Batch Fully Homomorphic Encryption over the Integers

  • Jung Hee Cheon
  • Jean-Sébastien Coron
  • Jinsu Kim
  • Moon Sung Lee
  • Tancrède Lepoint
  • Mehdi Tibouchi
  • Aaram Yun
Conference paper

DOI: 10.1007/978-3-642-38348-9_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7881)
Cite this paper as:
Cheon J.H. et al. (2013) Batch Fully Homomorphic Encryption over the Integers. In: Johansson T., Nguyen P.Q. (eds) Advances in Cryptology – EUROCRYPT 2013. EUROCRYPT 2013. Lecture Notes in Computer Science, vol 7881. Springer, Berlin, Heidelberg

Abstract

We extend the fully homomorphic encryption scheme over the integers of van Dijk et al.(DGHV) into a batch fully homomorphic encryption scheme, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintexts as a single ciphertext.

We present two variants in which the semantic security is based on different assumptions. The first variant is based on a new decisional problem, the Decisional Approximate-GCD problem, whereas the second variant is based on the more classical computational Error-Free Approximate-GCD problem but requires additional public key elements.

We also show how to perform arbitrary permutations on the underlying plaintext vector given the ciphertext and the public key. Our scheme offers competitive performance even with the bootstrapping procedure: we describe an implementation of the homomorphic evaluation of AES, with an amortized cost of about 12 minutes per AES ciphertext on a standard desktop computer; this is comparable to the timings presented by Gentry et al.at Crypto 2012 for their implementation of a Ring-LWE based fully homomorphic encryption scheme.

Keywords

Fully Homomorphic Encryption Batch Encryption Chinese Remainder Theorem Approximate GCD Homomorphic AES 

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Jung Hee Cheon
    • 1
  • Jean-Sébastien Coron
    • 2
  • Jinsu Kim
    • 1
  • Moon Sung Lee
    • 1
  • Tancrède Lepoint
    • 3
    • 4
  • Mehdi Tibouchi
    • 5
  • Aaram Yun
    • 6
  1. 1.Seoul National University (SNU)Republic of Korea
  2. 2.TranefFrance
  3. 3.CryptoExpertsFrance
  4. 4.École Normale SupérieureFrance
  5. 5.NTT Secure Platform LaboratoriesJapan
  6. 6.Ulsan National Institute of Science and Technology (UNIST)Republic of Korea

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