Fully Homomorphic Encryption over the Integers

  • Marten van Dijk
  • Craig Gentry
  • Shai Halevi
  • Vinod Vaikuntanathan
Conference paper

DOI: 10.1007/978-3-642-13190-5_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6110)
Cite this paper as:
van Dijk M., Gentry C., Halevi S., Vaikuntanathan V. (2010) Fully Homomorphic Encryption over the Integers. In: Gilbert H. (eds) Advances in Cryptology – EUROCRYPT 2010. EUROCRYPT 2010. Lecture Notes in Computer Science, vol 6110. Springer, Berlin, Heidelberg

Abstract

We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct a fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of our scheme is the conceptual simplicity.

We reduce the security of our scheme to finding an approximate integer gcd – i.e., given a list of integers that are near-multiples of a hidden integer, output that hidden integer. We investigate the hardness of this task, building on earlier work of Howgrave-Graham.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marten van Dijk
    • 1
  • Craig Gentry
    • 2
  • Shai Halevi
    • 2
  • Vinod Vaikuntanathan
    • 2
  1. 1.MIT CSAIL 
  2. 2.IBM Research 

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