A Provably Secure and Efficient Verifiable Shuffle based on a Variant of the Paillier Cryptosystem

@article{Nguyen2005APS,
  title={A Provably Secure and Efficient Verifiable Shuffle based on a Variant of the Paillier Cryptosystem},
  author={Lan Nguyen and Reihaneh Safavi-Naini and Kaoru Kurosawa},
  journal={J. UCS},
  year={2005},
  volume={11},
  pages={986-1010}
}
We propose a variant of the Paillier cryptosystem that improves efficiency in encryption, re-encryption and decryption while preserving the homomorphic property. We then use this variant to construct a new verifiable shuffle system and prove its security. We show that the new shuffle scheme has the least number of rounds and exponentiations compared to all known shuffle schemes. Finally, we show how to construct a publicly verifiable mix-net using the shuffle system. 

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