Results 11 to 20 of about 3,187 (201)
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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Isogeny Problems with Level Structure [PDF]
Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the behavior of the isogeny on a large enough subgroup, the problem can become easy, as recent ...
Luca De Feo +2 more
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Supersingular Elliptic Curve Isogeny Graphs [PDF]
, 2022 As quantum computers become more and more advanced, currently standard cryptographic protocol becomes weaker. Supersingular elliptic curve isogeny graphs are a promising new direction for post-quantum cryptographic protocol.
Arpin, Sarah
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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
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, 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
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An atlas of the Richelot isogeny graph
, 2022 International audienceWe describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny graph of principally polarized abelian surfaces, considering the action of automorphisms.
Florit, Enric, Smith, Benjamin
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Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph [PDF]
, 2021 International audienceWe investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular.
Florit, Enric, Smith, Benjamin
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Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF [PDF]
, 2021 In this paper, we investigate the problem of constructing postquantum-secure verifiable delay functions (VDFs), particularly based on supersingular isogenies.
Jorge Chavez-Saab +2 more
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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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Genus Two Isogeny Cryptography [PDF]
, 2022 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
Yan Bo Ti, E. V. Flynn
core +1 more source