Modulo reduction for Paillier encryptions and application to secure statistical analysis

J. Guajardo, B. Mennink, B. Schoenmakers

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

19 Citations (Scopus)
2 Downloads (Pure)


For the homomorphic Paillier cryptosystem we construct a protocol for secure modulo reduction, that on input of an encryption [[x]] with x of bit length l x and a public ‘modulus’ a of bit length l a outputs an encryption . As a result, a protocol for computing an encrypted integer division [[x div a]] is obtained. Surprisingly, efficiency of the protocol is independent of l x : the broadcast complexity of the protocol varies between O(nkl a ) and , for n parties and security parameter k, and it is very efficient in case of small l a (in practical cases l a often is much smaller than l x ). Our protocol allows for efficient multiparty computation of statistics such as the mean, the variance and the median, and it is therefore very applicable to surveys for the benefit of statistical analysis.
Original languageEnglish
Title of host publicationFinancial Cryptography and Data Security (14th International Conference, FC 2010, Tenerife, Canary Islands, January 25-28, 2010. Revised Selected Papers)
EditorsR. Sion
Place of PublicationBerlin
ISBN (Print)978-3-642-14576-6
Publication statusPublished - 2010

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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