Paper 2018/738 Original: eprint.iacr.org/2018/738 ↗

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

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.