Results 21 to 30 of about 1,885 (215)
Optimized CSIDH Implementation Using a 2-Torsion Point
Cryptography, 2020 The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when ...
Donghoe Heo +4 more
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Isogeny in superstable groups [PDF]
Archive for Mathematical Logic, 2014 We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
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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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Proposal of a New Isogeny-Based Cryptographic Protocol: Formal Analysis and Comparison [PDF]
Mathematics Interdisciplinary ResearchThis paper proposes a novel isogeny-based cryptographic protocol that leverages the dual hardness of the isogeny problem and linear code decoding for secure post-quantum key exchange.
mohammed EL BARAKA, Siham Ezzouak
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On the Performance Analysis for CSIDH-Based Cryptosystems
Applied Sciences, 2020 In this paper, we present the performance and security analysis for various commutative SIDH (CSIDH)-based algorithms. As CSIDH offers a smaller key size than SIDH and provides a relatively efficient signature scheme, numerous CSIDH-based key exchange ...
Donghoe Heo +3 more
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Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves
Journal of Mathematical Cryptology, 2021 Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
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Modular isogeny complexes [PDF]
Algebraic & Geometric Topology, 2012 Minor revisions for ...
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An efficient post-quantum KEM from CSIDH
Journal of Mathematical Cryptology, 2022 The SIDH and CSIDH are now the two most well-known post-quantum key exchange protocols from the supersingular isogeny-based cryptography, which have attracted much attention in recent years and served as the building blocks of other supersingular isogeny-
Qi Mingping
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Orientations and cycles in supersingular isogeny graphs [PDF]
, 2022 The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph.
Ha T. N. Tran +5 more
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Supersingular Elliptic Curve Isogeny Graphs
, 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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