Cryptology ePrint Archive: Report 2009/571

Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

N.P. Smart and F. Vercauteren

Abstract: We present a fully homomorphic encryption scheme which has both relatively small key and ciphertext size. Our 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, our scheme has smaller message expansion and key size than Gentry’s original scheme. In addition, our proposal allows efficient fully homomorphic encryption over any field of characteristic two.

Category / Keywords: public-key cryptography / Homomorphic encryption

Date: received 25 Nov 2009, last revised 22 Dec 2009

Contact author: nigel at cs bris ac uk,Frederik Vercauteren@esat kuleuven be

Available formats: PDF | BibTeX Citation

Note: Added clarification on the recryption proceedure and related circuit depths

Version: 20091222:115720 (All versions of this report)

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