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Isogenies on twisted Hessian curves [PDF]
Journal of Mathematical Cryptology, 2021 Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic
Perez Broon Fouazou Lontouo +3 more
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How to Compute an Isogeny on the Extended Jacobi Quartic Curves? [PDF]
International Journal of Electronics and Telecommunications, 2022 Computing isogenies between elliptic curves is a significant part of post-quantum cryptography with many practical applications (for example, in SIDH, SIKE, B-SIDH, or CSIDH algorithms).
Łukasz Dzierzkowski, Michał Wroński
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Journal of High Energy Physics, 2021 We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in ...
Hjalte Frellesvig +3 more
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Practical Usage of Radical Isogenies for CSIDH
IEEE Access, 2023 Recently, a radical isogeny was proposed to boost commutative supersingular isogeny Diffie–Hellman (CSIDH) implementation. Radical isogenies reduce the generation of a kernel of a small prime order when implementing CSIDH.
Donghoe Heo, Suhri Kim, Seokhie Hong
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Verifiable delay functions and delay encryptions from hyperelliptic curves
Cybersecurity, 2023 Verifiable delay functions (VDFs) and delay encryptions (DEs) are two important primitives in decentralized systems, while existing constructions are mainly based on time-lock puzzles.
Chao Chen, Fangguo Zhang
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Review of Chosen Isogeny-Based Cryptographic Schemes
Cryptography, 2022 Public-key cryptography provides security for digital systems and communication. Traditional cryptographic solutions are constantly improved, e.g., to suppress brute-force attacks.
Bartosz Drzazga, Łukasz Krzywiecki
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Isogeny graphs of ordinary abelian varieties [PDF]
, 2016 Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties.
Brooks, Ernest Hunter +2 more
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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 𝒪).
Biasse Jean-François +4 more
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Optimal Strategies for Computation of Degree ℓn Isogenies for SIDH [PDF]
International Journal of Electronics and Telecommunications, 2020 This article presents methods and algorithms for the computation of isogenies of degree ℓn. Some of these methods are obtained using recurrence equations and generating functions.
Michał Wroński, Andrzej Chojnacki
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