Results 11 to 20 of about 162 (153)
Proving knowledge of isogenies: a survey
Designs, Codes and Cryptography, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ward Beullens +3 more
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Derived isogenies and isogenies for abelian surfaces
, 2021 In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic $\neq 2,3$.
Li, Zhiyuan, Zou, Haitao
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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
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A trade-off between classical and quantum circuit size for an attack against CSIDH
Journal of Mathematical Cryptology, 2020 We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order đť’Ş).
Biasse Jean-François +4 more
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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
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On the supersingular GPST attack
Journal of Mathematical Cryptology, 2021 The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
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Optimal Strategies for Computation of Degree â„“n Isogenies for SIDH [PDF]
International Journal of Electronics and Telecommunications, 2020 This article presents methods and algorithms for the computation of isogenies of degree â„“n. Some of these methods are obtained using recurrence equations and generating functions.
Michał Wroński, Andrzej Chojnacki
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Isogeny in superstable groups [PDF]
Archive for Mathematical Logic, 2014 We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
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Modular isogeny complexes [PDF]
Algebraic & Geometric Topology, 2012 Minor revisions for ...
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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
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