Wednesday, November 2nd

I’m posting some suggested problems from the book to do with recent topics, you’ll want to use these to study over the next week:

  • Chapter 3, Number Theory, Exercises 33, 34
  • Chapter 8, Hash, Exercises 1, 3, 4
  • Chapter 9, Signatures, Exercises 1, 2, 5, 6, Computer Problem 1
  • Chapter 16, Elliptic Curves, Exercises 2, 3, 4, 5, 9, Computer Problem 2
  • I suggest you also find the full multiplication table for $y^2 + y = x^3$ over $\mathbb{F}_2$ (where it has 3 points) and over $\mathbb{F}_4$ (where it has 9 points).  Notice that $\mathbb{F}_2$ is a subfield of $\mathbb{F}_4$, so you’ve done part of the work already.  Don’t do all the multiplications out by hand, that’s tedious.  Instead, use cleverness to use just a few computations to fill out the whole table (as we did in class).