Results 31 to 40 of about 1,885 (215)
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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The isogeny conjecture for A-motives [PDF]
Inventiones mathematicae, 2011 ISSN:1432 ...
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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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Efficient Isogeny Proofs Using Generic Techniques [PDF]
, 2023 Generating supersingular elliptic curves of unknown endomorphism ring has been a problem vexing isogeny-based cryptographers for several years. A recent development has proposed a trusted setup protocol to generate such a curve, where each participant ...
Kelong Cong, Yi-Fu Lai, Shai Levin
core
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 the Security of Supersingular Isogeny Cryptosystems [PDF]
, 2016 We study cryptosystems based on supersingular isogenies. This is an active area of research in post-quantum cryptography. Our first contribution is to give a very powerful active attack on the supersingular isogeny encryption scheme. This attack can only be prevented by using a (relatively expensive) countermeasure.
Steven D. Galbraith +3 more
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Let us walk on the 3-isogeny graph: efficient, fast, and simple
Transactions on Cryptographic Hardware and Embedded SystemsConstructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions ...
Jesús-Javier Chi-Domínguez +2 more
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Mathematics of ComputationWe first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N ,
Corte-Real Santos, M, Flynn, EV
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Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
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The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, 2021 In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
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