## Cryptology ePrint Archive: Report 2011/471

Improved Key Generation For Gentry's Fully Homomorphic Encryption Scheme

P. Scholl and N.P. Smart

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.

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