Results 11 to 20 of about 1,885 (215)
Algebraic approaches for solving isogeny problems of prime power degrees
Journal of Mathematical Cryptology, 2020 Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach
Takahashi Yasushi +5 more
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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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An atlas of the Richelot isogeny graph
IACR Cryptol. ePrint Arch., 2021 We 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. Our diagrams are intended to build intuition for number theorists and cryptographers investigating isogeny graphs in dimension/genus 2, and the superspecial isogeny ...
Florit, Enric, Smith, Benjamin
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Isogeny graphs and Isogeny Volcanoes
, 2020 \textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the majority of the components of such a graph will be \textit{volcanoes}, see \cref{defn:pvolcano}.
Barakzahi, Hana
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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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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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Derived isogenies and isogenies for abelian surfaces
, 2021 In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic $\neq 2,3$.
Li, Zhiyuan, Zou, Haitao
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Isogeny Graphs and Cryptographic Applications [PDF]
, 2023 openIn this thesis, we aim to develop the theory of elliptic curves in order to understand the shape of isogeny graphs. This kind of graphs are used as a new cryptographic primitive to resist against quantum key-recovery attacks. We also prove that these
OSTUZZI, MASSIMO
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Karpatsʹkì Matematičnì Publìkacìï, 2013 A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional $(n\leq 3)$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal ...
V.I. Nesteruk
doaj +3 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
Yan Bo Ti, E. V. Flynn
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