Results 81 to 90 of about 2,168 (195)
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average [PDF]
, 2015 For an elliptic curve E/Q without complex multiplication we study the distribution of Atkin and Elkies primes l, on average, over all good reductions of E modulo primes p.
Andrew +2 more
core +2 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
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
Hasse principle for Kummer varieties in the case of generic 2‐torsion
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract Conditional on finiteness of relevant Shafarevich–Tate groups, Harpaz and Skorobogatov used Swinnerton‐Dyer's descent‐fibration method to establish the Hasse principle for Kummer varieties associated to a 2‐covering of a principally polarised abelian variety under certain largeness assumptions on its mod 2 Galois image.
Adam Morgan
wiley +1 more source
Exploring Post-Quantum Cryptography: Review and Directions for the Transition Process
TechnologiesAs quantum computing advances, current cryptographic protocols are increasingly vulnerable to quantum attacks, particularly those based on Public Key Infrastructure (PKI) like RSA or Elliptic Curve Cryptography (ECC).
Kanza Cherkaoui Dekkaki +2 more
doaj +1 more source
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
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A Subexponential Algorithm for Evaluating Large Degree Isogenies
, 2010 An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring,
Jao, David, Soukharev, Vladimir
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Towards quantum‐safe blockchain: Exploration of PQC and public‐key recovery on embedded systems
IET Blockchain, Volume 5, Issue 1, January/December 2025.This paper addresses the need for quantum‐safe blockchain solutions specifically for embedded systems by integrating Post‐Quantum Cryptography (PQC) into blockchain frameworks. We propose a quantum‐secure blockchain architecture using NIST‐standardized PQC algorithms, finding Falcon‐512 to be optimal for embedded environments due to its security and ...
Dominik Marchsreiter
wiley +1 more source
The Q-curve construction for endomorphism-accelerated elliptic curves [PDF]
, 2014 We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as ...
Smith, Benjamin
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Constructing Efficient Identity‐Based Signatures on Lattices
IET Information Security, Volume 2025, Issue 1, 2025.In this work, we explore the recent developments related to lattice‐based signature and preimage sampling, and specify a compact identity‐based signature (IBS) on an ideal lattice for practical use. Specifically, we first propose an ellipsoid version of the G + G signature scheme (Asiacrypt 2023) that achieves slightly better signature size and higher ...
Huiwen Jia +4 more
wiley +1 more source