern const curve448_scalar_t curve448_scalar_zero DECAF_API_VIS;
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/** The identity point on the curve. */
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extern const curve448_point_t curve448_point_identity DECAF_API_VIS;
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/** An arbitrarily chosen base point on the curve. */
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extern const curve448_point_t curve448_point_base DECAF_API_VIS;
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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 DECAF_API_VIS;
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/**
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* @brief Read a scalar from wire format or from bytes.
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*
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* @param [in] ser Serialized form of a scalar.
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* @param [out] out Deserialized form.
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*
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* @retval DECAF_SUCCESS The scalar was correctly encoded.
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* @retval DECAF_FAILURE The scalar was greater than the modulus,
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* and has been reduced modulo that modulus.
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*/
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decaf_error_t curve448_scalar_decode (
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curve448_scalar_t out,
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const unsigned char ser[DECAF_448_SCALAR_BYTES]
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) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Read a scalar from wire format or from bytes. Reduces mod
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* scalar prime.
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*
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* @param [in] ser Serialized form of a scalar.
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* @param [in] ser_len Length of serialized form.
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* @param [out] out Deserialized form.
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*/
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void curve448_scalar_decode_long (
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curve448_scalar_t out,
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const unsigned char *ser,
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size_t ser_len
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Serialize a scalar to wire format.
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*
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* @param [out] ser Serialized form of a scalar.
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* @param [in] s Deserialized scalar.
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*/
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void curve448_scalar_encode (
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unsigned char ser[DECAF_448_SCALAR_BYTES],
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const curve448_scalar_t s
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_NOINLINE;
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/**
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* @brief Add two scalars. The scalars may use the same memory.
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* @param [in] a One scalar.
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* @param [in] b Another scalar.
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* @param [out] out a+b.
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*/
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void curve448_scalar_add (
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curve448_scalar_t out,
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const curve448_scalar_t a,
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const curve448_scalar_t b
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Compare two scalars.
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* @param [in] a One scalar.
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* @param [in] b Another scalar.
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* @retval DECAF_TRUE The scalars are equal.
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* @retval DECAF_FALSE The scalars are not equal.
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*/
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decaf_bool_t curve448_scalar_eq (
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const curve448_scalar_t a,
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const curve448_scalar_t b
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) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Subtract two scalars. The scalars may use the same memory.
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* @param [in] a One scalar.
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* @param [in] b Another scalar.
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* @param [out] out a-b.
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*/
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void curve448_scalar_sub (
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curve448_scalar_t out,
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const curve448_scalar_t a,
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const curve448_scalar_t b
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Multiply two scalars. The scalars may use the same memory.
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* @param [in] a One scalar.
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* @param [in] b Another scalar.
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* @param [out] out a*b.
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*/
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void curve448_scalar_mul (
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curve448_scalar_t out,
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const curve448_scalar_t a,
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const curve448_scalar_t b
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Halve a scalar. The scalars may use the same memory.
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* @param [in] a A scalar.
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* @param [out] out a/2.
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*/
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void curve448_scalar_halve (
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curve448_scalar_t out,
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const curve448_scalar_t a
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Invert a scalar. When passed zero, return 0. The input and output may alias.
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* @param [in] a A scalar.
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* @param [out] out 1/a.
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* @return DECAF_SUCCESS The input is nonzero.
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*/
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decaf_error_t curve448_scalar_invert (
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curve448_scalar_t out,
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const curve448_scalar_t a
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) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Copy a scalar. The scalars may use the same memory, in which
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* case this function does nothing.
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* @param [in] a A scalar.
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* @param [out] out Will become a copy of a.
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*/
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static inline void DECAF_NONNULL curve448_scalar_copy (
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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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* @brief Set a scalar to an unsigned 64-bit integer.
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* @param [in] a An integer.
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* @param [out] out Will become equal to a.
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*/
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void curve448_scalar_set_unsigned (
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curve448_scalar_t out,
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uint64_t a
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) DECAF_API_VIS DECAF_NONNULL;
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/**
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* @brief Copy a point. The input and output may alias,
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* in which case this function does nothing.
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*
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* @param [out] a A copy of the point.
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* @param [in] b Any point.
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*/
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static inline void DECAF_NONNULL curve448_point_copy (
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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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* @brief Test whether two points are equal. If yes, return
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* DECAF_TRUE, else return DECAF_FALSE.
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*
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* @param [in] a A point.
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* @param [in] b Another point.
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* @retval DECAF_TRUE The points are equal.
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* @retval DECAF_FALSE The points are not equal.
