Paper 2013/036

Batch Fully Homomorphic Encryption over the Integers

Jean-Sébastien Coron, Tancrède Lepoint, and Mehdi Tibouchi


We extend the fully homomorphic encryption scheme over the integers of van Dijk et al. (DGHV) to batch fully homomorphic encryption, i.e. to a scheme that supports encrypting and homomorphically processing a vector of plaintext bits as a single ciphertext. Our variant remains semantically secure under the (error-free) approximate GCD problem. 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: we describe an implementation of the fully homomorphic evaluation of AES encryption, 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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. An extended abstract will appear at Eurocrypt 2013, merged with some independent but overlapping work from Cheon et al.
Fully Homomorphic EncryptionBatch EncryptionHomomorphic AES
Contact author(s)
jscoron @ tranef com
2013-01-29: received
Short URL
Creative Commons Attribution


      author = {Jean-Sébastien Coron and Tancrède Lepoint and Mehdi Tibouchi},
      title = {Batch Fully Homomorphic Encryption over the Integers},
      howpublished = {Cryptology ePrint Archive, Paper 2013/036},
      year = {2013},
      note = {\url{}},
      url = {}
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