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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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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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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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Faster computation of isogenies of large prime degree [PDF]
IACR Cryptology ePrint Archive, 2020 Let $\mathcal{E}/\mathbb{F}_q$ be an elliptic curve, and $P$ a point in $\mathcal{E}(\mathbb{F}_q)$ of prime order $\ell$. Velu's formulae let us compute a quotient curve $\mathcal{E}' = \mathcal{E}/\langle{P}\rangle$ and rational maps defining a ...
Daniel J. Bernstein +3 more
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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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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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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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Group signatures and more from isogenies and lattices: generic, simple, and efficient
Designs, Codes and Cryptography, 2023 We construct an efficient dynamic group signature (or more generally an accountable ring signature) from isogeny and lattice assumptions. Our group signature is based on a simple generic construction that can be instantiated by cryptographically hard ...
Ward Beullens +4 more
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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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