Honors Students' Abstracts
Elliptic Curves and Cryptography
In an era of global technology there is a growing need to be able to secure data and information using cryptography. As it turns out, the mathematics of elliptic curves has many applications in cryptography, both to encryption and decryption techniques. Examples of these include key exchanges, digital signatures, and factoring algorithms such as Lenstra's Elliptic Curve Method. In this poster I will give the necessary background for understanding elliptic curves over finite fields, focusing on the algebraic structure of these geometric objects. I then explain how this structure can be exploited for new methods in cryptography including attacks on encryption via factoring, a one round three-party key exchange, and homomorphic encryption.