/************************************************* * Prime Generation Source File * * (C) 1999-2007 Jack Lloyd * *************************************************/ #include #include #include #include namespace Botan { /************************************************* * Generate a random prime * *************************************************/ BigInt random_prime(u32bit bits, const BigInt& coprime, u32bit equiv, u32bit modulo) { if(bits < 48) throw Invalid_Argument("random_prime: Can't make a prime of " + to_string(bits) + " bits"); 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) { global_state().pulse(PRIME_SEARCHING); BigInt p = random_integer(bits); p.set_bit(bits - 2); p.set_bit(0); if(p % modulo != equiv) p += (modulo - p % modulo) + equiv; const u32bit sieve_size = std::min(bits / 2, PRIME_TABLE_SIZE); SecureVector sieve(sieve_size); for(u32bit j = 0; j != sieve.size(); ++j) { sieve[j] = p % PRIMES[j]; global_state().pulse(PRIME_SIEVING); } u32bit counter = 0; while(true) { if(counter == 4096 || p.bits() > bits) break; global_state().pulse(PRIME_SEARCHING); bool passes_sieve = true; ++counter; p += modulo; for(u32bit j = 0; j != sieve.size(); ++j) { sieve[j] = (sieve[j] + modulo) % PRIMES[j]; global_state().pulse(PRIME_SIEVING); if(sieve[j] == 0) passes_sieve = false; } if(!passes_sieve || gcd(p - 1, coprime) != 1) continue; global_state().pulse(PRIME_PASSED_SIEVE); if(passes_mr_tests(p)) { global_state().pulse(PRIME_FOUND); return p; } } } } }