stm32l5xx_crypto_pkc.c

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/**
 * @file stm32l5xx_crypto_pkc.c
 * @brief STM32L5 public-key hardware accelerator (PKA)
 *
 * @section License
 *
 * SPDX-License-Identifier: GPL-2.0-or-later
 *
 * Copyright (C) 2010-2024 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 2.4.4
 **/
 
//Switch to the appropriate trace level
#define TRACE_LEVEL CRYPTO_TRACE_LEVEL
 
//Dependencies
#include "stm32l5xx.h"
#include "stm32l5xx_hal.h"
#include "core/crypto.h"
#include "hardware/stm32l5xx/stm32l5xx_crypto.h"
#include "hardware/stm32l5xx/stm32l5xx_crypto_pkc.h"
#include "pkc/rsa.h"
#include "ecc/ec.h"
#include "ecc/ecdsa.h"
#include "ecc/curve25519.h"
#include "ecc/curve448.h"
#include "debug.h"
 
//Check crypto library configuration
#if (STM32L5XX_CRYPTO_PKC_SUPPORT == ENABLED)
 
 
/**
 * @brief PKA module initialization
 * @return Error code
 **/
 
error_t pkaInit(void)
{
   //Enable PKA peripheral clock
   __HAL_RCC_PKA_CLK_ENABLE();
 
   //Reset the PKA peripheral
   PKA->CR = 0;
 
   //Enable the PKA peripheral
   while((PKA->CR & PKA_CR_EN) == 0)
   {
      PKA->CR = PKA_CR_EN;
   }
 
   //Clear flags
   PKA->CLRFR = PKA_CLRFR_ADDRERRFC | PKA_CLRFR_RAMERRFC | PKA_CLRFR_PROCENDFC;
 
   //Successful processing
   return NO_ERROR;
}
 
 
/**
 * @brief Import byte array
 * @param[in] src Pointer to the byte array
 * @param[in] srcLen Length of the array to be copied, in bytes
 * @param[in] destLen Length of the operand, in bits
 * @param[in] offset PKA ram offset
 **/
 
void pkaImportArray(const uint8_t *src, size_t srcLen, uint_t destLen,
   uint_t offset)
{
   uint_t i;
   uint_t j;
   uint32_t temp;
 
   //Retrieve the length of the operand, in words
   destLen = (destLen + 31) / 32;
 
   //Copy the array to the PKA RAM
   for(i = 0, j = 0; i < srcLen; i++)
   {
      switch(i % 4)
      {
      case 0:
         temp = src[srcLen - i - 1];
         break;
      case 1:
         temp |= src[srcLen - i - 1] << 8;
         break;
      case 2:
         temp |= src[srcLen - i - 1] << 16;
         break;
      default:
         temp |= src[srcLen - i - 1] << 24;
         PKA->RAM[offset + j] = temp;
         j++;
         break;
      }
   }
 
   //Pad the operand with zeroes
   for(; i < (destLen * 4); i++)
   {
      switch(i % 4)
      {
      case 0:
         temp = 0;
         break;
      case 3:
         PKA->RAM[offset + j] = temp;
         j++;
         break;
      default:
         break;
      }
   }
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[offset + j] = 0;
}
 
 
/**
 * @brief Import multiple-precision integer
 * @param[in] a Pointer to the multiple-precision integer
 * @param[in] length Length of the operand, in bits
 * @param[in] offset PKA ram offset
 **/
 
void pkaImportMpi(const Mpi *a, uint_t length, uint_t offset)
{
   uint_t i;
   uint_t n;
 
   //Retrieve the length of the operand, in words
   length = (length + 31) / 32;
 
   //Get the actual length of the multiple-precision integer, in words
   n = mpiGetLength(a);
 
   //Copy the multiple-precision integer to the PKA RAM
   for(i = 0; i < n && i < length; i++)
   {
      PKA->RAM[offset + i] = a->data[i];
   }
 
   //Pad the operand with zeroes
   for(; i < length; i++)
   {
      PKA->RAM[offset + i] = 0;
   }
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[offset + i] = 0;
}
 
 
/**
 * @brief Export multiple-precision integer
 * @param[out] r Pointer to the multiple-precision integer
 * @param[in] length Length of the operand, in bits
 * @param[in] offset PKA ram offset
 * @return Error code
 **/
 
error_t pkaExportMpi(Mpi *r, uint_t length, uint_t offset)
{
   error_t error;
   uint_t i;
 
