Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2010: Advances in Cryptology – EUROCRYPT 2010 pp 506-522

A Simple BGN-Type Cryptosystem from LWE

  • Craig Gentry
  • Shai Halevi
  • Vinod Vaikuntanathan
Conference paper

DOI: 10.1007/978-3-642-13190-5_26

Volume 6110 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Gentry C., Halevi S., Vaikuntanathan V. (2010) A Simple BGN-Type Cryptosystem from LWE. 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 public-key encryption scheme that supports polynomially many additions and one multiplication, similar to the cryptosystem of Boneh, Goh, and Nissim (BGN). Security is based on the hardness of the learning with errors (LWE) problem, which is known to be as hard as certain worst-case lattice problems.

Some features of our cryptosystem include support for large message space, an easy way of achieving formula-privacy, a better message-to-ciphertext expansion ratio than BGN, and an easy way of multiplying two encrypted polynomials. Also, the scheme can be made identity-based and leakage-resilient (at the cost of a higher message-to-ciphertext expansion ratio).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Craig Gentry
    • 1
  • Shai Halevi
    • 1
  • Vinod Vaikuntanathan
    • 1
  1. 1.IBM Research