## Cryptology ePrint Archive: Report 2005/394

How to Shuffle in Public

Abstract: We show how to public-key obfuscate two commonly used shuffles: decryption shuffles which permute and decrypt ciphertexts, and re-encryption shuffles which permute and re-encrypt ciphertexts. Given a trusted party that samples and obfuscates a shuffle \emph{before} any ciphertexts are received, this reduces the problem of constructing a mix-net to verifiable joint decryption.

We construct a decryption shuffle from any additively homomorphic cryptosystem and show how it can be public-key obfuscated. This construction does not allow efficient distributed verifiable decryption. Then we show how to public-key obfuscate: a decryption shuffle based on the Boneh-Goh-Nissim (BGN) cryptosystem, and a re-encryption shuffle based on the Paillier cryptosystem. Both constructions allow \emph{efficient} distributed verifiable decryption. In the Paillier case we identify and exploit a previously overlooked homomorphic'' property of the cryptosystem.

Finally, we give a distributed protocol for sampling and obfuscating each of the above shuffles and show how it can be used in a trivial way to construct a universally composable mix-net. Our constructions are practical when the number of senders $N$ is reasonably small, e.g. $N=350$ in the BGN case and $N=2000$ in the Paillier case.

Category / Keywords: mixnet, obfuscation

Publication Info: paper in submission

Date: received 2 Nov 2005, last revised 18 Aug 2006

Contact author: ben at mit edu

Available format(s): PDF | BibTeX Citation

Note: new formalization in the public-key obfuscation model, with a UC proof, and numerous corrections.

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