RSA.cpp

#include <iostream>
#include <random>
#include <algorithm>
#include <chrono>
#include "RSA.h"
#include <gmpxx.h>

typedef std::mt19937 RNG;  // the Mersenne Twister with a popular choice of parameters
RNG rng( time(0) );

mpz_class gcd(mpz_class buff, mpz_class pbuff){			//pbuff is greater
	while( buff != 0 ){
		pbuff = pbuff % buff;
		std::swap(pbuff, buff);
	}
	return pbuff;
}

mpz_class inverse(mpz_class buff, mpz_class pbuff){
	mpz_class Prime = pbuff, coeff[2] = { 1 , 0 };
	while( buff != 1 ){
		coeff[1] = coeff[1] - (pbuff / buff) * coeff[0];
		pbuff = pbuff % buff;
		std::swap( pbuff, buff );
		std::swap( coeff[0], coeff[1]);
	}
	coeff[0] = coeff[0] % Prime;
	if( coeff[0] < 0 )	coeff[0] = Prime + coeff[0];
	return coeff[0];
}

mpz_class random( mpz_class ll, mpz_class ul ){
	std::uniform_int_distribution<int> D_dist(0, ul.get_ui() - ll.get_ui());
	return D_dist(rng) + ll;
}

mpz_class power(mpz_class Base, mpz_class Exponent, mpz_class Modulus){							//compute g^A (mod p) using binary representation of A
	mpz_class term( Base ), buff( 1 );
	
	while( Exponent != 0 ){
		mpz_class remainder = Exponent % 2;
		if( remainder != 0 )	buff = (buff * term) % Modulus;
		term = (term * term) % Modulus;
		Exponent = Exponent / 2;
	}
	return buff;
}

mpz_class gPrime(mpz_class ll, mpz_class ul){

	mpz_class Prime[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741 };
	mpz_class A = random(ll, ul);

	for( int i = 0 ; i < 400 ; i = i + 1 )
		if( A == Prime[i] )	return A;
		else if( A % Prime[i] == 0 ){
			//std::cout << "Prime " << A << "\t" << Prime[i] << std::endl;
			return 0;
		}	
	mpz_class y = random(1, A - 1);
	if( power( y, A - 1, A ) != 1 ){										//Fermat's primality test (on a single test case)
		//std::cout << "Fermat " << A << "\t" << y << std::endl;
		return 0;
	}
	
	for( int i = 0 ; i < 20 ; i = i + 1 ){
		mpz_class a = Prime[i], check[2] = {0, 0}, x = A - 1;
		while( x % 2 == 0 ){
			if( check[0] == 0 && power( a, x, A ) ==  1 )	check[0] = 1;
			x = x / 2;
		}
		//std::cout << count << std::endl;
		check[1] = (power( a, x, A ) == 1);
		if( check[0] != 1 && check[1] != 1 )	return 0;
	}
	
	for( int i = 0 ; i < 90 ; i = i + 1 ){								//Miller-Rabin's primality test (for 100 test cases)
		mpz_class a = random(0, A - 1), check[2] = {0, 0}, x = A - 1;
		while( x % 2 == 0 ){
			if( check[0] == 0 && power( a, x, A ) ==  1 )	check[0] = 1;
			x = x / 2;
		}
		//std::cout << count << std::endl;
		check[1] = (power( a, x, A ) == 1);
		if( check[0] != 1 && check[1] != 1 )	return 0;
	}
	
	return A;
}

void generateKey(){
	
	mpz_class EArr[5] = {3, 5, 17, 257, 65537};
	int	f = random(0,4).get_ui();
	
	mpz_class p(0), q(0);
	while( p == 0 || gcd( p - 1, EArr[f]) != 1 ) p = gPrime(100000, 1000000);
	std::cout << p << std::endl;
	while( q == 0 || gcd( q - 1, EArr[f]) != 1 ) q = gPrime(100000, 1000000);
	std::cout << q << std::endl;
	mpz_class n = p * q, phi = (p - 1) * (q - 1);
	
	//std::cout << EArr[f] << "\t" << phi << std::endl;
	mpz_class d = inverse(EArr[f], phi);
}