Recent work ([DGS20]) suggests that the hidden order groups need to be substantially larger in size that previously thought, in order to ensure the desired security level. Thus, in order to keep the communication complexity between the Prover and the the Verifier to a minimum, we have designed the protocols so that the proofs entail a constant number of group elements, independent of the number of the committed sets/multisets rather than just independent of the sizes of these sets/multisets.
If the underlying group of hidden order is an appropriate imaginary quadratic class group or a genus three Jacobian, the argument systems are transparent. Furthermore, since all challenges are public coin, the protocols can be made non-interactive using the Fiat-Shamir heuristic. We build on the techniques from [BBF19] and [Wes18].
Category / Keywords: cryptographic protocols / Arguments of knowledge, accumulators, hidden order groups, succinct, batching, non-interactive, commitments Date: received 30 Dec 2020, last revised 3 Jan 2021 Contact author: stevethakur01 at gmail com Available format(s): PDF | BibTeX Citation Version: 20210104:050228 (All versions of this report) Short URL: ia.cr/2020/1617