Results 61 to 70 of about 5,346 (174)
A Compact and Scalable Hardware/Software Co-design of SIKE
Transactions on Cryptographic Hardware and Embedded Systems, 2020 We present efficient and compact hardware/software co-design implementations of the Supersingular Isogeny Key Encapsulation (SIKE) protocol on field-programmable gate arrays (FPGAs).
Pedro Maat C. Massolino +3 more
doaj +1 more source
A local-global principle for isogenies of prime degree over number fields
, 2014 We give a description of the set of exceptional pairs for a number field $K$, that is the set of pairs $(\ell, j(E))$, where $\ell$ is a prime and $j(E)$ is the $j$-invariant of an elliptic curve $E$ over $K$ which admits an $\ell$-isogeny locally almost
Anni, Samuele
core +3 more sources
The geometry and arithmetic of bielliptic Picard curves
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley +1 more source
Constant time lattice reduction in dimension 4 with application to SQIsign
Transactions on Cryptographic Hardware and Embedded SystemsIn this paper we propose a constant time lattice reduction algorithm for integral dimension-4 lattices. Motivated by its application in the SQIsign postquantum signature scheme, we provide for the first time a constant time LLLlike algorithm with ...
Otto Hanyecz +4 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
core +1 more source
Weakly special threefolds and nondensity of rational points
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We verify part of a conjecture of Campana predicting that rational points on the weakly special nonspecial simply connected smooth projective threefolds constructed by Bogomolov–Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps, and prove a dimension bound for such moduli spaces
Finn Bartsch +2 more
wiley +1 more source
Digital Signature in Class Group of Isogenies Elliptic Curves
Безопасность информационных технологий, 2010 Digital signature protocol based on Schnorr protocol is proposed. Protection against quantum attacks is achieved by using isogenies computation problem.
J. V. Gel, A. G. Rostovtsev
doaj
On the Parallelization of Square-Root Vélu’s Formulas
Mathematical and Computational ApplicationsA primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab +2 more
doaj +1 more source
Mathematics of ComputationWe first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N , N ) (N,N) -isogenies, for any odd N N , both on the general Kummer surface and on the Fast model.
Corte-Real Santos, M, Flynn, EV
openaire +2 more sources
Constructing Permutation Rational Functions from Isogenies [PDF]
SIAM Journal on Discrete Mathematics, 2018 A permutation rational function $f\in \mathbb{F}_q(x)$ is a rational function that induces a bijection on $\mathbb{F}_q$, that is, for all $y\in\mathbb{F}_q$ there exists exactly one $x\in\mathbb{F}_q$ such that $f(x)=y$. Permutation rational functions are intimately related to exceptional rational functions, and more generally exceptional covers of ...
Bisson, Gaetan, Tibouchi, Mehdi
openaire +2 more sources