Results 21 to 30 of about 6,385 (201)
The Open Book Series, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that ...
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Transactions on Cryptographic Hardware and Embedded Systems, 2023 Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny ...
Kittiphon Phalakarn +3 more
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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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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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On certain isogenies between K3 surfaces [PDF]
, 2019 The aim of this paper is to construct "special" isogenies between K3 surfaces, which are not Galois covers between K3 surfaces, but are obtained by composing cyclic Galois covers, induced by quotients by symplectic automorphisms.
Camere, Chiara, Garbagnati, Alice
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Genus Two Isogeny Cryptography [PDF]
, 2019 We study \((\ell ,\ell )\)-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The \((\ell ,\ell )\)-isogeny graph has cycles of small length that can be used to break the collision resistance assumption of the genus two isogeny hash function suggested by Takashima.
Flynn, E, Ti, Y
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Transactions on Cryptographic Hardware and Embedded Systems, 2023 We propose a novel approach that generalizes interleaved modular multiplication algorithms for the computation of sums of products over large prime fields. This operation has widespread use and is at the core of many cryptographic applications.
Patrick Longa
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Class number formulas via 2-isogenies of elliptic curves [PDF]
, 2012 A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of ...
McLeman, Cam, Rasmussen, Christopher
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Let us walk on the 3-isogeny graph: efficient, fast, and simple
Transactions on Cryptographic Hardware and Embedded SystemsConstructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions ...
Jesús-Javier Chi-Domínguez +2 more
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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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