   //Retrieve the length of the operand, in words
   length = (length + 31) / 32;
 
   //Skip trailing zeroes
   while(length > 0 && PKA->RAM[offset + length - 1] == 0)
   {
      length--;
   }
 
   //Ajust the size of the multiple precision integer
   error = mpiGrow(r, length);
 
   //Check status code
   if(!error)
   {
      //Copy the multiple-precision integer from the PKA RAM
      for(i = 0; i < length; i++)
      {
         r->data[i] = PKA->RAM[offset + i];
      }
 
      //Pad the resulting value with zeroes
      for(; i < r->size; i++)
      {
         r->data[i] = 0;
      }
 
      //Set the sign
      r->sign = 1;
   }
 
   //Return status code
   return error;
}
 
 
/**
 * @brief Modular exponentiation
 * @param[out] r Resulting integer R = A ^ E mod P
 * @param[in] a Pointer to a multiple precision integer
 * @param[in] e Exponent
 * @param[in] p Modulus
 * @return Error code
 **/
 
error_t pkaModExp(Mpi *r, const Mpi *a, const Mpi *e, const Mpi *p)
{
   error_t error;
   uint_t modLen;
   uint_t expLen;
   uint32_t temp;
 
   //Retrieve the length of the modulus, in bits
   modLen = mpiGetBitLength(p);
   //Retrieve the length of the exponent, in bits
   expLen = mpiGetBitLength(e);
 
   //Check the length of the operands
   if(modLen <= PKA_MAX_ROS && expLen <= PKA_MAX_ROS)
   {
      //Reduce the operand first
      error = mpiMod(r, a, p);
 
      //Check status code
      if(!error)
      {
         //Acquire exclusive access to the PKA module
         osAcquireMutex(&stm32l5xxCryptoMutex);
 
         //Specify the length of the operand, in bits
         PKA->RAM[PKA_MODULAR_EXP_IN_OP_NB_BITS] = modLen;
         //Specify the length of the exponent, in bits
         PKA->RAM[PKA_MODULAR_EXP_IN_EXP_NB_BITS] = expLen;
 
         //Load input arguments into the PKA internal RAM
         pkaImportMpi(r, modLen, PKA_MODULAR_EXP_IN_EXPONENT_BASE);
         pkaImportMpi(e, expLen, PKA_MODULAR_EXP_IN_EXPONENT);
         pkaImportMpi(p, modLen, PKA_MODULAR_EXP_IN_MODULUS);
 
         //Disable interrupts
         PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
         //Write in the MODE field of PKA_CR register, specifying the operation
         //which is to be executed
         temp = PKA->CR & ~PKA_CR_MODE;
         PKA->CR = temp | (PKA_CR_MODE_MODULAR_EXP << PKA_CR_MODE_Pos);
 
         //Then assert the START bit in PKA_CR register
         PKA->CR |= PKA_CR_START;
 
         //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
         //indicating that the computation is complete
         while((PKA->SR & PKA_SR_PROCENDF) == 0)
         {
         }
 
         //Read the result data from the PKA internal RAM
         error = pkaExportMpi(r, modLen, PKA_MODULAR_EXP_OUT_SM_ALGO_ACC1);
 
         //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
         PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
         //Release exclusive access to the PKA module
         osReleaseMutex(&stm32l5xxCryptoMutex);
      }
   }
   else
   {
      //Perform modular exponentiation
      error = mpiExpMod(r, a, e, p);
   }
 
   //Return status code
   return error;
}
 
 
/**
 * @brief Modular exponentiation with CRT
 * @param[in] key RSA public key
 * @param[in] m Message representative
 * @param[out] c Ciphertext representative
 * @return Error code
 **/
 
error_t pkaRsaCrtExp(const RsaPrivateKey *key, const Mpi *c, Mpi *m)
{
   error_t error;
   uint_t nLen;
   uint_t pLen;
   uint_t qLen;
   uint_t dpLen;
   uint_t dqLen;
   uint_t qinvLen;
   uint32_t temp;
 
   //Retrieve the length of the private key
   nLen = mpiGetBitLength(&key->n);
   pLen = mpiGetBitLength(&key->p);
   qLen = mpiGetBitLength(&key->q);
   dpLen = mpiGetBitLength(&key->dp);
   dqLen = mpiGetBitLength(&key->dq);
   qinvLen = mpiGetBitLength(&key->qinv);
 
