Results 21 to 30 of about 4,471 (200)
An efficient post-quantum KEM from CSIDH
Journal of Mathematical Cryptology, 2022 The SIDH and CSIDH are now the two most well-known post-quantum key exchange protocols from the supersingular isogeny-based cryptography, which have attracted much attention in recent years and served as the building blocks of other supersingular isogeny-
Qi Mingping
doaj +1 more source
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
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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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
An Efficient Signature Scheme From Supersingular Elliptic Curve Isogenies
IEEE Access, 2019 Since supersingular elliptic curve isogenies are one of the several candidate sources of hardness for building post-quantum cryptographic primitives, the research of efficient signature schemes based on them is still a hot topic.
Yan Huang +3 more
doaj +1 more source