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*/
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decaf_bool_t curve448_point_eq (
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const curve448_point_t a,
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const curve448_point_t b
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) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Double a point. Equivalent to
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* curve448_point_add(two_a,a,a), but potentially faster.
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*
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* @param [out] two_a The sum a+a.
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* @param [in] a A point.
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*/
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void curve448_point_double (
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curve448_point_t two_a,
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const curve448_point_t a
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) DECAF_API_VIS DECAF_NONNULL;
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/**
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* @brief 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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* @param [out] scaled The scaled point base*scalar
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* @param [in] base The point to be scaled.
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* @param [in] scalar The scalar to multiply by.
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*
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* @retval DECAF_SUCCESS The scalarmul succeeded.
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* @retval DECAF_FAILURE The scalarmul didn't succeed, because the base
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* point is in a small subgroup.
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*/
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decaf_error_t decaf_x448 (
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uint8_t out[DECAF_X448_PUBLIC_BYTES],
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const uint8_t base[DECAF_X448_PUBLIC_BYTES],
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const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]
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) DECAF_API_VIS DECAF_NONNULL DECAF_WARN_UNUSED DECAF_NOINLINE;
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/**
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* @brief Multiply a point by DECAF_X448_ENCODE_RATIO,
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* 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 libdecaf's
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* points are always 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 DECAF_X448_ENCODE_RATIO times the X448
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* base point.
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*
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* @param [out] out The scaled and encoded point.
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* @param [in] p 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[DECAF_X448_PUBLIC_BYTES],
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const curve448_point_t p
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) DECAF_API_VIS DECAF_NONNULL;
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/** The base point for X448 Diffie-Hellman */
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extern const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] DECAF_API_VIS;
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/**
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* @brief RFC 7748 Diffie-Hellman base point scalarmul. This function uses
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* a different (non-Decaf) encoding.
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*
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* Does exactly the same thing as decaf_x448_generate_key,
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* but has a better name.
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*
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* @param [out] scaled The scaled point base*scalar
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* @param [in] scalar The scalar to multiply by.
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*/
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void decaf_x448_derive_public_key (
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uint8_t out[DECAF_X448_PUBLIC_BYTES],
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const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/* FUTURE: uint8_t curve448_encode_like_curve448) */
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/**
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* @brief Precompute a table for fast scalar multiplication.
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* Some implementations do not include precomputed points; for
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* those implementations, this implementation simply copies the
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* point.
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*
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* @param [out] a A precomputed table of multiples of the point.
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* @param [in] b Any point.
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*/
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void curve448_precompute (
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curve448_precomputed_s *a,
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const curve448_point_t b
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Multiply a precomputed base point by a scalar:
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* scaled = scalar*base.
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* Some implementations do not include precomputed points; for
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* those implementations, this function is the same as
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* curve448_point_scalarmul
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*
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* @param [out] scaled The scaled point base*scalar
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* @param [in] base The point to be scaled.
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* @param [in] scalar The scalar to multiply by.
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*/
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void curve448_precomputed_scalarmul (
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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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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Multiply two base points by two scalars:
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* scaled = 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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* @param [out] combo The linear combination scalar1*base + scalar2*base2.
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* @param [in] scalar1 A first scalar to multiply by.
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* @param [in] base2 A second point to be scaled.
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* @param [in] scalar2 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
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* used. It is designed for signature verification.
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*/
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void curve448_base_double_scalarmul_non_secret (
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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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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Constant-time decision between two scalars. If pick_b
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* is zero, out = a; else out = b.
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*
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* @param [out] out The output. It may be the same as either input.
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* @param [in] a Any scalar.
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* @param [in] b Any scalar.
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* @param [in] pick_b If nonzero, choose scalar b.
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*/
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void curve448_scalar_cond_sel (
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curve448_scalar_t out,
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const curve448_scalar_t a,
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const curve448_scalar_t b,
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decaf_word_t pick_b
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Test that a point is valid, for debugging purposes.
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*
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* @param [in] to_test The point to test.
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* @retval DECAF_TRUE The point is valid.
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* @retval DECAF_FALSE The point is invalid.
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*/
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decaf_bool_t curve448_point_valid (
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const curve448_point_t to_test
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) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Almost-Elligator-like hash to curve.
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*
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* Call this function with the output of a hash to make a hash to the curve.
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*
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* This function runs Elligator2 on the curve448 Jacobi quartic model. It then
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* uses the isogeny to put the result in twisted Edwards form. As a result,
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* it is safe (cannot produce points of order 4), and would be compatible with
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* hypothetical other implementations of Decaf using a Montgomery or untwisted
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* Edwards model.