   //Check the length of the operands
   if(nLen <= PKA_MAX_ROS && pLen <= (nLen / 2) && qLen <= (nLen / 2) &&
      dpLen <= (nLen / 2) && dqLen <= (nLen / 2) && qinvLen <= (nLen / 2))
   {
      //Acquire exclusive access to the PKA module
      osAcquireMutex(&stm32l5xxCryptoMutex);
 
      //Specify the length of the operand, in bits
      PKA->RAM[PKA_RSA_CRT_EXP_IN_MOD_NB_BITS] = nLen;
 
      //Load input arguments into the PKA internal RAM
      pkaImportMpi(&key->p, nLen / 2, PKA_RSA_CRT_EXP_IN_PRIME_P);
      pkaImportMpi(&key->q, nLen / 2, PKA_RSA_CRT_EXP_IN_PRIME_Q);
      pkaImportMpi(&key->dp, nLen / 2, PKA_RSA_CRT_EXP_IN_DP_CRT);
      pkaImportMpi(&key->dq, nLen / 2, PKA_RSA_CRT_EXP_IN_DQ_CRT);
      pkaImportMpi(&key->qinv, nLen / 2, PKA_RSA_CRT_EXP_IN_QINV_CRT);
      pkaImportMpi(c, nLen, PKA_RSA_CRT_EXP_IN_EXPONENT_BASE);
 
      //Disable interrupts
      PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
      //Write in the MODE field of PKA_CR register, specifying the operation
      //which is to be executed
      temp = PKA->CR & ~PKA_CR_MODE;
      PKA->CR = temp | (PKA_CR_MODE_RSA_CRT_EXP << PKA_CR_MODE_Pos);
 
      //Then assert the START bit in PKA_CR register
      PKA->CR |= PKA_CR_START;
 
      //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
      //indicating that the computation is complete
      while((PKA->SR & PKA_SR_PROCENDF) == 0)
      {
      }
 
      //Read the result data from the PKA internal RAM
      error = pkaExportMpi(m, nLen, PKA_RSA_CRT_EXP_OUT_RESULT);
 
      //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
      PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
      //Release exclusive access to the PKA module
      osReleaseMutex(&stm32l5xxCryptoMutex);
   }
   else
   {
      Mpi m1;
      Mpi m2;
      Mpi h;
 
      //Initialize multiple-precision integers
      mpiInit(&m1);
      mpiInit(&m2);
      mpiInit(&h);
 
      //Compute m1 = c ^ dP mod p
      error = pkaModExp(&m1, c, &key->dp, &key->p);
 
      //Check status code
      if(!error)
      {
         //Compute m2 = c ^ dQ mod q
         error = pkaModExp(&m2, c, &key->dq, &key->q);
      }
 
      //Check status code
      if(!error)
      {
         //Let h = (m1 - m2) * qInv mod p
         error = mpiSub(&h, &m1, &m2);
      }
 
      //Check status code
      if(!error)
      {
         error = mpiMulMod(&h, &h, &key->qinv, &key->p);
      }
 
      //Check status code
      if(!error)
      {
         //Let m = m2 + q * h
         error = mpiMul(m, &key->q, &h);
      }
 
      //Check status code
      if(!error)
      {
         error = mpiAdd(m, m, &m2);
      }
 
      //Free previously allocated memory
      mpiFree(&m1);
      mpiFree(&m2);
      mpiFree(&h);
   }
 
   //Return status code
   return error;
}
 
 
/**
 * @brief RSA encryption primitive
 * @param[in] key RSA public key
 * @param[in] m Message representative
 * @param[out] c Ciphertext representative
 * @return Error code
 **/
 
error_t rsaep(const RsaPublicKey *key, const Mpi *m, Mpi *c)
{
   size_t nLen;
   size_t eLen;
 
   //Retrieve the length of the public key
   nLen = mpiGetLength(&key->n);
   eLen = mpiGetLength(&key->e);
 
   //Sanity check
   if(nLen == 0 || eLen == 0)
      return ERROR_INVALID_PARAMETER;
 
   //The message representative m shall be between 0 and n - 1
   if(mpiCompInt(m, 0) < 0 || mpiComp(m, &key->n) >= 0)
      return ERROR_OUT_OF_RANGE;
 
   //Perform modular exponentiation (c = m ^ e mod n)
   return pkaModExp(c, m, &key->e, &key->n);
}
 
 
/**
 * @brief RSA decryption primitive
 * @param[in] key RSA private key
 * @param[in] c Ciphertext representative
 * @param[out] m Message representative
 * @return Error code
 **/
 
error_t rsadp(const RsaPrivateKey *key, const Mpi *c, Mpi *m)
{
   error_t error;
 
