Indifferentiable hashing to ordinary elliptic \(\mathbb{F}_{q} \)-curves of \(j=0\) with the cost of one exponentiation in \(\mathbb{F}_{q} \)

DOI10.1007/s10623-022-01012-8zbMath1483.14048OpenAlexW4221113063WikidataQ114849785 ScholiaQ114849785MaRDI QIDQ2115746

Dmitrii Koshelev

Publication date: 21 March 2022

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-022-01012-8

zbMATH Keywords

pairing-based cryptographycubic residue symbol and cubic rootshashing to ordinary elliptic curves of \(j\)-invariant 0indifferentiability from a random oracle

Mathematics Subject Classification ID

Elliptic curves (14H52) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (4)

Optimal Encodings to Elliptic Curves of \(\boldsymbol{j}\)-Invariants 0, 1728 ⋮ The most efficient indifferentiable hashing to elliptic curves of \(j\)-invariant 1728 ⋮ \textsc{SwiftEC}: Shallue-van de Woestijne indifferentiable function to elliptic curves. Faster indifferentiable hashing to elliptic curves ⋮ Hashing to elliptic curves through Cipolla-Lehmer-Müller's square root algorithm

Uses Software

• Magma
• GitHub
• Elligator

Cites Work

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• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
• New cube root algorithm based on the third order linear recurrence relations in finite fields
• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy
• Guide to Pairing-Based Cryptography
• How to Hash into Elliptic Curves
• Algebraic Function Fields and Codes
• Efficient Indifferentiable Hashing into Ordinary Elliptic Curves
• The Arithmetic of Elliptic Curves
• Points on elliptic curves over finite fields
• On the unirationality of higher dimensional Ueno-type manifolds

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