Optimization of isogeny computation algorithms for post-quantum cryptography
Scientific AfricanIsogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
doaj +1 more source
A subexponential-time, polynomial quantum space algorithm for inverting the CM group action
Journal of Mathematical Cryptology, 2020 We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David +3 more
doaj +1 more source
Easy decision-Diffie-Hellman groups [PDF]
, 2004 The decision-Diffie-Hellman problem (DDH) is a central computational problem in cryptography. It is known that the Weil and Tate pairings can be used to solve many DDH problems on elliptic curves.
Galbraith, Steven, Rotger, Victor
core +5 more sources
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory [PDF]
, 2020 The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory.
Chacón, Iván Blanco
core +2 more sources
On the cyclicity of the rational points group of abelian varieties over finite fields
, 2018 We propose a simple criterion to know if an abelian variety $A$ defined over a finite field $\mathbb{F}_q$ is cyclic, i.e., it has a cyclic group of rational points; this criterion is based on the endomorphism ring End$_{\mathbb{F}_q}(A)$.
Giangreco-Maidana, Alejandro J.
core +3 more sources
Explicit isogenies in quadratic time in any characteristic [PDF]
, 2016 Consider two elliptic curves $E,E'$ defined over the finite field $\mathbb{F}_q$, and suppose that there exists an isogeny $\psi$ between $E$ and $E'$.
De Feo, Luca +3 more
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Isogenies of Elliptic Curves: A Computational Approach [PDF]
, 2009 Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the reducibility of ...
Shumow, Daniel
core +2 more sources
Computing endomorphism rings of elliptic curves under the GRH [PDF]
, 2011 We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis ...
Bisson, Gaetan
core +6 more sources
On fixed‐point‐free involutions in actions of finite exceptional groups of Lie type
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract Let G$G$ be a nontrivial transitive permutation group on a finite set Ω$\Omega$. By a classical theorem of Jordan, G$G$ contains a derangement, which is an element with no fixed points on Ω$\Omega$. Given a prime divisor r$r$ of |Ω|$|\Omega |$, we say that G$G$ is r$r$‐elusive if it does not contain a derangement of order r$r$. In a paper from
Timothy C. Burness, Mikko Korhonen
wiley +1 more source
Towards Isogeny-Based Password-Authenticated Key Establishment
Journal of Mathematical Cryptology, 2020 Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure.
Taraskin Oleg +3 more
doaj +1 more source