x448.c

Go to the documentation of this file.

/**
 * @file x448.c
 * @brief X448 function implementation
 *
 * @section License
 *
 * SPDX-License-Identifier: GPL-2.0-or-later
 *
 * Copyright (C) 2010-2025 Oryx Embedded SARL. All rights reserved.
 *
 * This file is part of CycloneCRYPTO Open.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * @author Oryx Embedded SARL (www.oryx-embedded.com)
 * @version 2.5.0
 **/
 
//Switch to the appropriate trace level
#define TRACE_LEVEL CRYPTO_TRACE_LEVEL
 
//Dependencies
#include "core/crypto.h"
#include "ecc/ec.h"
#include "ecc/curve448.h"
#include "ecc/x448.h"
#include "debug.h"
 
//Check crypto library configuration
#if (X448_SUPPORT == ENABLED)
 
 
/**
 * @brief X448 function (scalar multiplication on Curve448)
 * @param[out] r Output u-coordinate
 * @param[in] k Input scalar
 * @param[in] u Input u-coordinate
 * @return Error code
 **/
 
error_t x448(uint8_t *r, const uint8_t *k, const uint8_t *u)
{
   int_t i;
   uint32_t b;
   uint32_t swap;
#if (CRYPTO_STATIC_MEM_SUPPORT == DISABLED)
   X448State *state;
#else
   X448State state[1];
#endif
 
   //Check parameters
   if(r == NULL || k == NULL || u == NULL)
      return ERROR_INVALID_PARAMETER;
 
#if (CRYPTO_STATIC_MEM_SUPPORT == DISABLED)
   //Allocate working state
   state = cryptoAllocMem(sizeof(X448State));
   //Failed to allocate memory?
   if(state == NULL)
      return ERROR_OUT_OF_MEMORY;
#endif
 
   //Copy scalar
   for(i = 0; i < 14; i++)
   {
      state->k[i] = LOAD32LE(k + i * 4);
   }
 
   //Set the two least significant bits of the first byte to 0, and the most
   //significant bit of the last byte to 1
   state->k[0] &= 0xFFFFFFFC;
   state->k[13] |= 0x80000000;
 
   //Copy input u-coordinate
   curve448Import(state->u, u);
 
   //Implementations must accept non-canonical values and process them as
   //if they had been reduced modulo the field prime (refer to RFC 7748,
   //section 5)
   curve448Canonicalize(state->u, state->u);
 
   //Set X1 = 1
   curve448SetInt(state->x1, 1);
   //Set Z1 = 0
   curve448SetInt(state->z1, 0);
   //Set X2 = U
   curve448Copy(state->x2, state->u);
   //Set Z2 = 1
   curve448SetInt(state->z2, 1);
 
   //Set swap = 0
   swap = 0;
 
   //Montgomery ladder
   for(i = CURVE448_BIT_LEN - 1; i >= 0; i--)
   {
      //The scalar is processed in a left-to-right fashion
      b = (state->k[i / 32] >> (i % 32)) & 1;
 
      //Conditional swap
      curve448Swap(state->x1, state->x2, swap ^ b);
      curve448Swap(state->z1, state->z2, swap ^ b);
 
      //Save current bit value
      swap = b;
 
      //Compute T1 = X2 + Z2
      curve448Add(state->t1, state->x2, state->z2);
      //Compute X2 = X2 - Z2
      curve448Sub(state->x2, state->x2, state->z2);
      //Compute Z2 = X1 + Z1
      curve448Add(state->z2, state->x1, state->z1);
      //Compute X1 = X1 - Z1
      curve448Sub(state->x1, state->x1, state->z1);
      //Compute T1 = T1 * X1
      curve448Mul(state->t1, state->t1, state->x1);
      //Compute X2 = X2 * Z2
      curve448Mul(state->x2, state->x2, state->z2);
      //Compute Z2 = Z2 * Z2
      curve448Sqr(state->z2, state->z2);
      //Compute X1 = X1 * X1
      curve448Sqr(state->x1, state->x1);
      //Compute T2 = Z2 - X1
      curve448Sub(state->t2, state->z2, state->x1);
      //Compute Z1 = T2 * a24
      curve448MulInt(state->z1, state->t2, CURVE448_A24);
      //Compute Z1 = Z1 + X1
      curve448Add(state->z1, state->z1, state->x1);
      //Compute Z1 = Z1 * T2
      curve448Mul(state->z1, state->z1, state->t2);
      //Compute X1 = X1 * Z2
      curve448Mul(state->x1, state->x1, state->z2);
      //Compute Z2 = T1 - X2
      curve448Sub(state->z2, state->t1, state->x2);
      //Compute Z2 = Z2 * Z2
      curve448Sqr(state->z2, state->z2);
      //Compute Z2 = Z2 * U
      curve448Mul(state->z2, state->z2, state->u);
      //Compute X2 = X2 + T1
      curve448Add(state->x2, state->x2, state->t1);
      //Compute X2 = X2 * X2
      curve448Sqr(state->x2, state->x2);
   }
 
   //Conditional swap
   curve448Swap(state->x1, state->x2, swap);
   curve448Swap(state->z1, state->z2, swap);
 
   //Retrieve affine representation
   curve448Inv(state->u, state->z1);
   curve448Mul(state->u, state->u, state->x1);
 
   //Reduce non-canonical values
   curve448Canonicalize(state->u, state->u);
 
   //Copy output u-coordinate
   curve448Export(state->u, r);
 
   //Erase working state
   osMemset(state, 0, sizeof(X448State));
 
#if (CRYPTO_STATIC_MEM_SUPPORT == DISABLED)
   //Release working state
   cryptoFreeMem(state);
#endif
 
   //Successful processing
   return NO_ERROR;
}
 
#endif