Fully Homomorphic Encryption With Relatively Small Key and Ciphertext Sizes

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Executive Summary

The authors present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size. The construction follows that of Gentry by producing a fully homomorphic scheme from a "Somewhat" homomorphic scheme. For the somewhat homomorphic scheme the public and private keys consist of two large integers (one of which is shared by both the public and private key) and the ciphertext consists of one large integer. As such, the scheme has smaller message expansion and key size than Gentry's original scheme. In addition, the proposal allows efficient fully homomorphic encryption over any field of characteristic two.

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