Practical homomorphic encryption over the integers for secure computation in the cloud
Practical homomorphic encryption over the integers for secure computation in the cloud
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DOI：
10.1007/s10207-019-00427-0
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发表时间：
2019-02
影响因子：
3.2
通讯作者：
James Dyer;M. Dyer;Jie Xu
中科院分区：
文献类型：
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作者：
James Dyer;M. Dyer;Jie Xu
我们提出了用于整数算术的新型同态加密方案，主要用于云中的安全单方计算。这些方案能够安全地同态计算任意次数多项式。在实践中，密文大小和运行时间限制了多项式次数，但这对于大多数实际应用来说似乎足够了。我们提出了四种方案，安全级别不断提高，但计算开销也随之增加。其中两种方案为高熵数据提供了强大的安全性。不管这个假设如何，剩下的两个方案都提供了强大的安全性。这四种算法形成了方案层次结构的前两级，我们还介绍了每种方案的一般情况。我们进一步阐述如何从我们的一般情况之一构建完全同态系统。此外，我们提出了一种基于中国剩余定理秘密共享的变体。我们通过计算低次多项式详细介绍了我们层次结构的前四种算法的广泛评估。即使与现有最好的方法相比，这些计算的时间也非常有利，并且远远优于许多广为人知的方案。结果清楚地证明了我们方案的实际适用性。
We present novel homomorphic encryption schemes for integer arithmetic, intended primarily for use in secure single-party computation in the cloud. These schemes are capable of securely computing arbitrary degree polynomials homomorphically. In practice, ciphertext size and running times limit the polynomial degree, but this appears sufficient for most practical applications. We present four schemes, with increasing levels of security, but increasing computational overhead. Two of the schemes provide strong security for high-entropy data. The remaining two schemes provide strong security regardless of this assumption. These four algorithms form the first two levels of a hierarchy of schemes, and we also present the general cases of each scheme. We further elaborate how a fully homomorphic system can be constructed from one of our general cases. In addition, we present a variant based upon Chinese Remainder Theorem secret sharing. We detail extensive evaluation of the first four algorithms of our hierarchy by computing low-degree polynomials. The timings of these computations are extremely favourable by comparison with even the best of existing methods and dramatically outperform many well-publicised schemes. The results clearly demonstrate the practical applicability of our schemes.