make_prm.cpp

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/*
* Prime Generation
* (C) 1999-2007 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
 
#include <botan/numthry.h>
#include <botan/parsing.h>
#include <algorithm>
 
namespace Botan {
 
/*
* Generate a random prime
*/
BigInt random_prime(RandomNumberGenerator& rng,
                    size_t bits, const BigInt& coprime,
                    size_t equiv, size_t modulo)
   {
   if(bits <= 1)
      throw Invalid_Argument("random_prime: Can't make a prime of " +
                             to_string(bits) + " bits");
   else if(bits == 2)
      return ((rng.next_byte() % 2) ? 2 : 3);
   else if(bits == 3)
      return ((rng.next_byte() % 2) ? 5 : 7);
   else if(bits == 4)
      return ((rng.next_byte() % 2) ? 11 : 13);
 
   if(coprime <= 0)
      throw Invalid_Argument("random_prime: coprime must be > 0");
   if(modulo % 2 == 1 || modulo == 0)
      throw Invalid_Argument("random_prime: Invalid modulo value");
   if(equiv >= modulo || equiv % 2 == 0)
      throw Invalid_Argument("random_prime: equiv must be < modulo, and odd");
 
   while(true)
      {
      BigInt p(rng, bits);
 
      // Force lowest and two top bits on
      p.set_bit(bits - 1);
      p.set_bit(bits - 2);
      p.set_bit(0);
 
      if(p % modulo != equiv)
         p += (modulo - p % modulo) + equiv;
 
      const size_t sieve_size = std::min(bits / 2, PRIME_TABLE_SIZE);
      SecureVector<size_t> sieve(sieve_size);
 
      for(size_t j = 0; j != sieve.size(); ++j)
         sieve[j] = p % PRIMES[j];
 
      size_t counter = 0;
      while(true)
         {
         if(counter == 4096 || p.bits() > bits)
            break;
 
         bool passes_sieve = true;
         ++counter;
         p += modulo;
 
         if(p.bits() > bits)
            break;
 
         for(size_t j = 0; j != sieve.size(); ++j)
            {
            sieve[j] = (sieve[j] + modulo) % PRIMES[j];
            if(sieve[j] == 0)
               passes_sieve = false;
            }
 
         if(!passes_sieve || gcd(p - 1, coprime) != 1)
            continue;
         if(check_prime(p, rng))
            return p;
         }
      }
   }
 
/*
* Generate a random safe prime
*/
BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits)
   {
   if(bits <= 64)
      throw Invalid_Argument("random_safe_prime: Can't make a prime of " +
                             to_string(bits) + " bits");
 
   BigInt p;
   do
      p = (random_prime(rng, bits - 1) << 1) + 1;
   while(!check_prime(p, rng));
   return p;
   }
 
}