Results 71 to 80 of about 3,965 (252)
The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$ [PDF]
, 2022 Stephanie Chan
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Spectra of subrings of cohomology generated by characteristic classes for fusion systems
Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 1990-2005, July 2025.Abstract If F$\mathcal {F}$ is a saturated fusion system on a finite p$p$‐group S$S$, we define the Chern subring Ch(F)${\operatorname{Ch}}(\mathcal {F})$ of F$\mathcal {F}$ to be the subring of H∗(S;Fp)$H^*(S;{\mathbb {F}}_p)$ generated by Chern classes of F$\mathcal {F}$‐stable representations of S$S$. We show that Ch(F)${\operatorname{Ch}}(\mathcal {
Ian J. Leary, Jason Semeraro
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Efficiency of SIDH-based signatures (yes, SIDH)
Journal of Mathematical CryptologyIn 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 +2 more
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Towards Isogeny-Based Password-Authenticated Key Establishment
Journal of Mathematical Cryptology, 2020 Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure.
Taraskin Oleg +3 more
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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
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Hasse principle for Kummer varieties in the case of generic 2‐torsion
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract Conditional on finiteness of relevant Shafarevich–Tate groups, Harpaz and Skorobogatov used Swinnerton‐Dyer's descent‐fibration method to establish the Hasse principle for Kummer varieties associated to a 2‐covering of a principally polarised abelian variety under certain largeness assumptions on its mod 2 Galois image.
Adam Morgan
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Parabolic subgroups in characteristics 2 and 3
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract This text brings to an end the classification of non‐reduced parabolic subgroups in positive characteristic, especially 2 and 3: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result and deduce a few geometric consequences on rational projective homogeneous varieties.
Matilde Maccan
wiley +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
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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
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RAPOPORT–ZINK SPACES OF HODGE TYPE
Forum of Mathematics, Sigma, 2018 When $p>2$ , we construct a Hodge-type analogue of Rapoport–Zink spaces under the unramifiedness assumption, as formal schemes parametrizing ‘deformations’ (up to quasi-isogeny) of $p ...
WANSU KIM
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