   //The ciphertext representative c shall be between 0 and n - 1
   if(mpiCompInt(c, 0) < 0 || mpiComp(c, &key->n) >= 0)
      return ERROR_OUT_OF_RANGE;
 
   //Use the Chinese remainder algorithm?
   if(mpiGetLength(&key->n) > 0 && mpiGetLength(&key->p) > 0 &&
      mpiGetLength(&key->q) > 0 && mpiGetLength(&key->dp) > 0 &&
      mpiGetLength(&key->dq) > 0 && mpiGetLength(&key->qinv) > 0)
   {
      //Perform modular exponentiation (with CRT)
      error = pkaRsaCrtExp(key, c, m);
   }
   else if(mpiGetLength(&key->n) > 0 && mpiGetLength(&key->d) > 0)
   {
      //Perform modular exponentiation (without CRT)
      error = pkaModExp(m, c, &key->d, &key->n);
   }
   else
   {
      //Invalid parameters
      error = ERROR_INVALID_PARAMETER;
   }
 
   //Return status code
   return error;
}
 
 
/**
 * @brief Scalar multiplication
 * @param[in] params EC domain parameters
 * @param[out] r Resulting point R = d.S
 * @param[in] d An integer d such as 0 <= d < p
 * @param[in] s EC point
 * @return Error code
 **/
 
error_t ecMult(const EcDomainParameters *params, EcPoint *r, const Mpi *d,
   const EcPoint *s)
{
   error_t error;
   uint_t modLen;
   uint_t scalarLen;
   uint32_t temp;
 
   //Retrieve the length of the modulus, in bits
   modLen = mpiGetBitLength(&params->p);
   //Retrieve the length of the scalar, in bits
   scalarLen = mpiGetBitLength(d);
 
   //Check the length of the operands
   if(modLen <= PKA_MAX_EOS && scalarLen <= PKA_MAX_EOS)
   {
      //Acquire exclusive access to the PKA module
      osAcquireMutex(&stm32l5xxCryptoMutex);
 
      //Specify the length of the modulus, in bits
      PKA->RAM[PKA_ECC_SCALAR_MUL_IN_OP_NB_BITS] = modLen;
      //Specify the length of the scalar, in bits
      PKA->RAM[PKA_ECC_SCALAR_MUL_IN_EXP_NB_BITS] = scalarLen;
      //Set the sign of the coefficient A
      PKA->RAM[PKA_ECC_SCALAR_MUL_IN_A_COEFF_SIGN] = 0;
 
      //Load input arguments into the PKA internal RAM
      pkaImportMpi(&params->p, modLen, PKA_ECC_SCALAR_MUL_IN_MOD_GF);
      pkaImportMpi(&params->a, modLen, PKA_ECC_SCALAR_MUL_IN_A_COEFF);
      pkaImportMpi(d, scalarLen, PKA_ECC_SCALAR_MUL_IN_K);
      pkaImportMpi(&s->x, modLen, PKA_ECC_SCALAR_MUL_IN_INITIAL_POINT_X);
      pkaImportMpi(&s->y, modLen, PKA_ECC_SCALAR_MUL_IN_INITIAL_POINT_Y);
 
      //Disable interrupts
      PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
      //Write in the MODE field of PKA_CR register, specifying the operation
      //which is to be executed
      temp = PKA->CR & ~PKA_CR_MODE;
      PKA->CR = temp | (PKA_CR_MODE_ECC_MUL << PKA_CR_MODE_Pos);
 
      //Then assert the START bit in PKA_CR register
      PKA->CR |= PKA_CR_START;
 
      //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
      //indicating that the computation is complete
      while((PKA->SR & PKA_SR_PROCENDF) == 0)
      {
      }
 
      //Copy the x-coordinate of the result
      error = pkaExportMpi(&r->x, modLen, PKA_ECC_SCALAR_MUL_OUT_RESULT_X);
 
      //Check status code
      if(!error)
      {
         //Copy the y-coordinate of the result
         error = pkaExportMpi(&r->y, modLen, PKA_ECC_SCALAR_MUL_OUT_RESULT_Y);
      }
 
      //Check status code
      if(!error)
      {
         //Set the z-coordinate of the result
         error = mpiSetValue(&r->z, 1);
      }
 
      //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
      PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
      //Release exclusive access to the PKA module
      osReleaseMutex(&stm32l5xxCryptoMutex);
   }
   else
   {
      //Report an error
      error = ERROR_FAILURE;
   }
 
