Results 81 to 90 of about 6,385 (201)
, 2022 Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / \mathbb{Q}$ that admits a rational isogeny of degree $p$, then $p \in \{2,3,5,7,11,13,17,19,37,43,67,163 \}$. This result is one of the cornerstones of the theory of elliptic curves and plays a crucial role in the proof of Fermat's Last Theorem.
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Multiplicative isogeny estimates [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1998 AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’.
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Jordan correspondence and block distribution of characters
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract We complete the determination of the ℓ$\ell$‐block distribution of characters for quasi‐simple exceptional groups of Lie type up to some minor ambiguities relating to non‐uniqueness of Jordan decomposition. For this, we first determine the ℓ$\ell$‐block distribution for finite reductive groups whose ambient algebraic group defined in ...
Radha Kessar, Gunter Malle
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Hard isogeny problems over RSA moduli and groups with infeasible inversion [PDF]
, 2019 We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over these graphs are hard, and provide a comprehensive list of cryptanalytic ...
Altug, Salim Ali, Chen, Yilei
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Towards quantum‐safe blockchain: Exploration of PQC and public‐key recovery on embedded systems
IET Blockchain, Volume 5, Issue 1, January/December 2025.This paper addresses the need for quantum‐safe blockchain solutions specifically for embedded systems by integrating Post‐Quantum Cryptography (PQC) into blockchain frameworks. We propose a quantum‐secure blockchain architecture using NIST‐standardized PQC algorithms, finding Falcon‐512 to be optimal for embedded environments due to its security and ...
Dominik Marchsreiter
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Generic Construction of Dual‐Server Public Key Authenticated Encryption With Keyword Search
IET Information Security, Volume 2025, Issue 1, 2025.In this paper, we propose a generic construction of dual‐server public key authenticated encryption with keyword search (DS‐PAEKS) from PAEKS, public key encryption, and signatures. We also show that previous DS‐PAEKS scheme is vulnerable by providing a concrete attack. That is, the proposed generic construction yields the first DS‐PAEKS schemes.
Keita Emura, Puttamadappa C.
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Constructing Efficient Identity‐Based Signatures on Lattices
IET Information Security, Volume 2025, Issue 1, 2025.In this work, we explore the recent developments related to lattice‐based signature and preimage sampling, and specify a compact identity‐based signature (IBS) on an ideal lattice for practical use. Specifically, we first propose an ellipsoid version of the G + G signature scheme (Asiacrypt 2023) that achieves slightly better signature size and higher ...
Huiwen Jia +4 more
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Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
SciPost PhysicsWe study how the global structure of rank-one 4d $\mathcal{N}=2$ supersymmetric field theories is encoded into global aspects of the Seiberg-Witten elliptic fibration.
Cyril Closset, Horia Magureanu
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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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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}.
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