16.2, due on December 1

1. (Difficult) Understanding possible attacks on discrete logarithms on elliptic curves is difficult.  In addition, I don't see the clear analog between classical discrete logarithms and discrete logs on elliptic curves.  I also don't fully understand why we need to find a number that's a square, mod p, when mapping plain text to a point on the curve, but I suspect it's because the left-hand-side of the equation is y^2.
2. (Reflective) I think that, in general, I could get the intuition behind these types of elliptic curves.  They seem to be just normal equations, mod a prime.  I don't understand everything that a system being mod a prime means, but we have worked with it some before.  I am anxious to see if I will have a general understanding for how elliptic curve cryptography works by the time we are done studying this.  I hope, specifically, I have some understanding that will help me comprehend the basics of identity-based encryption.