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*
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* Unlike Elligator, this function may be up to 4:1 on [0,(p-1)/2]:
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* A factor of 2 due to the isogeny.
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* A factor of 2 because we quotient out the 2-torsion.
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*
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* This makes it about 8:1 overall, or 16:1 overall on curves with cofactor 8.
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*
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* Negating the input (mod q) results in the same point. Inverting the input
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* (mod q) results in the negative point. This is the same as Elligator.
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*
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* This function isn't quite indifferentiable from a random oracle.
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* However, it is suitable for many protocols, including SPEKE and SPAKE2 EE.
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* Furthermore, calling it twice with independent seeds and adding the results
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* is indifferentiable from a random oracle.
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*
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* @param [in] hashed_data Output of some hash function.
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* @param [out] pt The data hashed to the curve.
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*/
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void
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curve448_point_from_hash_nonuniform (
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curve448_point_t pt,
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const unsigned char hashed_data[DECAF_448_HASH_BYTES]
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Indifferentiable hash function encoding to curve.
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*
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* Equivalent to calling curve448_point_from_hash_nonuniform twice and adding.
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*
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* @param [in] hashed_data Output of some hash function.
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* @param [out] pt The data hashed to the curve.
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*/
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void curve448_point_from_hash_uniform (
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curve448_point_t pt,
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const unsigned char hashed_data[2*DECAF_448_HASH_BYTES]
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) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
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/**
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* @brief Inverse of elligator-like hash to curve.
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*
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* This function writes to the buffer, to make it so that
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* curve448_point_from_hash_nonuniform(buffer) = pt if
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* possible. Since there may be multiple preimages, the
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* "which" parameter chooses between them. To ensure uniform
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* inverse sampling, this function succeeds or fails
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* independently for different "which" values.
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*
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* This function isn't guaranteed to find every possible
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* preimage, but it finds all except a small finite number.
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* In particular, when the number of bits in the modulus isn't
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* a multiple of 8 (i.e. for curve25519), it sets the high bits
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* independently, which enables the generated data to be uniform.
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* But it doesn't add p, so you'll never get exactly p from this
|
|
* function. This might change in the future, especially if
|
|
* we ever support eg Brainpool curves, where this could cause
|
|
* real nonuniformity.
|
|
*
|
|
* @param [out] recovered_hash Encoded data.
|
|
* @param [in] pt The point to encode.
|
|
* @param [in] which A value determining which inverse point
|
|
* to return.
|
|
*
|
|
* @retval DECAF_SUCCESS The inverse succeeded.
|
|
* @retval DECAF_FAILURE The inverse failed.
|
|
*/
|
|
decaf_error_t
|
|
curve448_invert_elligator_nonuniform (
|
|
unsigned char recovered_hash[DECAF_448_HASH_BYTES],
|
|
const curve448_point_t pt,
|
|
uint32_t which
|
|
) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
|
|
|
|
/**
|
|
* @brief Inverse of elligator-like hash to curve.
|
|
*
|
|
* This function writes to the buffer, to make it so that
|
|
* curve448_point_from_hash_uniform(buffer) = pt if
|
|
* possible. Since there may be multiple preimages, the
|
|
* "which" parameter chooses between them. To ensure uniform
|
|
* inverse sampling, this function succeeds or fails
|
|
* independently for different "which" values.
|
|
*
|
|
* @param [out] recovered_hash Encoded data.
|
|
* @param [in] pt The point to encode.
|
|
* @param [in] which A value determining which inverse point
|
|
* to return.
|
|
*
|
|
* @retval DECAF_SUCCESS The inverse succeeded.
|
|
* @retval DECAF_FAILURE The inverse failed.
|
|
*/
|
|
decaf_error_t
|
|
curve448_invert_elligator_uniform (
|
|
unsigned char recovered_hash[2*DECAF_448_HASH_BYTES],
|
|
const curve448_point_t pt,
|
|
uint32_t which
|
|
) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
|
|
|
|
/**
|
|
* @brief Overwrite scalar with zeros.
|
|
*/
|
|
void curve448_scalar_destroy (
|
|
curve448_scalar_t scalar
|
|
) DECAF_NONNULL DECAF_API_VIS;
|
|
|
|
/**
|
|
* @brief Overwrite point with zeros.
|
|
*/
|
|
void curve448_point_destroy (
|
|
curve448_point_t point
|
|
) DECAF_NONNULL DECAF_API_VIS;
|
|
|
|
#ifdef __cplusplus
|
|
} /* extern "C" */
|
|
#endif
|
|
|
|
#endif /* __DECAF_POINT_448_H__ */
|