Modulo Reduction for Paillier Encryptions and Application to Secure Statistical Analysis

Abstract. 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 x and a public ‘modulus’ a of bit length a outputs an encryption x mod a . As a result, a protocol for computing an encrypted integer division x div a is obtained. Surprisingly, efficiency of the protocol is independent of x: the broadcast complexity of the protocol varies between O(nk a) and O(n2 k a), for n parties and security parameter k, and is very efficient in case of small a (in practical cases a often is much smaller than x). Our protocol allows for efficient multiparty computation of statistics like mean, variance and median. Therefore, the protocol can be used in the context of medical surveys for the benefit of statistical analysis: medical data are very sensitive information, and people are generally reluctant to share these data. Implementing these surveys using multiparty statistics protocols offers an approa...

• Type: Conference
• Year: 2010
• Where: FC
• Authors: Jorge Guajardo, Bart Mennink, Berry Schoenmakers
• Keywords: Bit Length, Cryptology, FC 2010, Modulo Reduction, Multiparty Computation