Results 61 to 70 of about 2,050 (182)
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem [PDF]
, 2017 Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication.
Jetchev, Dimitar, Wesolowski, Benjamin
core +1 more source
Quantum blockchain: Trends, technologies, and future directions
IET Quantum Communication, Volume 5, Issue 4, Page 516-542, December 2024.This article surveys the current state of blockchain technology, emphasising its security, authentication protocols, AI integration, and the emerging field of quantum blockchain. It highlights how quantum computing can enhance blockchain security and the necessity for quantum‐resistant designs to ensure the robustness of blockchain networks against ...
Manjula Gandhi S +15 more
wiley +1 more source
New Techniques for SIDH-based NIKE
Journal of Mathematical Cryptology, 2020 We consider the problem of producing an efficient, practical, quantum-resistant non-interactive key exchange (NIKE) protocol based on Supersingular Isogeny Diffie-Hellman (SIDH).
Urbanik David, Jao David
doaj +1 more source
A survey analysis of quantum computing adoption and the paradigm of privacy engineering
SECURITY AND PRIVACY, Volume 7, Issue 6, November/December 2024.Abstract This study investigates the adoption of quantum computing (QC) technology using the diffusion of innovation (DOI) theory and provides an extensive literature review. We deployed structural equation modeling to analyze data from a survey conducted among 96 top managers in various industries from Canada, the US, and Europe, including IT‐based ...
Nour Mousa, Farid Shirazi
wiley +1 more source
On extensions of the Jacobson–Morozov theorem to even characteristic
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract Let G$G$ be a simple algebraic group over an algebraically closed field k$\mathbb {k}$ of characteristic 2. We consider analogues of the Jacobson–Morozov theorem in this setting. More precisely, we classify those nilpotent elements with a simple 3‐dimensional Lie overalgebra in g:=Lie(G)$\mathfrak {g}:=\operatorname{Lie}(G)$ and also those ...
David I. Stewart, Adam R. Thomas
wiley +1 more source
Fast Large Integer Modular Addition in GF(p) Using Novel Attribute-Based Representation
IEEE Access, 2019 Addition is an essential operation in all cryptographic algorithms. Higher levels of security require larger key sizes and this becomes a limiting factor in GF(p) using large integers because of the carry propagation problem.
Bader Alhazmi, Fayez Gebali
doaj +1 more source
On isogeny classes of Edwards curves over finite fields [PDF]
, 2011 We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is ...
Ahmadi, Omran, Granger, Robert
core +1 more source
Hard isogeny problems over RSA moduli and groups with infeasible inversion [PDF]
, 2019 We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over these graphs are hard, and provide a comprehensive list of cryptanalytic ...
Altug, Salim Ali, Chen, Yilei
core +1 more source
, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper
Sutherland, Andrew V.
core +1 more source
Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves
CryptographyThe 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 +2 more
doaj +1 more source