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Practical Homomorphic Encryption Over the Integers for Secure Computation in the Cloud

机译：整数上的实用同态加密，用于云中的安全计算

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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 which require linearly decreasing entropy. We have evaluated these four algorithms by computing low-degree polynomials. The timings of these computations are extremely favourable by comparison with even the best of existing methods, and dramatically out-perform running times of directly comparable schemes by a factor of up to 1000, and considerably more than that for fully homomorphic schemes, used in the same context. The results clearly demonstrate the practical applicability of our schemes.
机译：我们提出了用于整数算术的新颖同态加密方案，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的多项式。实际上，密文的大小和运行时间限制了多项式的次数，但这对于大多数实际应用而言似乎足够了。我们提出了四种方案，它们的安全级别有所提高，但计算开销却有所增加。其中两种方案为高熵数据提供了强大的安全性。不管此假设如何，其余两种方案都提供了强大的安全性。这四种算法构成了要求线性降低熵的方案层次结构的前两个级别。我们通过计算低次多项式评估了这四种算法。与什至是最好的现有方法相比，这些计算的时间安排都是极其有利的，并且与直接可比方案的运行时间相比，其运行时间显着地超出了多达1000倍，远远超过了用于同构方案的完全同态方案的运行时间。相同的上下文。结果清楚地证明了我们方案的实际适用性。

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