Math 480, Spring 2015, Assignment 14

Carefully define the following terms:

1. Elliptic curve (over an arbitrary field of characteristic not 2 or 3).
2. Elliptic curve (over a field of characteristic 2).
3. Elliptic curve (over a field of characteristic 3).
4. Binary field.

Carefully describe the following algorithms:

1. Algorithm to generate an elliptic curve point of known finite order.
2. Elliptic curve Diffie-Hellman algorithm.
3. Elliptic curve ElGamal encryption.

Solve the following problems:

1. Problems 5.5(a), 5.6(a), 5.8, and 5.13(a-b).

Coding projects:

1. (Government-approved elliptic curve) Implement the arithmetic of at least one of the curves described in the document "Recommended elliptic curves for Federal Government use".
2. (Elliptic curve Diffie-Hellman) Implement Diffie-Hellman key exchange using the elliptic curve you implemented above.

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