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 …

The ideal class group of hyperelliptic curves can be used in cryptosystems based on the
discrete logarithm problem. In this article we present explicit formulae to perform the group …

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 …

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 …

We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3
over prime fields. To achieve a fair comparison between the different types of groups, we …

For any finite field k= F q, we explicitly describe the k-isogeny classes of abelian surfaces
defined over k and their behavior under finite field extension. In particular, we determine the …

Groups of unknown order are of major interest due to their applications including time-lock
puzzles, verifiable delay functions, and accumulators. In this paper we focus on trustless …

Groups of unknown order are of major interest due to their applications including time-lock
puzzles, verifiable delay functions, and accumulators. In this paper we focus on trustless …

In the paper an upper bound is established for certain exponential sums, analogous to
Gaussian sums, defined on the points of an elliptic curve over a prime finite field. The bound …

We extend the explicit formulae for arithmetic on genus two curves of Takahashi and
Miyamoto, Doi, Matsuo, Chao, and Tsuji to fields of even characteristic and to arbitrary …