Background Elliptic curve cryptographic schemes were proposed independently in 1985 by
Neal Koblitz (Koblitz 1987) and Victor Miller (Miller 1986). They are the elliptic curve …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

In this paper a compact FPGA architecture for the AES algorithm with 128-bitkey targeted for
low-costembedded applications is presented. Encryption, decryption and key schedule are …

In this paper we look in detail at the curves which arise in the method of Galbraith and Smart
for producing curves in the Weil restriction of an elliptic curve over a finite field of …

Frey and Rück gave a method to transform the discrete logarithm problem in the divisor
class group of a curve over F _q into a discrete logarithm problem in some finite field …

We consider the basic version of the asymmetric cryptosy-stem HFE from Eurocrypt 96. We
propose a notion of non-trivial equations as a tentative to account for a large class of attacks …

In this article, we examine how the index calculus approach for computing discrete
logarithms in small genus hyperelliptic curves can be improved by introducing a double …

We propose an index calculus algorithm for the discrete logarithm problem on general
abelian varieties of small dimension. The main difference with the previous approaches is …

In this paper, we highlight the benefits of using genus 2 curves in public-key cryptography.
Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 …

We present a variation of the index calculus attack by Gaudry which can be used to solve the
discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm has a …