A sender verifiable mix-net and a new proof of a shuffle

  • Authors:
  • Douglas Wikström

  • Affiliations:
  • Royal Institute of Technology (KTH), KTH, Nada, Stockholm, Sweden

  • Venue:
  • ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
  • Year:
  • 2005

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Abstract

We introduce the first El Gamal based mix-net in which each mix-server partially decrypts and permutes its input, i.e., no re-encryption is necessary. An interesting property of the construction is that a sender can verify non-interactively that its message is processed correctly. We call this sender verifiability. The mix-net is provably UC-secure against static adversaries corrupting any minority of the mix-servers. The result holds under the decision Diffie-Hellman assumption, and assuming an ideal bulletin board and an ideal zero-knowledge proof of knowledge of a correct shuffle. Then we construct the first proof of a decryption-permutation shuffle, and show how this can be transformed into a zero-knowledge proof of knowledge in the UC-framework. The protocol is sound under the strong RSA-assumption and the discrete logarithm assumption. Our proof of a shuffle is not a variation of existing methods. It is based on a novel idea of independent interest, and we argue that it is at least as efficient as previous constructions.