Results 51 to 60 of about 274 (176)

A note on local formulae for the parity of Selmer ranks

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.
Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley   +1 more source

Pairing Optimizations for Isogeny-Based Cryptosystems

IET Information Security
In isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing
Shiping Cai, Kaizhan Lin, Chang-An Zhao
doaj   +1 more source

A trade-off between classical and quantum circuit size for an attack against CSIDH

Journal of Mathematical Cryptology, 2020
We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order 𝒪).
Biasse Jean-François, Bonnetain Xavier, Pring Benjamin, Schrottenloher André, Youmans William   +4 more
doaj   +1 more source

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, Patrick Longa, Joost Renes, Lejla Batina   +3 more
doaj   +1 more source

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

Efficiency of SIDH-based signatures (yes, SIDH)

Journal of Mathematical Cryptology
In this note, we assess the efficiency of a supersingular isogeny Diffie-Hellman (SIDH)-based digital signature built on a weaker variant of a recent identification protocol proposed by Basso et al.
Ghantous Wissam, Pintore Federico, Veroni Mattia   +2 more
doaj   +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 , 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

Cyclic cubic points on higher genus curves

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract The distribution of degree d$d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: d=3$d = 3$. For curves of genus at least 5, we show cubic points with Galois group C3$C_3$ arise from well‐structured morphisms, along with providing ...
James Rawson
wiley   +1 more source

On the supersingular GPST attack

Journal of Mathematical Cryptology, 2021
The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
doaj   +1 more source