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 …

We propose a new suite of algorithms that significantly improve the performance of
supersingular isogeny Diffie-Hellman (SIDH) key exchange. Subsequently, we present a full …

An important open problem in supersingular isogeny-based cryptography is to produce,
without a trusted authority, concrete examples of 'hard supersingular curves' that is …

We discuss the-adic case of Mazur's 'Program B'over: the problem of classifying the possible
images of-adic Galois representations attached to elliptic curves E over, equivalently …

A multifunctional cryptosystem RCNIE on isogenies of non-supersingular Edwards curves is
proposed, which solves the problems of Diffie-Hellman secret sharing, digital signature, and …

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 investigate the isogeny graphs of supersingular elliptic curves over $\mathbb {F} _ {p^ 2}
$ equipped with a $ d $-isogeny to their Galois conjugate. These curves are interesting …

Pairings are useful tools in isogeny-based cryptography and have been used in SIDH/SIKE
and other protocols. As a general technique, pairings can be used to move problems about …

We summarize efficient isogeny sequence computations on elliptic and genus 2 Jacobians.
For cryptographic purposes, sequences of low-degree isogenies are important. Then we …

We propose two authenticated key exchange protocols from supersingular isogenies. Our
protocols are the first post-quantum one-round Diffie–Hellman type authenticated key …