Results 11 to 20 of about 4,401 (158)
Algebraic theories of power operations
Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023 Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
wiley +1 more source
Families of ϕ‐congruence subgroups of the modular group
Mathematika, Volume 69, Issue 4, Page 1104-1144, October 2023., 2023 Abstract We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed ϕ‐congruence subgroups, are obtained by reducing homomorphisms ϕ from the modular group into a linear algebraic group modulo integers.
Angelica Babei +2 more
wiley +1 more source
Class numbers, cyclic simple groups, and arithmetic
Journal of the London Mathematical Society, Volume 108, Issue 1, Page 238-272, July 2023., 2023 Abstract Here, we initiate a program to study relationships between finite groups and arithmetic–geometric invariants in a systematic way. To do this, we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock Jacobi forms.
Miranda C. N. Cheng +2 more
wiley +1 more source
A two‐dimensional arithmetic André–Oort problem
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1459-1488, June 2023., 2023 Abstract We state and investigate an integral analogue of the André–Oort conjecture (in integral models of Shimura varieties). We establish an instance of this conjecture: the case of a modular curve, as a scheme over Z$\mathbf {Z}$. Our approach relies on equidistribution estimates related to subconvexity in analytic number theory and our result is ...
Rodolphe Richard
wiley +1 more source
Torsion point attacks on ‘SIDH‐like’ cryptosystems
IET Information Security, Volume 17, Issue 2, Page 161-170, March 2023., 2023 Abstract Isogeny‐based cryptography is a promising approach for post‐quantum cryptography. The best‐known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA‐secure key encapsulation mechanism SIKE, which was submitted to and remains in the third round of NIST's post ...
Péter Kutas, Christophe Petit
wiley +1 more source
Quantum algorithms for attacking hardness assumptions in classical and post‐quantum cryptography
IET Information Security, Volume 17, Issue 2, Page 171-209, March 2023., 2023 Abstract In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post‐quantum secure cryptosystems.
J.‐F. Biasse +4 more
wiley +1 more source
International Journal of Intelligent Systems, Volume 2023, Issue 1, 2023., 2023 With the rapid development of Internet of Things (IoT), designing a secure two‐factor authentication scheme for IoT is becoming increasingly demanding. Two‐factor protocols are deployed to achieve a higher security level than single‐factor protocols.
Behnam Zahednejad +4 more
wiley +1 more source
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Scalar multiplications are considered an essential aspect of implementations of isogeny‐based cryptography. The efficiency of scalar multiplication depends on the equation of the underlying elliptic curves and the addition chain employed. Bos and Friedberger recently stated that, for larger scalar multiplication, addition‐subtraction chains will become
Sookyung Eom +3 more
wiley +1 more source
Optimized CSIDH Implementation Using a 2-Torsion Point
Cryptography, 2020 The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when ...
Donghoe Heo +4 more
doaj +1 more source
Superspecial rank of supersingular abelian varieties and Jacobians [PDF]
, 2015 An abelian variety defined over an algebraically closed field k of positive characteristic is supersingular if it is isogenous to a product of supersingular elliptic curves and is superspecial if it is isomorphic to a product of supersingular elliptic ...
Achter, Jeff, Pries, Rachel
core +2 more sources