Supporting Non-membership Proofs with Bilinear-map Accumulators

In this short note, we present an extension of Nguyen’s bilinear-map based accumulator scheme [8] to support non-membership witnesses and corresponding 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 et al. [7] for the RSA accumulator [2, 3, 5], making the functionality of the bilinear-map accumulator equivalent to that of the RSA accumulator. Our non-membership extension of Nguyen’s scheme [8] makes use of the q-Strong Diffie-Hellman assumption the security of the original scheme is based on.