International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Andreas Stein

Affiliation: University of Waterloo

Publications

Year
Venue
Title
2010
EPRINT
Cryptographic Aspects of Real Hyperelliptic Curves
In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols, and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2; and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.
2001
EPRINT
Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent
We provide a concrete instance of the discrete logarithm problem on an elliptic curve over F_{2^{155}} which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index-calculus methods for hyperelliptic curves over characteristic two finite fields, and discuss the cryptographic implications of our results.