print("Welcome to ElGamal Cryptosystems");
print("Enter help() for further information");

help(c)=
{
	print("ElGamal Cryptosystems");
	print("");
	print("Enter :");
	print("- setP(P)		: to set the prime number P");
	print("- setG(g)		: to set the generator g");
	print("- setKey(u)		: to set the private key u");
	print("- encrypt(m)		: to encrypt a message m. The output is (a, b).");
	print("- decrypt(a, b)		: to decrypt (a, b). The output is plaintext.");
	print("");
	print("Automatic Generation");
	print("- genP(l)		: to generate P with size l bits and then set an appropriate generator g");
	print("");
	print("Print Setting:");
	print("- printSetting()	: to print the value of p and g");

}

setP(P)=
{
	if(isprime(P), p = P, print("P is not a prime number") );
}

setG(G)=
{
	x = lift(Mod(G^((p-1)/2),p));

	if(x != 1, g = G, print("Sorry, alpha must be a primitive element"));
}

setKey(U)=
{
	u = U;
	y = lift(Mod(g^u,p));
}

encrypt(m)=
{
	k = random(p-1);
	while(gcd(k,p-1) != 1, k = random(p-1));

	a = lift(Mod(g^k, p));
	b = lift(Mod(y^k * m, p));

	print("Ciphertext : (" a ", " b ")");
}

decrypt(a,b)=
{
	pm = lift(Mod(b * a^(p-1-u), p));

	print("Plaintext : " pm);
}

printSetting(ps) =
{

print ("The current settings:");

print ("p = " p);
print ("g = " g);
print ("y = " y);
}

genP(l)=
{
	p = primes(1000)[random(1000) + 1];

	while(floor(log(p)/log(2)) != l, p = primes(1000)[random(1000) + 1]);

	print("p = " p);

	xx = random(p-1);
	if(lift(Mod(xx^((p-1)/2),p)) != 1, g = xx, g = lift(Mod(-xx, p)));

	print("g = " g);
}