Results 31 to 40 of about 3,187 (201)

Modular isogeny complexes [PDF]

Algebraic & Geometric Topology, 2012
Minor revisions for ...
openaire   +3 more sources

Hash functions from superspecial genus-2 curves using Richelot isogenies

Journal of Mathematical Cryptology, 2020
In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter, Decru Thomas, Smith Benjamin   +2 more
doaj   +1 more source

Let us walk on the 3-isogeny graph: efficient, fast, and simple

Transactions on Cryptographic Hardware and Embedded Systems
Constructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions ...
Jesús-Javier Chi-Domínguez, Eduardo Ochoa-Jiménez, Ricardo-Neftalí Pontaza-Rodas   +2 more
doaj   +1 more source

A Post-Quantum Zero-Knowledge Identification Scheme [PDF]

Mathematics Interdisciplinary Research
‎In this paper‎, ‎we introduce a zero-knowledge identification protocol designed for authentication within the supersingular isogeny Diffie-Hellman (SIDH) key exchange framework‎.
Maryam Rezaei Kashi, Mojtaba Bahramian
doaj   +1 more source

Hyperbolicity and fundamental groups of complex quasi‐projective varieties (III): Applications

Proceedings of the London Mathematical Society, Volume 133, Issue 5, November 2026.
Abstract This paper is Part III of a series of three. We begin by introducing the notion of h$h$‐special varieties, which can be seen as varieties “chain‐connected by the Zariski closures of entire curves.” We prove that if X$X$ is either a special smooth complex quasi‐projective variety in the sense of Campana or an h$h$‐special variety, then for any ...
Benoît Cadorel, Ya Deng, Katsutoshi Yamanoi   +2 more
wiley   +1 more source

Optimization of isogeny computation algorithms for post-quantum cryptography

Scientific African
Isogeny-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

The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type

Forum of Mathematics, Sigma, 2021
In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
doaj   +1 more source

Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Mathematische Nachrichten, Volume 299, Issue 8, Page 1894-1916, August 2026.
ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley   +1 more source

Isogenies on Kummer Surfaces

Mathematics of Computation
We 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 ,
Corte-Real Santos, M, Flynn, EV
openaire   +2 more sources

Efficient Constant-Time Implementation of terSIDH

IEEE Access
Since supersingular isogeny Diffie-Hellman (SIDH) was broken by a polynomial-time attack, several countermeasures were proposed as it was regarded as the most efficient algorithm among isogeny-based cryptosystems. Among them, terSIDH has been highlighted
Taehun Kang, Donghoe Heo, Jeonghwan Lee, Suhri Kim, Changmin Lee   +4 more
doaj   +1 more source