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

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

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 …

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 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 …

Given two ordinary elliptic curves over a finite field having the same cardinality and
endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but …

Supersingular isogeny-based cryptography is one of the more recent families of post-
quantum proposals. An interesting feature is the comparatively low bandwidth occupation in …

Let A/F _p and A'/F _p be superspecial principally polarized abelian varieties of dimension
g> 1. For any prime ℓ ≠ p, we give an algorithm that finds a path ϕ: A → A'in the (ℓ,\dots, ℓ) …

We propose a quantum algorithm for computing an isogeny between two elliptic curves E_1,
E_2 defined over a finite field such that there is an imaginary quadratic order O satisfying O …