Results 11 to 20 of about 3,064 (192)
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
core +6 more sources
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
openaire +5 more sources
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
core +8 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
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 +4 more sources
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
E. V. Flynn, Yan Bo Ti
core +1 more source
Isogeny-based Signatures with Randomizable Keys
Digital signature schemes based on isogenies are among the most compact signatures achieving post-quantum security. Recent advances, especially those leveraging higher-dimensional isogenies, have also made such schemes practically efficient.
Invernizzi, Riccardo +7 more
core +8 more sources
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
openaire +5 more sources
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
core +1 more source