   //Return status code
   return error;
}
 
 
/**
 * @brief ECDSA signature generation
 * @param[in] prngAlgo PRNG algorithm
 * @param[in] prngContext Pointer to the PRNG context
 * @param[in] params EC domain parameters
 * @param[in] privateKey Signer's EC private key
 * @param[in] digest Digest of the message to be signed
 * @param[in] digestLen Length in octets of the digest
 * @param[out] signature (R, S) integer pair
 * @return Error code
 **/
 
error_t ecdsaGenerateSignature(const PrngAlgo *prngAlgo, void *prngContext,
   const EcDomainParameters *params, const EcPrivateKey *privateKey,
   const uint8_t *digest, size_t digestLen, EcdsaSignature *signature)
{
   error_t error;
   size_t modLen;
   size_t orderLen;
   uint32_t temp;
   Mpi k;
 
   //Check parameters
   if(params == NULL || privateKey == NULL || digest == NULL || signature == NULL)
      return ERROR_INVALID_PARAMETER;
 
   //Retrieve the length of the modulus, in bits
   modLen = mpiGetBitLength(&params->p);
   //Retrieve the length of the base point order, in bits
   orderLen = mpiGetBitLength(&params->q);
 
   //Check the length of the operands
   if(modLen > PKA_MAX_EOS || orderLen > PKA_MAX_EOS)
      return ERROR_FAILURE;
 
   //Initialize multiple precision integers
   mpiInit(&k);
 
   //Generate a random number k such as 0 < k < q - 1
   error = mpiRandRange(&k, &params->q, prngAlgo, prngContext);
 
   //Check status code
   if(!error)
   {
      //Acquire exclusive access to the PKA module
      osAcquireMutex(&stm32l5xxCryptoMutex);
 
      //Specify the length of the modulus, in bits
      PKA->RAM[PKA_ECDSA_SIGN_IN_MOD_NB_BITS] = modLen;
      //Specify the length of the base point order, in bits
      PKA->RAM[PKA_ECDSA_SIGN_IN_ORDER_NB_BITS] = orderLen;
      //Set the sign of the coefficient A
      PKA->RAM[PKA_ECDSA_SIGN_IN_A_COEFF_SIGN] = 0;
 
      //Load input arguments into the PKA internal RAM
      pkaImportMpi(&params->p, modLen, PKA_ECDSA_SIGN_IN_MOD_GF);
      pkaImportMpi(&params->a, modLen, PKA_ECDSA_SIGN_IN_A_COEFF);
      pkaImportMpi(&params->g.x, modLen, PKA_ECDSA_SIGN_IN_INITIAL_POINT_X);
      pkaImportMpi(&params->g.y, modLen, PKA_ECDSA_SIGN_IN_INITIAL_POINT_Y);
      pkaImportMpi(&params->q, orderLen, PKA_ECDSA_SIGN_IN_ORDER_N);
      pkaImportMpi(&privateKey->d, orderLen, PKA_ECDSA_SIGN_IN_PRIVATE_KEY_D);
      pkaImportMpi(&k, orderLen, PKA_ECDSA_SIGN_IN_K);
 
      //Keep the leftmost bits of the hash value
      digestLen = MIN(digestLen, (orderLen + 7) / 8);
      //Load the hash value into the PKA internal RAM
      pkaImportArray(digest, digestLen, orderLen, PKA_ECDSA_SIGN_IN_HASH_E);
 
      //Clear error code
      PKA->RAM[PKA_ECDSA_SIGN_OUT_ERROR] = PKA_STATUS_INVALID;
 
      //Disable interrupts
      PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
      //Write in the MODE field of PKA_CR register, specifying the operation
      //which is to be executed
      temp = PKA->CR & ~PKA_CR_MODE;
      PKA->CR = temp | (PKA_CR_MODE_ECDSA_SIGN << PKA_CR_MODE_Pos);
 
      //Then assert the START bit in PKA_CR register
      PKA->CR |= PKA_CR_START;
 
      //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
      //indicating that the computation is complete
      while((PKA->SR & PKA_SR_PROCENDF) == 0)
      {
      }
 
      //Successful computation?
      if(PKA->RAM[PKA_ECDSA_SIGN_OUT_ERROR] == PKA_STATUS_SUCCESS)
      {
         error = NO_ERROR;
      }
      else
      {
         error = ERROR_FAILURE;
      }
 
