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Paper: How to Shuffle in Public

Authors:
Ben Adida
Douglas Wikstr\"{o}m
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URL: http://eprint.iacr.org/2005/394
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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.
BibTeX
@misc{eprint-2005-12728,
  title={How to Shuffle in Public},
  booktitle={IACR Eprint archive},
  keywords={mixnet, obfuscation},
  url={http://eprint.iacr.org/2005/394},
  note={paper in submission ben@mit.edu 13378 received 2 Nov 2005, last revised 18 Aug 2006},
  author={Ben Adida and Douglas Wikstr\"{o}m},
  year=2005
}