Results 1 to 10 of about 274 (176)
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
doaj +6 more sources
A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Álvaro Lozano-Robledo
exaly +2 more sources
Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
exaly +2 more sources
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.
David Jao
exaly +2 more sources
Journal of High Energy Physics, 2021 AbstractWe 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 full and loop-by-loop variants).
Frellesvig, Hjalte +3 more
openaire +6 more sources
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
doaj +1 more source
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
doaj +1 more source
Comptes Rendus. MathématiqueIn this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field $K$ of characteristic $p$ are isogenous. Specifically, assuming that their endomorphism algebras tensored with $\mathbb{Q}
Chiarellotto, Bruno, Trihan, Fabien
doaj +2 more sources
, 2020 sponsorship: This work was supported in part by the Research Council KU Leuven grants C14/18/067 and STG/17/019, by CyberSecurity Research Flanders with reference number VR20192203, and by the Research Foundation Flanders (FWO) through the WOG Coding Theory and Cryptography. (Research Council KU Leuven|C14/18/067, Research Council KU Leuven|STG/17/019,
Castryck, Wouter +2 more
openaire +2 more sources
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
doaj +1 more source