Results 51 to 60 of about 159 (153)
Mathematics of Isogeny Based Cryptography
, 2017 These lectures notes were written for a summer school on Mathematics for post-quantum cryptography in Thi s, Senegal. They try to provide a guide for Masters' students to get through the vast literature on elliptic curves, without getting lost on their way to learning isogeny based cryptography.
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A High-Performance and Scalable Hardware Architecture for Isogeny-Based Cryptography
IEEE Transactions on Computers, 2018 In this work, we present a high-performance and scalable architecture for isogeny-based cryptosystems. In particular, we use the architecture in a fast, constant-time FPGA implementation of the quantum-resistant supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol.
Brian Koziel +2 more
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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
Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves
CryptographyThe article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor ...
Anatoly Bessalov +2 more
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Efficiency of SIDH-based signatures (yes, SIDH)
Journal of Mathematical CryptologyIn this note, we assess the efficiency of a supersingular isogeny Diffie-Hellman (SIDH)-based digital signature built on a weaker variant of a recent identification protocol proposed by Basso et al.
Ghantous Wissam +2 more
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Optimized SeaSign for Enhanced Efficiency
IEEE AccessThis paper optimized SeaSign – an isogeny-based digital signature algorithm that combines the class group actions of CSIDH with the notion of Fiat-Shamir with abort.
Suhri Kim
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Finding Practical Parameters for Isogeny-based Cryptography
IACR Communications in CryptologyIsogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer
Maria Santos +3 more
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Paving the Way for SQIsign: Toward Efficient Deployment on 32-bit Embedded Devices
MathematicsThe threat of quantum computing has spurred research into post-quantum cryptography. SQIsign, a candidate submitted to the standardization process of the National Institute of Standards and Technology, is emerging as a promising isogeny-based signature ...
Yue Hu, Shiyu Shen, Hao Yang, Weize Wang
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On the Parallelization of Square-Root Vélu’s Formulas
Mathematical and Computational ApplicationsA primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab +2 more
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Quaternion Algrebras and isogeny-based cryptography
, 2022 L'avènement de l'ordinateur quantique est une menace pour la cryptographie en permettant de résoudre les problèmes sur lesquels reposent la sécurité de nombreux protocoles. La cryptographie à base d'isogénies est une famille de protocoles reposant sur la difficulté de trouver une isogénie entre deux courbes elliptiques supersingulières, un problème ...
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