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The Open Book Series, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that ...
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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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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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Machine learning for moduli space of genus two curves and an application to isogeny-based cryptography [PDF]
Journal of Algebraic CombinatoricsWe use machine learning to study the moduli space of genus two curves, specifically focusing on detecting whether a genus two curve has (n, n)-split Jacobian.
Elira Shaska, Tanush Shaska
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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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Ordinary isogeny graphs with level structure [PDF]
Canadian mathematical bulletinWe study $\ell $ -isogeny graphs of ordinary elliptic curves defined over $\mathbb {F}_q$ with an added level structure. Given an integer N coprime to p and $\ell ,$ we look at the graphs obtained by adding $\Gamma _0(N)$ , $\Gamma _1(N),$ and
Derek Perrin, J. Voloch
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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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Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
IEEE Access, 2021 In this paper, we present the analysis of Huff curves for implementing isogeny-based cryptography. In this regard, we first investigate the computational cost of the building blocks when compression functions are used for Huff curves.
Suhri Kim
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Transactions on Cryptographic Hardware and Embedded Systems, 2023 Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny ...
Kittiphon Phalakarn +3 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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