Isogenies are the morphisms between elliptic curves and are, accordingly, a topic of interest
in the subject. As such, they have been well studied, and have been used in several …

In this paper, we give a survey and discuss new developments and computational results for
a high order accurate numerical boundary condition based on finite difference methods for …

A paper by Karati and Sarkar at Asiacrypt'17 has pointed out the potential for Kummer lines
in genus 1, by observing that their SIMD-friendly arithmetic is competitive with the status quo …

An addition law for an elliptic curve is complete if it is defined for all possible pairs of input
points on the elliptic curve. In Elliptic Curve Cryptography (ECC), a complete addition law …

In this paper we look at three families of elliptic curves with rational 3-torsion over a finite
field. These families include Hessian curves, twisted Hessian curves, and a new family we …

arxiv:1112.5714v1 [math.AG] 24 Dec 2011 On the Number of Distinct Legendre, Jacobi and
Hessian Curves Page 1 arxiv:1112.5714v1 [math.AG] 24 Dec 2011 On the Number of Distinct …

We present a collection of several natural questions about elliptic curves, mostly over finite
fields, that have led to some interesting number theoretic questions and whose solutions …

The main theme (and title) of this thesis is “modern curve-based cryptography”. Indeed, the
history of cryptography is long and leads back to the early Egyptians and Romans. Its …

This thesis investigates the efficiency of batching the verification of elliptic curve signatures.
The first signature scheme considered is a modification of ECDSA proposed by Antipa et …

It is well known supersingular curves due to pairing of Weil and pairing of Tate are used in
identity-based cryptosystems so we find criterion of supersingularity of Montgomery and …