Private Membership Test Protocol with Low Communication Complexity

 Conclusion: Homomorphic encryption allows server to search in the matrix without knowledge of client’s keys. The proposed protocol has significantly smaller communication complexity than prior art.  Protocol: Our protocol is based on a real world scenario. A server possesses 2 malware samples and stores their hash values in 16 different subsets, based on the first 4 bits of the hash value. Each subset has 2 items. Client Wants to privately search for an item with hash value equal to h. Server • Divides each subset into 64 segments based on the next 6 bits of the hash value (bits 5,...,10). Each segment has 2 items. • Inserts each segment into a Bloom filter with 10 hash functions. Each filter has 2 bits. • Divides each filter into 16 parts and arranges sixteen 2 × 2matrices M, with parts of the filters as their elements, in such a way that the concatenation of all 16 elements in a particular position of all matrices, results to one of the Bloom filters. Client • Generates two distinct 2 − bits prime numbers p and q based on the setting of Paillier cryptosystem. N = pq so N has 2 bits. • Calculates the integer corresponding to 5th, 6th and 7th bits of h as i and the integer corresponding to 8th, 9th and 10th bits as j. • Arranges an 8-component vector T (resp. T), where all the components are 0 except the component i (resp. j), that is equal to 1. • Encrypts the components of T (resp. T) and generates vector (αi) (resp. (βj)).