14.1-14.2

1. I'm sorry; is it easy to find square roots mod a prime? Am I totally blanking on this? Why is the modulus a product of two primes?

2. I think this is actually a pretty important concept vis à vis cryptography. The need to prove that you know something without divulging what that something is is kind of the same as a shared secret. People do this in everyday life. Or at least my family does. My mom calls me and asks what various passwords are for accounts and stuff, but I don't want to have to go to a private location to divulge it (and who knows who's eavesdropping the line itself) so we rely on a shared secret. I say, remember the name of my fourth grade teacher? or something like that. In this case, however, one is able to prove they know the shared secret without divulging it.