Results 61 to 70 of about 3,187 (201)

Dual Isogenies and Their Application to Public-Key Compression for Isogeny-Based Cryptography

, 2019
The isogeny-based protocols SIDH and SIKE have received much attention for being post-quantum key agreement candidates that retain relatively small keys. A recent line of work has proposed and further improved compression of public keys, leading to the inclusion of public-key compression in the SIKE proposal for Round 2 of the NIST Post-Quantum ...
Naehrig, M., Renes, J.
openaire   +3 more sources

Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros, Changho Han, Oana Padurariu, Sun Woo Park   +3 more
wiley   +1 more source

Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])$\operatorname{GL}_2(\mathbb {F}_q[T])$

Mathematika, Volume 72, Issue 2, April 2026.
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley   +1 more source

Optimized One-Dimensional SQIsign Verification on Intel and Cortex-M4

Transactions on Cryptographic Hardware and Embedded Systems
SQIsign is a well-known post-quantum signature scheme due to its small combined signature and public-key size. However, SQIsign suffers from notably long signing times, and verification times are not short either.
Marius A. Aardal, Gora Adj, Arwa Alblooshi, Diego F. Aranha, Isaac A. Canales-Martínez, Jorge Chávez-Saab, Décio Luiz Gazzoni Filho, Krijn Reijnders, Francisco Rodríguez-Henríquez   +8 more
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

Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms

Mathematika, Volume 72, Issue 2, April 2026.
Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
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

Graph potentials and topological quantum field theories

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
wiley   +1 more source

Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph [PDF]

, 2022
We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular.
Enric Florit, Benjamin Smith
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