Results 91 to 100 of about 8,681 (237)

On the Parallelization of Square-Root Vélu’s Formulas

Mathematical and Computational Applications
A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab, Odalis Ortega, Amalia Pizarro-Madariaga   +2 more
doaj   +1 more source

A survey analysis of quantum computing adoption and the paradigm of privacy engineering

SECURITY AND PRIVACY, Volume 7, Issue 6, November/December 2024.
Abstract This study investigates the adoption of quantum computing (QC) technology using the diffusion of innovation (DOI) theory and provides an extensive literature review. We deployed structural equation modeling to analyze data from a survey conducted among 96 top managers in various industries from Canada, the US, and Europe, including IT‐based ...
Nour Mousa, Farid Shirazi
wiley   +1 more source

On extensions of the Jacobson–Morozov theorem to even characteristic

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract Let G$G$ be a simple algebraic group over an algebraically closed field k$\mathbb {k}$ of characteristic 2. We consider analogues of the Jacobson–Morozov theorem in this setting. More precisely, we classify those nilpotent elements with a simple 3‐dimensional Lie overalgebra in g:=Lie(G)$\mathfrak {g}:=\operatorname{Lie}(G)$ and also those ...
David I. Stewart, Adam R. Thomas
wiley   +1 more source

Galois invariants of finite abelian descent and Brauer sets

Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3240-3256, October 2024.
Abstract For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer–Manin obstructions. Given a Galois extension of the ground field, one can consider similar sets over the extension and take Galois invariants.
Brendan Creutz, Jesse Pajwani, José Felipe Voloch   +2 more
wiley   +1 more source

Uniformizing the Stacks of Abelian Sheaves

, 2004
Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects "of dimension 1 ...
A. Blum, A. Genestier, A. Grothendieck, A. Grothendieck, A. Grothendieck, C. S. Seshadri, D. Eisenbud, D. Knutson, G. Anderson, G. Faltings, G. Laumon, G. Laumon, G. Laumon, I. Y. Potemine, J.-F. Boutot, L. Lafforgue, L. Lafforgue, M. Harris, M. Rapoport, M. Raynaud, M. Rosen, N. Katz, P. Deligne, P. Deligne, R. Hartshorne, S. Bosch, Th. Hausberger, U. Stuhler, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. Čerednik, Y. I. Manin, Y. Taguchi   +35 more
core   +5 more sources

Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies

IACR Cryptology ePrint Archive
We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing the limitations of existing isogeny-based ring signatures.
Giacomo Borin, Yi-Fu Lai, Antonin Leroux
semanticscholar   +1 more source

On the Security of Supersingular Isogeny Cryptosystems [PDF]

, 2016
We study cryptosystems based on supersingular isogenies. This is an active area of research in post-quantum cryptography. Our first contribution is to give a very powerful active attack on the supersingular isogeny encryption scheme. This attack can only be prevented by using a (relatively expensive) countermeasure.
Galbraith, Steven S.D., Petit, Christophe, Shani, Barak, Ti, Yan Bo   +3 more
openaire   +2 more sources

Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$

Mathematika, Volume 70, Issue 4, October 2024.
Abstract In this paper, we study the integer solutions of a family of Fermat‐type equations of signature (2,2n,n)$(2, 2n, n)$, Cx2+qky2n=zn$Cx^2 + q^ky^{2n} = z^n$. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant BC,q$B_{C, q}$ such that if n>BC,q$n > B_{C,q}$, there are no solutions (x,y ...
Pedro‐José Cazorla García
wiley   +1 more source

Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories

SciPost Physics
We study how the global structure of rank-one 4d $\mathcal{N}=2$ supersymmetric field theories is encoded into global aspects of the Seiberg-Witten elliptic fibration.
Cyril Closset, Horia Magureanu
doaj   +1 more source

Essential dimension of isogenies

Pure and Applied Mathematics Quarterly
We give a lower bound for the essential dimension of isogenies of complex abelian varieties. The bound is sharp in many cases. In particular, the multiplication-by-$m$ map is incompressible for every $m\geq 2$, confirming a conjecture of Brosnan.
Kollár, János, Zhuang, Ziquan
openaire   +2 more sources