Results 1 to 10 of about 4,641 (196)

Practical Usage of Radical Isogenies for CSIDH

IEEE Access, 2023
Recently, a radical isogeny was proposed to boost commutative supersingular isogeny Diffie–Hellman (CSIDH) implementation. Radical isogenies reduce the generation of a kernel of a small prime order when implementing CSIDH.
Donghoe Heo, Suhri Kim, Seokhie Hong
doaj   +3 more sources

Efficient (3, 3)-isogenies on fast Kummer surfaces [PDF]

Research in Number Theory
We give an alternative derivation of (N, N)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formulæ for the case of N=3\documentclass[12pt]{minimal}
Maria Corte-Real Santos, Craig Costello, Benjamin Smith   +2 more
semanticscholar   +4 more sources

Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves

Journal of Mathematical Cryptology, 2020
We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be ...
Boneh Dan, Glass Darren, Krashen Daniel, Lauter Kristin, Sharif Shahed, Silverberg Alice, Tibouchi Mehdi, Zhandry Mark   +7 more
doaj   +2 more sources

Fast change of level and applications to isogenies

Research in Number Theory, 2022
Let (A,L,Θn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(A ...
D. Lubicz, Damien Robert
semanticscholar   +3 more sources

Constructing elliptic curve isogenies in quantum subexponential time

Journal of Mathematical Cryptology, 2014
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 finding such an isogeny is believed to be computationally difficult.
Childs Andrew, Jao David, Soukharev Vladimir   +2 more
doaj   +2 more sources

Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

Journal of Mathematical Cryptology, 2014
We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
De Feo Luca, Jao David, Plût Jérôme
doaj   +2 more sources

SQIPrime: A dimension 2 variant of SQISignHD with non-smooth challenge isogenies

Lecture Notes in Computer Science
. We introduce SQIPrime, a post-quantum digital signature scheme based on the Deuring correspondence and Kani’s Lemma. Compared to its predecessors that are SQISign and especially SQISignHD, SQIPrime further expands the use of high dimensional isogenies,
Max Duparc, T. Fouotsa
semanticscholar   +3 more sources

Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves

Cryptography
The article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor ...
Anatoly Bessalov, Volodymyr Sokolov, Serhii Abramov   +2 more
doaj   +2 more sources

SQISign: compact post-quantum signatures from quaternions and isogenies

Lecture Notes in Computer Science, 2020
L. De Feo, D. Kohel, Antonin Leroux, Christophe Petit, B. Wesolowski   +4 more
semanticscholar   +3 more sources

Verifiable delay functions and delay encryptions from hyperelliptic curves

Cybersecurity, 2023
Verifiable delay functions (VDFs) and delay encryptions (DEs) are two important primitives in decentralized systems, while existing constructions are mainly based on time-lock puzzles.
Chao Chen, Fangguo Zhang
doaj   +1 more source