@inproceedings {26619,
	title = {Efficient Non-Interactive Zero Knowledge Arguments for Set Operations},
	journal = {FC 2014: Financial Cryptography and Data Security},
	volume = {8437261970},
	year = {2014},
	pages = {216 - 233},
	publisher = {Springer Berlin Heidelberg},
	address = {Berlin, Heidelberg},
	abstract = {We propose a non-interactive zero knowledge\&nbsp;pairwise multiset sum equality test (PMSET)argument of knowledge in the common reference string (CRS) model that allows a prover to show that the given committed multisets\&nbsp;Aj for\&nbsp;j∈{1,2,3,4} satisfy\&nbsp;A1⊎A2=A3⊎A4, i.e., every element is contained in\&nbsp;A1 and\&nbsp;A2 exactly as many times as in\&nbsp;A3 and\&nbsp;A4. As a corollary to the\&nbsp;PMSET argument, we present arguments that enable to efficiently verify the correctness of various (multi)set operations, for example, that one committed set is the intersection or union of two other committed sets. The new arguments have constant communication and verification complexity (in group elements and group operations, respectively), whereas the CRS length and the prover{\textquoteright}s computational complexity are both proportional to the cardinality of the (multi)sets. We show that one can shorten the CRS length at the cost of a small increase of the communication and the verifier{\textquoteright}s computation.},
	isbn = {978-3-662-45471-8},
	issn = {0302-9743},
	doi = {10.1007/978-3-662-45472-510.1007/978-3-662-45472-5_14},
	url = {https://link.springer.com/chapter/10.1007/978-3-662-45472-5_14},
	author = {Fauzi, Prastudy and Lipmaa, Helger and Zhang, Bingsheng},
	editor = {Christin, Nicolas and Safavi-Naini, Reihaneh}
}
@inproceedings {26616,
	title = {Efficient Modular NIZK Arguments from Shift and Product},
	journal = {Cryptology and Network Security (CANS 2013)},
	volume = {8257371918411522619174},
	year = {2013},
	pages = {92 - 121},
	publisher = {Springer International Publishing},
	address = {Cham},
	abstract = {We propose a non-interactive product argument, that is more efficient than the one by Groth and Lipmaa, and a novel shift argument. We then use them to design several novel non-interactive zero-knowledge (NIZK) arguments. We obtain the first range proof with constant communication and subquadratic prover{\textquoteright}s computation. We construct NIZK arguments for\&nbsp;NP-complete languages,\&nbsp;Set-Partition,\&nbsp;Subset-Sum\&nbsp;and\&nbsp;Decision-Knapsack, with constant communication, subquadratic prover{\textquoteright}s computation and linear verifier{\textquoteright}s computation.},
	isbn = {978-3-319-02936-8},
	issn = {0302-9743},
	doi = {10.1007/978-3-319-02937-510.1007/978-3-319-02937-5_6},
	url = {https://link.springer.com/chapter/10.1007/978-3-319-02937-5_6},
	author = {Fauzi, Prastudy and Lipmaa, Helger and Zhang, Bingsheng},
	editor = {Hutchison, David and Kanade, Takeo and Kittler, Josef and Jon M. {Kleinberg} and Mattern, Friedemann and John C. {Mitchell} and Naor, Moni and Nierstrasz, Oscar and Rangan, Pandu and Steffen, Bernhard and Sudan, Madhu and Terzopoulos, Demetri and Tygar, Doug and Moshe Y. {Vardi} and Weikum, Gerhard and Abdalla, Michel and Nita-Rotaru, Cristina and Dahab, Ricardo}
}
