14.1-14.2, due on November 17

1. (Difficult) I think the math presented in this section should be comprehensible, but again, with a shallow reading, I did not comprehend it all.
   I am somewhat confused about the general theme of demonstrating knowledge of square roots.  I know we have discussed how learning square roots, mod n, is computationally equivalent to learning factors of n, but I think a little explanation of what these schemes are trying to do, and why, would be helpful.
2. (Reflective) I wonder if public-key-based proofs of knowledge can count as "zero-knowledge" techniques.  For example Victor generates a random number r, and encrypts is with Peggy's public key.  Peggy retrieves r with her private key, and then encrypts r with Victor's public key and sends it back to Victor.  In this way, Peggy has demonstrated that she knows her private key.  It seems an eavesdropper couldn't use this information, unless Victor happened to use the same random number again.  I think this idea is used in authentication systems.  Would it count as a "zero-knowledge proof?"