      //Check status code
      if(!error)
      {
         //Copy integer R
         error = pkaExportMpi(&signature->r, orderLen, PKA_ECDSA_SIGN_OUT_SIGNATURE_R);
      }
 
      //Check status code
      if(!error)
      {
         //Copy integer S
         error = pkaExportMpi(&signature->s, orderLen, PKA_ECDSA_SIGN_OUT_SIGNATURE_S);
      }
 
      //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
      PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
      //Release exclusive access to the PKA module
      osReleaseMutex(&stm32l5xxCryptoMutex);
   }
 
   //Release multiple precision integer
   mpiFree(&k);
 
   //Return status code
   return error;
}
 
 
/**
 * @brief ECDSA signature verification
 * @param[in] params EC domain parameters
 * @param[in] publicKey Signer's EC public key
 * @param[in] digest Digest of the message whose signature is to be verified
 * @param[in] digestLen Length in octets of the digest
 * @param[in] signature (R, S) integer pair
 * @return Error code
 **/
 
error_t ecdsaVerifySignature(const EcDomainParameters *params,
   const EcPublicKey *publicKey, const uint8_t *digest, size_t digestLen,
   const EcdsaSignature *signature)
{
   error_t error;
   size_t modLen;
   size_t orderLen;
   uint32_t temp;
 
   //Check parameters
   if(params == NULL || publicKey == NULL || digest == NULL || signature == NULL)
      return ERROR_INVALID_PARAMETER;
 
   //The verifier shall check that 0 < r < q
   if(mpiCompInt(&signature->r, 0) <= 0 ||
      mpiComp(&signature->r, &params->q) >= 0)
   {
      //If the condition is violated, the signature shall be rejected as invalid
      return ERROR_INVALID_SIGNATURE;
   }
 
   //The verifier shall check that 0 < s < q
   if(mpiCompInt(&signature->s, 0) <= 0 ||
      mpiComp(&signature->s, &params->q) >= 0)
   {
      //If the condition is violated, the signature shall be rejected as invalid
      return ERROR_INVALID_SIGNATURE;
   }
 
   //Retrieve the length of the modulus, in bits
   modLen = mpiGetBitLength(&params->p);
   //Retrieve the length of the base point order, in bits
   orderLen = mpiGetBitLength(&params->q);
 
   //Check the length of the operands
   if(modLen > PKA_MAX_EOS || orderLen > PKA_MAX_EOS)
      return ERROR_FAILURE;
 
   //Acquire exclusive access to the PKA module
   osAcquireMutex(&stm32l5xxCryptoMutex);
 
   //Specify the length of the modulus, in bits
   PKA->RAM[PKA_ECDSA_VERIF_IN_MOD_NB_BITS] = modLen;
   //Specify the length of the base point order, in bits
   PKA->RAM[PKA_ECDSA_VERIF_IN_ORDER_NB_BITS] = orderLen;
   //Set the sign of the coefficient A
   PKA->RAM[PKA_ECDSA_VERIF_IN_A_COEFF_SIGN] = 0;
 
   //Load input arguments into the PKA internal RAM
   pkaImportMpi(&params->p, modLen, PKA_ECDSA_VERIF_IN_MOD_GF);
   pkaImportMpi(&params->a, modLen, PKA_ECDSA_VERIF_IN_A_COEFF);
   pkaImportMpi(&params->g.x, modLen, PKA_ECDSA_VERIF_IN_INITIAL_POINT_X);
   pkaImportMpi(&params->g.y, modLen, PKA_ECDSA_VERIF_IN_INITIAL_POINT_Y);
   pkaImportMpi(&params->q, orderLen, PKA_ECDSA_VERIF_IN_ORDER_N);
   pkaImportMpi(&publicKey->q.x, modLen, PKA_ECDSA_VERIF_IN_PUBLIC_KEY_POINT_X);
   pkaImportMpi(&publicKey->q.y, modLen, PKA_ECDSA_VERIF_IN_PUBLIC_KEY_POINT_Y);
   pkaImportMpi(&signature->r, orderLen, PKA_ECDSA_VERIF_IN_SIGNATURE_R);
   pkaImportMpi(&signature->s, orderLen, PKA_ECDSA_VERIF_IN_SIGNATURE_S);
 
   //Keep the leftmost bits of the hash value
   digestLen = MIN(digestLen, (orderLen + 7) / 8);
   //Load the hash value into the PKA internal RAM
   pkaImportArray(digest, digestLen, orderLen, PKA_ECDSA_VERIF_IN_HASH_E);
 
