Results 21 to 30 of about 4,610 (199)
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
The most efficient indifferentiable hashing to elliptic curves of j-invariant 1728
Journal of Mathematical Cryptology, 2022 This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic ...
Koshelev Dmitrii
doaj +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
Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
doaj +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
Algebraic approaches for solving isogeny problems of prime power degrees
Journal of Mathematical Cryptology, 2020 Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach
Takahashi Yasushi +5 more
doaj +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
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