In this paper, we propose a scheme to simultaneously prove the correctness of both shuffling and decryption. Our scheme is the most efficient of all previous schemes, as a total, in proving the correctness of both shuffling and decryption of ElGamal ciphertexts. We also propose a formal definition for the core requirement of unlinkability in verifiable shuffle-decryption, and then prove that our scheme satisfies this requirement. The proposed definition may be also useful for proving the security of verifiable shuffle-decryption, hybrid mix network, and other mix-nets.
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