How to store large numbers?

Question

I have to make a RSA signature (on a state machine) in C on a 32bit board. I am limited on memory so I can not store decimals in a vector or something like that.

The best thing would be if I could store bits and to have easy access to them; what storage method would be best?

I made this one:

#if (CPU_TYPE == CPU_TYPE_32)

typedef uint32_t word;
#define word_length 32
typedef struct BigNumber {
    word words[64];
} BigNumber;

#elif (CPU_TYPE == CPU_TYPE_16)

typedef uint16_t word;
#define word_length 16
typedef struct BigNumber {
    word words[128];
} BigNumber;

#else  
#error Unsupported CPU_TYPE  
#endif

This seems hard to use. How can I simplify it?

Answer 1

You may simply use the BigNumber API from OpenSSL. You can find the full API here.

And, you can use this code sample as a start:

#include <stdio.h>

#include <openssl/crypto.h>
#include <openssl/bn.h>

int main(int argc, char *argv[])
{
  static const char num1[] = "18446744073709551616";
  static const char num2[] = "36893488147419103232";

  BIGNUM *bn1 = NULL;
  BIGNUM *bn2 = NULL;
  BN_CTX *ctx = BN_CTX_new();

  BN_dec2bn(&bn1, num1); // convert the string to BIGNUM
  BN_dec2bn(&bn2, num2);

  BN_add(bn1, bn1, bn2); // bn1 = bn1 + bn2

  char *result_str = BN_bn2dec(bn1);  // convert the BIGNUM back to string
  printf("%s + %s = %s\n", num1, num2, result_str);
  OPENSSL_free(result_str);

  BN_free(bn1);
  BN_free(bn2);
  BN_CTX_free(ctx);

  return 0;
}

Compile it with:

#> gcc -Wall -Wextra -g -o sample sample.c -lcrypto

You should get something like this when executing it:

18446744073709551616 + 36893488147419103232 = 55340232221128654848