Here is the response I sent to Peter Simons: Well, your example that you sent isn't even correct! Your example said: p = 5 q = 7 xy = 4*6+1 = 25 x=5 y=5 Well, you just chose some bad primes. Here is a better example: p = 5 q = 11 N = pq = 55 m = (p-1)(q-1) = 4*10 = 40 Now, we need to choose our public and private decryptors, E and d, such that Ed = 1 mod (m): E = 3 d = 27 So, the Public Key (N, E) is (55, 3) and the Private (Secret) Key (p, q, m, d) is (5, 11, 40, 27). Now, to encrypt a message, S, you take C = S^E mod N, and to decrypt you get S = C^d mod N. So, say the message you want to send is, oh, "8" (for lack of a better example off the top of my head). So, you try to encrypt this message, and you get: C = 8^3 mod 55 = 512 mod 55 = 17 You then send this message to the recipient, who then calculates the message back: S = 17^27 mod 55 = 1667711322168688287513535727415473 mod 55 = 8 And you get the original message back. -derek