Efran (O): "Efficient Scalar Homomorphic Scheme on MapReduce for Data Privacy Preserving"

Privacy protection is one of most concerned issues in big data and cloud applications in the last decade. Thereby, mapreduce which is a programming scheme with an associated parallel implementation for processing and generating large data sets on the heart of cloud applications needs to be securely implemented. Thus the security of map workers' data (intermediate data) of mapreduce model must be well protected. But the traditional operations on ciphertexts were not applicable at the reduce stage. So to provide a secure mapreduce scheme, there is a paramount need to protect the data, as well as to allow specific types of computations to be carried out on encrypted intermediate data. Therefore some homomorphic based models have been proposed to address this issue, which could compute over encrypted data without decrypting it. However those existing schemes have to send their private encryption key to untrusted server (DGHV model) or key's parameters (Gen10 scheme by Gentry) which drastically leaks either the plaintext or information about the cryptosystem. In this paper, we propose a secure homomorphic model (FHE_SHCR algorithm) which efficiently retrieves ciphertexts (R_c) at reduce phase without passing any parameters or private key to untrusted server. Also for the efficiency of our solution in terms of computation cost and security analysis, we use a scalar homomorphic approach rather than applying blinding algorithm (probabilistic, polynomial-time algorithm) which is computationally expensive. Doing so, we efficiently achieve a probabilistic and improved security level through our model which is proved feasible.