A secure homomorphic encryption algorithm over integers for data privacy protection in clouds

Abstract

If a secure and efficient fully homomorphic encryption algorithm exists, it should be the ultimate solution for securing data privacy in clouds, where cloud servers can apply any operation directly over the homomorphically encrypted ciphertexts without having to decrypt them. With such encryption algorithms, clients’ data privacy can be preserved since cloud service providers can operate on these encrypted data without knowing the content of these data. Currently only one fully homomorphic encryption algorithm proposed by Gentry in 2009 and some of its variants are available in literature. However, because of the prohibitively expensive computing cost, these Gentry-like algorithms are not practical to be used to securing data in clouds. Due to the difficulty in developing practical fully homomorphic algorithms, partially homomorphic algorithms have also been studied in literature, especially for those algorithms homomorphic on arithmetic operations over integers. This paper presents a secure variant algorithm to an existing homomorphic algorithm over integers. The original algorithm allows unlimited number of arithmetic additions and multiplications but suffers on a security weakness. The variant algorithm patches the weakness by adding a random padding before encryption. This paper first describes the original algorithm briefly and then points out it’s security problem before we present the variant algorithm. An efficiency analysis for both the original and the variant algorithms will be presented at the end of the paper.