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A Verifiable Secret Shuffle of Homomorphic Encryptions

Groth, J; (2010) A Verifiable Secret Shuffle of Homomorphic Encryptions. J CRYPTOL , 23 (4) 546 - 579. 10.1007/s00145-010-9067-9.

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Abstract

A shuffle consists of a permutation and re-encryption of a set of input ciphertexts. One application of shuffles is to build mix-nets. We suggest an honest verifier zero-knowledge argument for the correctness of a shuffle of homomorphic encryptions.Our scheme is more efficient than previous schemes both in terms of communication and computation. The honest verifier zero-knowledge 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 and batch-verification techniques.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.

Type:Article
Title:A Verifiable Secret Shuffle of Homomorphic Encryptions
DOI:10.1007/s00145-010-9067-9
Keywords:Shuffle, Honest verifier zero-knowledge argument, Homomorphic encryption, Mix-net, PUBLIC-KEY CRYPTOSYSTEM, ZERO-KNOWLEDGE PROTOCOLS, PRACTICAL MIX, EFFICIENT, SECURE, SCHEME, NETWORK, DESIGN, NETS
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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