Paper 2008/538

Supporting Non-membership Proofs with Bilinear-map Accumulators

Ivan Damgård and Nikos Triandopoulos

Abstract

In this short note, we present an extension of Nguyen's bilinear-map based accumulator scheme to support \emph{non-membership witnesses} and corresponding \emph{non-membership proofs}, i.e., cryptographic proofs that an element has not been accumulated to a given set. This complements the non-membership proofs developed by Li \emph{et al.} for the RSA accumulator, making the functionality of the bilinear-map accumulator equivalent to that of the RSA accumulator. Our non-membership extension of Nguyen's scheme makes use of the $q$-Strong Diffie-Hellman assumption the security of the original scheme is based on.