Results 41 to 50 of about 10,757 (241)
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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Descent via (3,3)-isogeny on Jacobians of genus 2 curves [PDF]
, 2014 We give parametrisation of curves C of genus 2 with a maximal isotropic (ZZ/3)^2 in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny.
Bruin, Nils +2 more
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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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Isogeny-based post-quantum key exchange protocols [PDF]
, 2020 The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves.
Sorinas Capdevila, Ernest
core
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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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.
openaire +3 more sources
Ramanujan graphs in cryptography [PDF]
, 2018 In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in ...
Costache, Anamaria +4 more
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Hash functions from superspecial genus-2 curves using Richelot isogenies
Journal of Mathematical Cryptology, 2020 In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter +2 more
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On isogeny classes of Edwards curves over finite fields
Journal of Number Theory, 2012 Omran Ahmadi
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Rational Isogenies from Irrational Endomorphisms
, 2020 In this paper, we introduce a polynomial-time algorithm to compute a connecting \(\mathcal {O}\)-ideal between two supersingular elliptic curves over \(\mathbb {F}_p\) with common \(\mathbb {F}_p\)-endomorphism ring \(\mathcal {O}\), given a description of their full endomorphism rings.
Castryck, Wouter +2 more
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