We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. ...
Constructing pairing-friendly hyperelliptic curves with small ρ-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe...
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
For counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof’s algorithm. We present several improvements on...
The hyperelliptic curve cryptosystems take most of the time for computing a scalar multiplication kD of an element D in the Jacobian JC of a hyperelliptic curve C for an integer k....