In arithmetic and algebraic geometry, superspecial (s. sp. for short) curves are one of the
most important objects to be studied, with applications to cryptography and coding theory. If …

In arithmetic and algebraic geometry, superspecial curves have been studied as one of the
most important objects, with practical applications to cryptography and coding theory. The …

In algebraic geometry, enumerating or finding superspecial curves in positive characteristic
$ p $ is important both in theory and in computation. In this paper, we propose feasible …

This paper presents algorithmic approaches to study superspecial hyperelliptic curves. The
algorithms proposed in this paper are: an algorithm to enumerate superspecial hyperelliptic …

In this paper, we enumerate superspecial hyperelliptic curves of genus 4 over finite fields F
_q for small q. This complements our preceding results in the non-hyperelliptic case. We …

We present a simple and direct method of counting the number of the isomorphism classes
of hyperelliptic curves of genus 2 over finite fields with characteristic different from 5. In this …

In this paper, an algorithm to enumerate non-hyperelliptic superspecial curves of genus $4 $
over finite fields of characteristic $ p\geq 5$ is constructed. As an application, the algorithm …

As a generalization of group of points of elliptic curves, the Jacobians of hyperelliptic curves
are used in cryptography. The attack by Duursma-Gaudry-Morain [2] is feasible if the …

To obtain efficient cryptosystems based on hyperelliptic curves, we studied genus 2
isomorphism classes of hyperelliptic curves in characteristic 2. We found general and …

Counting rational points on Jacobian varieties of hyperelliptic curves over finite fields is very
important for constructing hyperelliptic curve cryptosystems (HCC), but known algorithms for …