@inproceedings {26618,
	title = {An Efficient Pairing-Based Shuffle Argument},
	journal = {ASIACRYPT 2017},
	volume = {10626},
	year = {2017},
	pages = {97 - 127},
	publisher = {Springer International Publishing},
	address = {Cham},
	abstract = {We construct the most efficient known pairing-based NIZK shuffle argument. It consists of three subarguments that were carefully chosen to obtain optimal efficiency of the shuffle argument:1. A same-message argument based on the linear subspace QANIZK argument of Kiltz and Wee,\&nbsp;2. A (simplified) permutation matrix argument of Fauzi, Lipmaa, and Zaj{\k a}c,\&nbsp;3. A (simplified) consistency argument of Groth and Lu.We prove the knowledge-soundness of the first two subarguments in the generic bilinear group model, and the culpable soundness of the third subargument under a KerMDH assumption. This proves the soundness of the shuffle argument. We also discuss our partially optimized implementation that allows one to prove a shuffle of\&nbsp;100000100000\&nbsp;ciphertexts in less than a minute and verify it in less than 1.5\&nbsp;min.},
	keywords = {Common Reference String, Generic group model, Mix-net, Shuffle argument, Zero knowledge},
	isbn = {978-3-319-70696-2},
	issn = {0302-9743},
	doi = {10.1007/978-3-319-70697-910.1007/978-3-319-70697-9_4},
	url = {http://link.springer.com/10.1007/978-3-319-70697-9_4},
	author = {Fauzi, Prastudy and Lipmaa, Helger and Zaj{\k a}c, Micha{\l} and Siim, Janno},
	editor = {Takagi, Tsuyoshi and Peyrin, Thomas}
}
@inproceedings {26617,
	title = {A Shuffle Argument Secure in the Generic Model},
	journal = {International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT 2016)},
	volume = {1003223592127},
	year = {2016},
	month = {12/2016},
	pages = {841 - 872},
	publisher = {Springer Berlin Heidelberg},
	address = {Berlin, Heidelberg},
	abstract = {We propose a new random oracle-less NIZK shuffle argument. It has a simple structure, where the first verification equation ascertains that the prover has committed to a permutation matrix, the second verification equation ascertains that the same permutation was used to permute the ciphertexts, and the third verification equation ascertains that input ciphertexts were {\textquotedblleft}correctly{\textquotedblright} formed. The new argument has 3.5 times more efficient verification than the up-to-now most efficient shuffle argument by Fauzi and Lipmaa (CT-RSA 2016). Compared to the Fauzi-Lipmaa shuffle argument, we (i) remove the use of knowledge assumptions and prove our scheme is sound in the generic bilinear group model, and (ii) prove standard soundness, instead of culpable soundness.},
	isbn = {978-3-662-53889-0},
	issn = {0302-9743},
	doi = {10.1007/978-3-662-53890-610.1007/978-3-662-53890-6_28},
	url = {http://link.springer.com/10.1007/978-3-662-53890-6_28},
	author = {Fauzi, Prastudy and Lipmaa, Helger and Zaj{\k a}c, Micha{\l}},
	editor = {Jung Hee {Cheon} and Takagi, Tsuyoshi}
}
