Results 51 to 60 of about 3,965 (252)
Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH
IET Information Security, 2021 The supersingular isogeny Diffie–Hellman key exchange protocol (SIDH) was introduced by Jao and De Feo in 2011. SIDH operates on supersingular elliptic curves defined over Fp2, where p is a large prime number of the form p=4eA3eB−1 and eA and eB are ...
Daniel Cervantes‐Vázquez +2 more
doaj +1 more source
A note on the cohomology of moduli spaces of local shtukas
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3709-3729, December 2025.Abstract We study localized versions of spectral action of Fargues–Scholze, using methods from higher algebra. As our main motivation and application, we deduce a formula for the cohomology of moduli spaces of local shtukas under certain genericity assumptions, and discuss its relation with the Kottwitz conjecture.
David Hansen, Christian Johansson
wiley +1 more source
Algebraic Geometry, 2016 We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$.
Marcucci, Valeria +2 more
openaire +7 more sources
Highly Vectorized SIKE for AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2022 It is generally accepted that a large-scale quantum computer would be capable to break any public-key cryptosystem used today, thereby posing a serious threat to the security of the Internet’s public-key infrastructure.
Hao Cheng +3 more
doaj +1 more source
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
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
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
Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
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Finding Practical Parameters for Isogeny-based Cryptography
IACR Cryptology ePrint ArchiveIsogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of
Maria Corte-Real Santos +3 more
semanticscholar +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