Math 480, Spring 2015, Assignment 13

Carefully define the following terms:

1. Elliptic curve (over $\mathbb{R}$).
2. Chord-tangent law (on an elliptic curve).
3. Group operation on an elliptic curve.

Carefully describe the following algorithms:

1. Index calculus (for solving the discrete log problem in $\mathbb{Z}_p^*$).

Carefully state the following theorems (you do not need to prove them):

1. Expected time complexity of the index calculus.

Solve the following problems:

1. Problems 3.35, 5.1, and 5.4 (note that many books, including ours, use $+$ or $\oplus$ to denote the group operation on elliptic curves, whereas we have been using multiplicative notation in class).

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