An Approach to Reduce Storage for Homomorphic Computations

We introduce a hybrid homomorphic encryption by combining public key encryption (PKE) and somewhat homomorphic encryption (SHE) to reduce storage for most applications of somewhat or fully homomorphic encryption (FHE). In this model, one encrypts messages with a PKE and computes on encrypted data using a SHE or a FHE after homomorphic decryption. To obtain efficient homomorphic decryption, our hybrid schemes is constructed by combining IND-CPA PKE schemes without complicated message paddings with SHE schemes with large integer message space. Furthermore, we remark that if the underlying PKE is multiplicative on a domain closed under addition and multiplication, this scheme has an important advantage that one can evaluate a polynomial of arbitrary degree without recryption. We propose such a scheme by concatenating ElGamal and Goldwasser-Micali scheme over a ring $\Z_N$ for a composite integer $N$ whose message space is $\Z_N^\times$. To be used in practical applications, homomorphic decryption of the base PKE is too expensive. We accelerate the homomorphic evaluation of the decryption by introducing a method to reduce the degree of exponentiation circuit at the cost of additional public keys. Using same technique, we give an efficient solution to the open problem~\cite{KLYC13} partially. As an independent interest, we obtain another generic conversion method from private key SHE to public key SHE. Differently from Rothblum~\cite{RothTCC11}, it is free to choose the message space of SHE

Privacy-preserving Data clustering in Cloud Computing based on Fully Homomorphic Encryption

Cloud infrastructure with its massive storage and computing power is an ideal platform to perform large scale data analysis tasks to extract knowledge and support decision-making. However, there are critical data privacy and security issues associated with this platform, as the data is stored in a public infrastructure. Recently, fully homomorphic data encryption has been proposed as a solution due to its capabilities in performing computations over encrypted data. However, it is demonstrably slow for practical data mining applications. To address this and related concerns, we introduce a fully homomorphic and distributed data processing framework that utilizes MapReduce to perform distributed computations for data clustering tasks on a large number of cloud Virtual Machines (VMs). We illustrate how a variety of fully homomorphic-based computations can be carried out to accomplish data clustering tasks independently in the cloud and show that the distributed execution of data clustering tasks based on MapReduce can significantly reduce the execution time overhead caused by fully homomorphic computations. To evaluate our framework, we performed experiments using electricity consumption measurement data on the Google cloud platform with 100 VMs. We found the proposed distributed data processing framework to be highly efficient when compared to a centralized approach and as accurate as a plaintext implementation