We present signature schemes whose security relies on computational assumptions relating
to isogeny graphs of supersingular elliptic curves. We give two schemes, both of them based …

We provide a new identification protocol and new signature schemes based on isogeny
problems. Our identification protocol relies on the hardness of the endomorphism ring …

We present new candidates for quantum-resistant public-key cryptosystems based on the
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …

We study two important families of problems in isogeny-based cryptography and how they
relate to each other: computing the endomorphism ring of supersingular elliptic curves, and …

We study cryptosystems based on supersingular isogenies. This is an active area of
research in post-quantum cryptography. Our first contribution is to give a very powerful active …

We present an overview of supersingular isogeny cryptography and how it fits into the broad
theme of post-quantum public-key crypto. The paper also gives a brief tutorial of elliptic …

We introduce a new signature scheme, SQISign,(for Short Quaternion and Isogeny
Signature) from isogeny graphs of supersingular elliptic curves. The signature scheme is …

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 …

In this paper, we study several related computational problems for supersingular elliptic
curves, their isogeny graphs, and their endomorphism rings. We prove reductions between …

The Deuring correspondence defines a bijection between isogenies of supersingular elliptic
curves and ideals of maximal orders in a quaternion algebra. We present a new algorithm to …