Paper 2009/571

Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

N. P. Smart and F. Vercauteren


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.

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

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Homomorphic encryption
Contact author(s)
nigel @ cs bris ac uk
Frederik Vercauteren @ esat kuleuven be
2009-12-22: last of 2 revisions
2009-12-01: received
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      author = {N. P.  Smart and F.  Vercauteren},
      title = {Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes},
      howpublished = {Cryptology ePrint Archive, Paper 2009/571},
      year = {2009},
      note = {\url{}},
      url = {}
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