Results 61 to 70 of about 274 (176)
Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source
Optimized One-Dimensional SQIsign Verification on Intel and Cortex-M4
Transactions on Cryptographic Hardware and Embedded SystemsSQIsign 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 +8 more
doaj +1 more source
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
wiley +1 more source
Heuristics on pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2012 We present a heuristic asymptotic formula as for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree , with fixed discriminant, with rho-value bounded by a fixed such that , and with prime ...
Boxall John
doaj +1 more source
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
doaj +1 more source
A Comparison of Security and its Performance for Key Agreements in Post-Quantum Cryptography
IEEE Access, 2020 Nowadays, we are surrounded by devices collecting and transmitting private information. Currently, the two main mathematical problems that guarantee security on the Internet are the Integer Factorization Problem and the Discrete Logarithm Problem ...
Fabio Borges +2 more
doaj +1 more source
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
wiley +1 more source
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
Journal of Mathematical Cryptology, 2014 We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
De Feo Luca, Jao David, Plût Jérôme
doaj +1 more source
, 2022 Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / \mathbb{Q}$ that admits a rational isogeny of degree $p$, then $p \in \{2,3,5,7,11,13,17,19,37,43,67,163 \}$. This result is one of the cornerstones of the theory of elliptic curves and plays a crucial role in the proof of Fermat's Last Theorem.
openaire +2 more sources
Multiplicative isogeny estimates [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1998 AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’.
openaire +3 more sources