A Universally Composable Mix-Net

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 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 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 o...

• Type: Conference
• Year: 2004
• Where: TCC
• Authors: Douglas Wikström
• Keywords: Cryptography, Decryption Shuffle, Public-key Obfuscate, TCC 2004, Verifiable Decryption