Improved Key Generation for Gentry’s Fully Homomorphic Encryption Scheme

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Abstract

A key problem with the original implementation of the Gentry Fully Homomorphic Encryption scheme was the slow key generation process. Gentry and Halevi provided a fast technique for 2-power cyclotomic fields. We present an extension of the Gentry–Halevi key generation technique for arbitrary cyclotomic fields. Our new method is roughly twice as efficient as the previous best methods. Our estimates are backed up with experimental data.