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. In this paper, we propose a scheme to simultaneously prove the correctness of both shuing,and decryption. Our scheme is the most ecient,of all previous schemes, as a total, in proving the correctness of both shuing,and decryption of ElGamal ciphertexts. We also propose a formal definition for the core requirement of unlinkability in verifiable shue-decryption, and then prove that our scheme satisfies this require- ment. The proposed definition may be also useful for proving the security of verifiable shue-decryption, hybrid mix network, and other mix-nets. Keywords: Voting, Shue, Decryption, Permutation Hiding

Efficient, Verifiable Shuffle Decryption and Its Requirement of Unlinkability