   //Clear result
   PKA->RAM[PKA_ECDSA_VERIF_OUT_RESULT] = PKA_STATUS_INVALID;
 
   //Disable interrupts
   PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
   //Write in the MODE field of PKA_CR register, specifying the operation
   //which is to be executed
   temp = PKA->CR & ~PKA_CR_MODE;
   PKA->CR = temp | (PKA_CR_MODE_ECDSA_VERIFY << PKA_CR_MODE_Pos);
 
   //Then assert the START bit in PKA_CR register
   PKA->CR |= PKA_CR_START;
 
   //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
   //indicating that the computation is complete
   while((PKA->SR & PKA_SR_PROCENDF) == 0)
   {
   }
 
   //Test if the ECDSA signature is valid
   if(PKA->RAM[PKA_ECDSA_VERIF_OUT_RESULT] == PKA_STATUS_SUCCESS)
   {
      error = NO_ERROR;
   }
   else
   {
      error = ERROR_INVALID_SIGNATURE;
   }
 
   //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
   PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
   //Release exclusive access to the PKA module
   osReleaseMutex(&stm32l5xxCryptoMutex);
 
   //Return status code
   return error;
}
 
 
#if (X25519_SUPPORT == ENABLED || ED25519_SUPPORT == ENABLED)
 
/**
 * @brief Modular multiplication
 * @param[out] r Resulting integer R = (A * B) mod p
 * @param[in] a An integer such as 0 <= A < p
 * @param[in] b An integer such as 0 <= B < p
 **/
 
void curve25519Mul(uint32_t *r, const uint32_t *a, const uint32_t *b)
{
   uint_t i;
   uint64_t temp;
   uint32_t u[16];
 
   //Acquire exclusive access to the PKA module
   osAcquireMutex(&stm32l5xxCryptoMutex);
 
   //Specify the length of the operands, in bits
   PKA->RAM[PKA_ARITHMETIC_MUL_NB_BITS] = 255;
 
   //Load the first operand into the PKA internal RAM
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1] = a[0];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 1] = a[1];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 2] = a[2];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 3] = a[3];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 4] = a[4];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 5] = a[5];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 6] = a[6];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 7] = a[7];
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 8] = 0;
 
   //Load the second operand into the PKA internal RAM
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2] = b[0];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 1] = b[1];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 2] = b[2];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 3] = b[3];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 4] = b[4];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 5] = b[5];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 6] = b[6];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 7] = b[7];
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 8] = 0;
 
   //Disable interrupts
   PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
   //Write in the MODE field of PKA_CR register, specifying the operation
   //which is to be executed
   temp = PKA->CR & ~PKA_CR_MODE;
   PKA->CR = temp | (PKA_CR_MODE_ARITHMETIC_MUL << PKA_CR_MODE_Pos);
 
   //Then assert the START bit in PKA_CR register
   PKA->CR |= PKA_CR_START;
 
   //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
   //indicating that the computation is complete
   while((PKA->SR & PKA_SR_PROCENDF) == 0)
   {
   }
 
   //Read the result data from the PKA internal RAM
   u[0] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT];
   u[1] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 1];
   u[2] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 2];
   u[3] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 3];
   u[4] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 4];
   u[5] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 5];
   u[6] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 6];
   u[7] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 7];
   u[8] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 8];
   u[9] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 9];
   u[10] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 10];
   u[11] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 11];
   u[12] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 12];
   u[13] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 13];
   u[14] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 14];
   u[15] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 15];
 
   //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
   PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
   //Release exclusive access to the PKA module
   osReleaseMutex(&stm32l5xxCryptoMutex);
 
   //Reduce bit 255 (2^255 = 19 mod p)
   temp = (u[7] >> 31) * 19;
   //Mask the most significant bit
   u[7] &= 0x7FFFFFFF;
 
   //Perform fast modular reduction (first pass)
   for(i = 0; i < 8; i++)
   {
      temp += u[i];
      temp += (uint64_t) u[i + 8] * 38;
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   //Reduce bit 256 (2^256 = 38 mod p)
   temp *= 38;
   //Reduce bit 255 (2^255 = 19 mod p)
   temp += (u[7] >> 31) * 19;
   //Mask the most significant bit
   u[7] &= 0x7FFFFFFF;
 
   //Perform fast modular reduction (second pass)
   for(i = 0; i < 8; i++)
   {
      temp += u[i];
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   //Reduce non-canonical values
   curve25519Red(r, u);
}
 
