Abstract Supersingular Isogeny Graphs were introduced as a source of hard problems in
cryptography by Charles, Goren, and Lauter for the construction of cryptographic hash …

In this paper we investigate various arithmetic techniques which can be used to potentially
enhance the performance in the supersingular isogeny Diffie-Hellman (SIDH) key-exchange …

Presence of quantum computers is a real threat against the security of currently used public
key cryptographic algorithms such as RSA and Elliptic curve cryptography. Isogeny …

Given an elliptic curve E over a field of positive characteristic p, we consider how to
efficiently determine whether E is ordinary or supersingular. We analyze the complexity of …

Along with the resistance against quantum computers, isogeny-based cryptography offers
attractive cryptosystems due to small key sizes and compatibility with the current elliptic …

We give a systematic overview of techniques to compute arithmetic modulo 2 xpy±1 and
propose improvements. This is useful for computations in the supersingular isogeny Diffie …

Genus-2 curves and Jacobians with a given number of points Page 1 LMS J. Comput. Math.
18 (1) (2015) 170–197 C 2015 Authors doi:10.1112/S1461157014000461 Genus-2 curves …

The key exchange protocol of Diffie and Hellman, which can be defined for any group, has
the special feature of using only exponentiations. In particular, it can also be instantiated in …

The multivariate public key cryptosystem (MPKC), which is based on the problem of solving
a set of multivariate systems of quadratic equations over a finite field, is expected to be …

Elliptic curve cryptographic schemes performed between a pair of cryptographic
correspondent computing devices. In an aspect, a first entity generates a first basis point in a …