An introduction to elliptic curves over the rationals and finite fields. The focus is on both theoretical and computational aspects; subjects covered will include the study of endomorphism rings, Weil pairing, torsion points, group structure, and effective implementation of point addition. Applications to cryptography will be discussed, including elliptic curve-based Diffie-Helman key exchange, El Gamal encryption, and digital signatures, as well as the associated computational problems on which their security is based.
This course may not be repeated for credit.

Sections