On the exact decryption range for Gentry-Halevi's implementation of fully homomorphic encryption

Masaya Yasuda, Kazuhiro Yokoyama, Takeshi Shimoyama, Jun Kogure, Takeshi Koshiba

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1 Citation (Scopus)


In this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, and its decryption range is deeply related with the FHE construction. Gentry and Halevi gave an experimental evaluation of the decryption range, but theoretical evaluations have not been given so far. Moreover, we give a theoretical upper bound, and reconsider suitable parameters for theoretically obtaining an FHE scheme. In particular, while Gentry and Halevi use the Euclidean norm evaluation in the noise management of ciphertexts, our theoretical bound enables us to use the ∞-norm evaluation, and hence it helps to lower the difficulty of controlling the noise density of ciphertexts.

Original languageEnglish
Pages (from-to)305-329
Number of pages25
JournalJournal of Mathematical Cryptology
Issue number3
Publication statusPublished - Sep 1 2014
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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