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 Verification of a Paillier based shuffle using representations of the symmetric group Bull. Korean Math. Soc. 2009 Vol. 46, No. 4, 771-787 https://doi.org/10.4134/BKMS.2009.46.4.771Printed July 1, 2009 Soojin Cho and Manpyo Hong Ajou University Abstract : We use an idea of linear representations of the symmetric group to reduce the number of communication rounds in the verification protocol, proposed in Crypto 2005 by Peng et al., of a shuffling. We assume Paillier encryption scheme with which we can apply some known zero-knowledge proofs following the same line of approaches of Peng et al. Incidence matrices of $1$-subsets and $2$-subsets of a finite set is intensively used for the implementation, and the idea of $\lambda$-designs is employed for the improvement of the computational complexity. Keywords : proof of shuffle, mix-net, representation of symmetric group, homomorphic encryption, $\lambda$-designs MSC numbers : Primary 94A60; Secondary 11T71 Downloads: Full-text PDF