Mathematics Colloquium: Low Genus Curves and Cryptography

2008-02-19

4:10 pm Neill 5W

Ning Shang

Abstract: Preserving a strong connection between mathematics and information security, elliptic and hyperelliptic curve cryptography is playing an increasingly important role during the past decade. In this talk we shall discuss some research that relates low genus algebraic curves and cryptography. It includes a high-level application of Jacobians of low genus curves to a problem of access control, the explicit divisor arithmetic for genus 2 real hyperelliptic curves, and a new method of generating parameters for the complex multiplication (CM) construction of cryptographically strong genus 2 curves. If time allows, an ongoing research project for generating pairing-friendly genus 2 curves over prime fields via the CM method will also be mentioned. These are interesting and important problems from both points of view of computational number theory and information security. (Mr. Shang is a candidate for the faculty position in Discrete Mathematics at WSU)