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2018 | OriginalPaper | Buchkapitel

Towards Static Assumption Based Cryptosystem in Pairing Setting: Further Applications of DéjàQ and Dual-Form Signature (Extended Abstract)

verfasst von : Sanjit Chatterjee, R. Kabaleeshwaran

Erschienen in: Provable Security

Verlag: Springer International Publishing

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Abstract

A large number of parameterized complexity assumptions have been introduced in the bilinear pairing setting to design novel cryptosystems and an important question is whether such “q-type” assumptions can be replaced by some static one. Recently Ghadafi and Groth captured several such parameterized assumptions in the pairing setting in a family called bilinear target assumption (BTA). We apply the DéjàQ techniques for all q-type assumptions in the BTA family. In this process, first we formalize the notion of extended adaptive parameter-hiding property and use it in the Chase-Meiklejohn’s DéjàQ framework to reduce those q-type assumptions from subgroup hiding assumption in the asymmetric composite-order pairing. In addition, we extend the BTA family further into BTA1 and BTA2 and study the relation between different BTA variants. We also discuss the inapplicability of DéjàQ techniques on the q-type assumptions that belong to BTA1 or BTA2 family. We then provide one further application of Gerbush et al.’s dual-form signature techniques to remove the dependence on a q-type assumption for which existing DéjàQ techniques are not applicable. This results in a variant of Abe et al.’s structure-preserving signature with security based on a static assumption in composite order setting.

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Vorheriges Kapitel A Code-Based Linkable Ring Signature Scheme

Nächstes Kapitel Digital Signatures from the Middle-Product LWE

For BTA in \(\mathbb G_T\), the degree of the challenge term polynomials are bounded by 2d, as given the d degree polynomials in both source groups, one can use the pairing to compute the product of these polynomials in \(\mathbb G_T\).

We say that the BTA assumption defined in the asymmetric pairing setting is one-sided, if the secret vector \(\mathbf {x}\) associated with the polynomial representation occurs in exactly one of the source groups. Otherwise we say that the assumption is two-sided.

Even if \(N=p_1\ldots p_n\), we decompose G using two of its subgroups \(G_1\) and \(G_2\) such that \(G_1\) (resp. \(G_2\)) is a subgroup of order \(p_1\ldots p_{n-1}\) (resp. \(p_n\)).

As similar to BTA assumption, hardness of Assumption 4 ensures that the instance and challenge terms should satisfy certain linearly independent condition that corresponds to Eq. 1. However we directly prove the hardness of Assumption 4 in Corollary 1. This guarantees that the above condition automatically satisfies and hence we do not need to explicitly state such condition here.

First we check A (resp. D) belongs to G (resp. H) by verifying \(A^N=1_{G}\) (resp. \(D^N=1_{H}\)). Then the pairing equation \(e(A, D)=e(g_1, h_1)\) ensures that D indeed belongs to subgroup \(H_1\).

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Titel: Towards Static Assumption Based Cryptosystem in Pairing Setting: Further Applications of DéjàQ and Dual-Form Signature (Extended Abstract)
verfasst von: Sanjit Chatterjee
R. Kabaleeshwaran
Verlag: Springer International Publishing
Buch: Provable Security
Print ISBN: 978-3-030-01445-2

Electronic ISBN: 978-3-030-01446-9

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-030-01446-9_13

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