Number Theory & Cryptography - Assignement 2 - Question 3: Implement RSA Cryptosystem. - Done with Aviral - November 10, 2011

rsa.gp

/* Question 3: Implement RSA Cryptosystem. */

/*
   Call keygen function first.
   Use the key generated to encrypt and decrypt message using
   corresponding functions.
*/

fastexp(a, x, n) = {
	c = 0;
	d = 1;
	m = binary(x);
	i = length(m);
	while( (i>0),
		c = 2 * c;
		d = (d*d) % n; 
		if( ( m[i]==1 ),
			c = c + 1;
			d = (a*d) % n;
		); 
		i = i - 1;
	);
	return(d);
}

rsaen(p, e, n) = {
	C = fastexp(p, e, n);
	print("Encrypted value is ", C);
}

rsadec(c, d, n) = {
	p = fastexp(c, d, n);
	print("Decrypted value is ", p);
}

/* p, q are large distinct prime numbers */
rsakeygen(p, q) = {
	n = p * q;
	phi = (p-1) * (q-1);
	e = random(phi); 
	while( gcd(e,phi) != 1,
		 e = random(phi)
	);
	d = 1;
	while( ( ((e*d) % phi) != 1 ),
		d++;
	);
	print("Public key is n = "n", e = " e);
	print("Private key is d = " d);
}