Practical Homomorphic Encryption Over the Integers

TL;DR

This paper introduces practical homomorphic encryption schemes for integer arithmetic, enabling secure computations in the cloud with manageable key and ciphertext sizes, suitable for low-degree polynomial evaluations.

Contribution

The paper presents new homomorphic encryption schemes optimized for integer operations, including a fully homomorphic system capable of arbitrary Boolean circuit evaluation.

Findings

Efficient evaluation of low-degree inner products

Practical key and ciphertext sizes for certain schemes

A fully homomorphic system capable of arbitrary Boolean circuits

Abstract

We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this appears sufficient for most practical applications. In this setting, our schemes lead to practical key and ciphertext sizes. We present a sequence of generalisations of our basic schemes, with increasing levels of security, but decreasing practicality. We have evaluated the first four of these algorithms by computing a low-degree inner product. The timings of these computations are extremely favourable. Finally, we use our ideas to derive a fully homomorphic system, which appears impractical, but can homomorphically evaluate arbitrary Boolean circuits.