Speaker: Michelle Manes (UH Mānoa)

Title: Curve-based cryptography, a tour of recent developments

Abstract: Elliptic curve cryptography (ECC) was first proposed in the mid 1980s, but it took 20 years for ECC algorithms to become widely used. Researchers are currently laying the mathematical foundations for cryptosystems based on genus 2 and more recently on genus 3 curves. If we’re successful, these systems may be widely used in another 10 years or so. Many of the breakthroughs in this area have come from research collaborations forged at the Women in Numbers and Sage Days for Women conferences.

In this talk, I’ll give a brief introduction to the idea of cryptosystems based on the “discrete log problem,” including ECC and higher genus curves. I’ll trace the story of the recent results, and I’ll provide some mathematical details for the most recent work on genus 3 curves.