Speaker: Dr. Renate Scheidler, University of Calgary
Location: Mathematical Sciences 431
Date: Thursday, March 16, 2017
Title: A Gentle Introduction to (Hyper-)Elliptic Curves and their Use in Cryptography
Abstract: Elliptic and low genus hyperelliptic curves represent a highly suitable setting for cryptography, due to their small space requirements, efficient arithmetic, and excellent security properties. Elliptic curve cryptography, for example, currently provides information protection in the Blackberry smartphone, Blu-ray technology, and other real world applications. Unfortunately, curve cryptosystems fall victim to quantum attacks, as does the widely used RSA scheme. Nevertheless, our devices are safe until researchers actually manage to build a large-scale quantum computer. Moreover, elliptic and genus two hyperelliptic curves have become the subject of intense research into quantum resistant cryptography.
This talk will provide a gentle introduction to arithmetic on elliptic and hyperelliptic curves as well as their context in cryptography. It is targeted at an audience with no or minimal exposure to cryptography and no prior knowledge of algebraic curves or number theory.