Exam Review
MAT 3930
When: In class part, April 22, 11:00-12:50, Take home given out Monday, April 20, due Friday, April 24.
What material: Factoring, index calculus, Elliptic Curve Cryptography
What to bring: A calculator. You will need the calculator for basic arithmetic and mods. The mods will be small
enough to be done on a TI-83. The test will be designed to minimize the advantage of a TI-89 or TI-92.
Knowledge you need:
You should have a working knowledge of the following definitions (working means you can define it directly, and
you can use it in a problem):
 Mod
 Fp and Z/nZ
 Multiplicative inverse (mod p)
 Order (both in Fp and in an elliptic curve)
 Primitive root
 B-smooth numbers
 Elliptic Curve Discrete Log Problem
 Factoring Problem
 Root Problem
You should be able to perform or describe the following algorithms:
 Pollard p-1
 Difference of squares factoring
 Difference of squares factoring with B-smooth numbers
 Simplified Number Field Sieve (with Gaussian integers only)
 Index calculus to solve DLP
 Pound operation on elliptic curves (considered geometrically)
 Elliptic curve addition on real numbers (from formula and geometrically)
 Elliptic curve addition mod p (from formula)
 Elliptic curve key exchange
 Elliptic curve ElGamal
 Square root of a number mod p
 Black-box group addition and DLP
Concepts you should understand:
 Similarities and differences between DLP and ECDLP.
 Best known solutions to DLP and ECDLP.
 Why B-smooth numbers are good for factoring and DLP.
Take-home exam:
 These will be Maple questions or questions that I don’t think you could answer in a timed environment.
 You will be asked to perform algorithms using big numbers.
 You will be asked understanding questions, ones that require thought versus Maple computations.
 You will be asked to perform algorithms that would be too time consuming/computationally intensive in
an in-class environment.