In this paper, we describe a quantum algorithm for computing an isogeny between any two
supersingular elliptic curves defined over a given finite field. The complexity of our method is …

This paper analyzes and optimizes quantum circuits for computing discrete logarithms on
binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication …

We propose an efficient commutative group action suitable for non-interactive key exchange
in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev …

These lectures notes were written for a summer school on Mathematics for post-quantum
cryptography in Thi\es, Senegal. They try to provide a guide for Masters' students to get …

CSIDH is a recent proposal for post-quantum non-interactive key-exchange, based on
supersingular elliptic curve isogenies. It is similar in design to a previous scheme by …

We give precise quantum resource estimates for Shor's algorithm to compute discrete
logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of …

A recent paper by Costello and Hisil at Asiacrypt'17 presents efficient formulas for computing
isogenies with odd-degree cyclic kernels on Montgomery curves. We provide a constructive …

Nowadays, we are surrounded by devices collecting and transmitting private information.
Currently, the two main mathematical problems that guarantee security on the Internet are …

Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a
notoriously hard task, despite several isogeny-based protocols relying on such an object. A …

Abstract We study (ℓ, ℓ)-isogeny graphs of principally polarised supersingular abelian
surfaces (PPSSAS). The (ℓ, ℓ)-isogeny graph has cycles of small length that can be used to …