Our scheme is more efficient than previous schemes in terms of both communication and computational complexity. Indeed, the HVZK argument has a size that is independent of the actual cryptosystem being used and will typically be smaller than the size of the shuffle itself. Moreover, our scheme is well suited for the use of multi-exponentiation techniques and batch-verification.
Additionally, we suggest a more efficient honest verifier zero-knowledge argument for a commitment containing a permutation of a set of publicly known messages. We also suggest an honest verifier zero-knowledge argument for the correctness of a combined shuffle-and-decrypt operation that can be used in connection with decrypting mix-nets based on ElGamal encryption.
All our honest verifier zero-knowledge arguments can be turned into honest verifier zero-knowledge proofs. We use homomorphic commitments as an essential part of our schemes. When the commitment scheme is statistically hiding we obtain statistical honest verifier zero-knowledge arguments, when the commitment scheme is statistically binding we obtain computational honest verifier zero-knowledge proofs.Category / Keywords: public-key cryptography / Shuffle, honest verifier zero-knowledge argument, homomorphic encryption, mix-net Publication Info: PKC 2003 Date: received 27 Jul 2005 Contact author: jg at cs ucla edu Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Note: An improved an extended version of the PKC 2003 paper. Version: 20050730:162805 (All versions of this report) Short URL: ia.cr/2005/246 Discussion forum: Show discussion | Start new discussion