Let's look at an example of RSA in action, albeit one with numbers far too small to resist factoring. For this example, I borrow directly from Schneier (see Resources).

Let p = 47 and q = 71. We calculate n = p * q = 3337. The encryption exponent e must have no factors in common with:

		    (p-1)*(q-1) = 46 * 70 = 3220
		    

We may therefore choose e = 79 (we could have used other values equally well). We now calculate:

		    d = 79^-1 mod 3220 = 1019
		    

Publish [e, n], keep d secret, and discard p and q. Each message we can encrypt in the example must be a number smaller than 3337. In other words, we might divide an actual plain text into 11-bit blocks and encrypt each block in the same manner. The cipher text simply concatenates the encrypted blocks (maybe padding to 12 bits to include every cipher text possible).

For example, suppose that one of our correspondent's 11-bit blocks is "01010110000"; in decimal, this is 688. Our correspondent creates a cipher text block by calculating:

		    C = 688^79 mod 3337 = 1570 = "011000100010"
		    

Our correspondent sends us the message, "011000100010," and we can decrypt it by calculating:

		    M = 1570^1019 mod 3337 = 688 = "01010110000"
		    

Of course, factoring 3337 is hardly an insurmountable obstacle for a determined attacker with a couple of pages of scratch paper and a pencil. By using keys hundreds of times this long, we set the bar higher than even attackers with millions of MIP-years can surmount (or so it is believed).