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A Secure Homomorphic Encryption Algorithm over Integers for Data Privacy Protection in Clouds

机译：一种用于整数的安全同态加密算法，用于云中的数据隐私保护

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摘要

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.
机译：如果存在安全高效的完全同态加密算法，则它应该是保护云中数据隐私的最终解决方案，其中云服务器可以直接对同态加密密文应用任何操作，而不必解密它们。使用这种加密算法，可以保留客户的数据隐私，因为云服务提供商可以在不知道这些数据内容的情况下对这些加密数据进行操作。目前，Gentry在2009年提出的一种全同态加密算法及其某些变体在文献中均可用。但是，由于计算成本过高，因此这些类似于Gentry的算法不实用，无法用于保护云中的数据。由于难以开发实用的完全同态算法，因此文献中也对部分同态算法进行了研究，特别是对于那些对整数进行算术运算同态的算法。本文针对整数上的现有同态算法提出了一种安全的变体算法。原始算法允许无限数量的算术加法和乘法，但是存在安全漏洞。变体算法通过在加密之前添加随机填充来修补漏洞。本文首先简要介绍了原始算法，然后在提出变体算法之前指出了它的安全性问题。本文末尾将对原始算法和变体算法进行效率分析。

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