Biblio

Protocols for securely testing the equality of two encrypted integers are common building blocks for a number of proposals in the literature that aim for privacy preservation. Being used repeatedly in many cryptographic protocols, designing efficient equality testing protocols is important in terms of computation and communication overhead. In this work, we consider a scenario with two parties where party A has two integers encrypted using an additively homomorphic scheme and party B has the decryption key. Party A would like to obtain an encrypted bit that shows whether the integers are equal or not but nothing more. We propose three secure equality testing protocols, which are more efficient in terms of communication, computation or both compared to the existing work. To support our claims, we present experimental results, which show that our protocols achieve up to 99% computation-wise improvement compared to the state-of-the-art protocols in a fair experimental set-up.

Due to privacy threats associated with computation of outsourced data, processing data on the encrypted domain has become a viable alternative. Secure computation of encrypted data is relevant for analysing datasets in areas (such as genome processing, private data aggregation, cloud computations) that require basic arithmetic operations. Performing division operation over-all encrypted inputs has not been achieved using homomorphic schemes in non-interactive modes. In interactive protocols, the cost of obtaining an encrypted quotient (from encrypted values) is computationally expensive. To the best of our knowledge, existing homomorphic solutions on encrypted division are often relaxed to consider public or private divisor. We acknowledge that there are other techniques such as secret sharing and garbled circuits adopted to compute secure division, but we are interested in homomorphic solutions. We propose an efficient and interactive two-party protocol that computes the fixed-point quotient of two encrypted inputs, using an efficient and secure comparison protocol as a sub-protocol. Our proposal provides a computational advantage, with a linear complexity in the digit precision of the quotient. We provide proof of security in the universally composable framework and complexity analyses. We present experimental results for two cryptosystem implementations in order to compare performance. An efficient prototype of our protocol is implemented using additive homomorphic scheme (Paillier), whereas a non-efficient fully-homomorphic scheme (BGV) version is equally presented as a proof of concept and analyses of our proposal.