Abstract
We show how to obfuscate a secret shuffle of ciphertexts: shuffling becomes a public operation. Given a trusted party that samples and obfuscates a shuffle before any ciphertexts are received, this reduces the problem of constructing a mix-net to verifiable joint decryption.
We construct public-key obfuscations of a decryption shuffle based on the Boneh-Goh-Nissim (BGN) cryptosystem and a re-encryption shuffle based on the Paillier cryptosystem. Both allow efficient distributed verifiable decryption.
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 small, yet large enough to handle a number of practical cases, e.g. N = 350 in the BGN case and N = 2000 in the Paillier case.
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Adida, B., Wikström, D. (2007). How to Shuffle in Public. In: Vadhan, S.P. (eds) Theory of Cryptography. TCC 2007. Lecture Notes in Computer Science, vol 4392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70936-7_30
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DOI: https://doi.org/10.1007/978-3-540-70936-7_30
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