#endif
#if (X448_SUPPORT == ENABLED || ED448_SUPPORT == ENABLED)
 
/**
 * @brief Modular multiplication
 * @param[out] r Resulting integer R = (A * B) mod p
 * @param[in] a An integer such as 0 <= A < p
 * @param[in] b An integer such as 0 <= B < p
 **/
 
void curve448Mul(uint32_t *r, const uint32_t *a, const uint32_t *b)
{
   uint_t i;
   uint64_t c;
   uint64_t temp;
   uint32_t u[28];
 
   //Acquire exclusive access to the PKA module
   osAcquireMutex(&stm32l5xxCryptoMutex);
 
   //Specify the length of the operands, in bits
   PKA->RAM[PKA_ARITHMETIC_MUL_NB_BITS] = 448;
 
   //Load the first operand into the PKA internal RAM
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1] = a[0];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 1] = a[1];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 2] = a[2];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 3] = a[3];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 4] = a[4];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 5] = a[5];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 6] = a[6];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 7] = a[7];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 8] = a[8];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 9] = a[9];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 10] = a[10];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 11] = a[11];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 12] = a[12];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 13] = a[13];
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP1 + 14] = 0;
 
   //Load the second operand into the PKA internal RAM
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2] = b[0];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 1] = b[1];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 2] = b[2];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 3] = b[3];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 4] = b[4];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 5] = b[5];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 6] = b[6];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 7] = b[7];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 8] = b[8];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 9] = b[9];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 10] = b[10];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 11] = b[11];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 12] = b[12];
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 13] = b[13];
 
   //An additional word with all bits equal to zero must be added
   PKA->RAM[PKA_ARITHMETIC_MUL_IN_OP2 + 14] = 0;
 
   //Disable interrupts
   PKA->CR &= ~(PKA_CR_ADDRERRIE | PKA_CR_RAMERRIE | PKA_CR_PROCENDIE);
 
   //Write in the MODE field of PKA_CR register, specifying the operation
   //which is to be executed
   temp = PKA->CR & ~PKA_CR_MODE;
   PKA->CR = temp | (PKA_CR_MODE_ARITHMETIC_MUL << PKA_CR_MODE_Pos);
 
   //Then assert the START bit in PKA_CR register
   PKA->CR |= PKA_CR_START;
 
   //Wait until the PROCENDF bit in the PKA_SR register is set to 1,
   //indicating that the computation is complete
   while((PKA->SR & PKA_SR_PROCENDF) == 0)
   {
   }
 
   //Read the result data from the PKA internal RAM
   u[0] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT];
   u[1] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 1];
   u[2] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 2];
   u[3] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 3];
   u[4] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 4];
   u[5] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 5];
   u[6] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 6];
   u[7] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 7];
   u[8] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 8];
   u[9] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 9];
   u[10] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 10];
   u[11] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 11];
   u[12] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 12];
   u[13] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 13];
   u[14] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 14];
   u[15] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 15];
   u[16] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 16];
   u[17] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 17];
   u[18] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 18];
   u[19] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 19];
   u[20] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 20];
   u[21] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 21];
   u[22] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 22];
   u[23] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 23];
   u[24] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 24];
   u[25] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 25];
   u[26] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 26];
   u[27] = PKA->RAM[PKA_ARITHMETIC_MUL_OUT_RESULT + 27];
 
   //Then clear PROCENDF bit by setting PROCENDFC bit in PKA_CLRFR
   PKA->CLRFR = PKA_CLRFR_PROCENDFC;
 
   //Release exclusive access to the PKA module
   osReleaseMutex(&stm32l5xxCryptoMutex);
 
   //Perform fast modular reduction (first pass)
   for(temp = 0, i = 0; i < 7; i++)
   {
      temp += u[i];
      temp += u[i + 14];
      temp += u[i + 21];
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   for(i = 7; i < 14; i++)
   {
      temp += u[i];
      temp += u[i + 7];
      temp += (uint64_t) u[i + 14] << 1;
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   //Perform fast modular reduction (second pass)
   for(c = temp, i = 0; i < 7; i++)
   {
      temp += u[i];
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   for(temp += c, i = 7; i < 14; i++)
   {
      temp += u[i];
      u[i] = temp & 0xFFFFFFFF;
      temp >>= 32;
   }
 
   //Reduce non-canonical values
   curve448Red(r, u, (uint32_t) temp);
}
 
#endif
#endif