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Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

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Part of the book series:Lecture Notes in Computer Science ((LNSC,volume 6056))

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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.

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Author information

Authors and Affiliations

  1. Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom

    N. P. Smart

  2. COSIC - Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001, Heverlee, Belgium

    F. Vercauteren

Authors
  1. N. P. Smart
  2. F. Vercauteren

Editor information

Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Phong Q. Nguyen  & David Pointcheval  & 

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Smart, N.P., Vercauteren, F. (2010). Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes. In: Nguyen, P.Q., Pointcheval, D. (eds) Public Key Cryptography – PKC 2010. PKC 2010. Lecture Notes in Computer Science, vol 6056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13013-7_25

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