Indifferentiable hashing to ordinary elliptic \(\mathbb{F}_{q} \)-curves of \(j=0\) with the cost of one exponentiation in \(\mathbb{F}_{q} \)
type: Item
instance of: scholarly article
title: Indifferentiable hashing to ordinary elliptic \(\mathbb{F}_{q} \)-curves of \(j=0\) with the cost of one exponentiation in \(\mathbb{F}_{q} \)
zbMATH Open document ID: 1483.14048
author: Dmitrii Koshelev
published in: Designs, Codes and Cryptography
publication date: 2022-03-21T00:00:00Z
review text: On of the most important branches of elliptic curve cryptography is the pairing cryptography, especially in secure multi-party computations. It uses mainly elliptic curves \(E_b : y^2 = x^3+b\) defined over finite fields \(\mbox{F}_q \) of characteristic \(> 3\) whose the \(j\)-invariant is 0, since the pairing computations on them is the most efficient. Many pairing-based protocols (for example, the BLS multi-signature scheme) use a hash function of the form \(H : \{0, 1\}^* \rightarrow E_b(\mbox{F}_q)\). It is desirable that \(H\) is indifferentiable from a random oracle and constant time, that is the computation time of its value is independent of an input argument. All such previously proposed hash functions compute two exponentiations in \(\mbox{F}_q\). In this paper, provided that \(\sqrt{b}\in \mbox{F}_q\) and \(q \not \equiv 1\ (\bmod\ 27)\), a new constant-time hash function \(H : \{0, 1\}^* \rightarrow E_b(\mbox{F}_q)\) indifferentiable from a random oracle is proposed which computes only one exponentiation in \(\mbox{F}_q\). Note that this work essentially improves the ideas of the author presented in [``Efficient indifferentiable hashing to elliptic curves \(y^2 = x^3 + b\) provided that \(b\) is a quadratic residue'', Preprint, \url{https://eprint.iacr.org/2020/1070}].
Mathematics Subject Classification ID: 14G50
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14Q20
zbMATH DE Number: 7494014
zbMATH Keywords: cubic residue symbol and cubic roots
zbMATH Keywords: hashing to ordinary elliptic curves of \(j\)-invariant 0
zbMATH Keywords: indifferentiability from a random oracle
zbMATH Keywords: pairing-based cryptography
reviewed by: Dimitros Poulakis
describes a project that uses: Magma
describes a project that uses: Elligator
describes a project that uses: GitHub
MaRDI profile type: Publication
full work available at URL: s10623-022-01012-8
OpenAlex ID: W4221113063
Wikidata QID: Q114849785
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DOI: 10.1007/S10623-022-01012-8
description: scientific article; zbMATH DE number 7494014