(Batch) Fully Homomorphic Encryption over Integers for Non-Binary Message Spaces

  • Koji NuidaEmail author
  • Kaoru Kurosawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9056)


In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space \(\mathbb {Z}_Q\) for any prime \(Q\). Even for the binary case \(Q=2\), our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from \(O(\lambda (\log \lambda )^2)\) to \(O(\lambda )\), where \(\lambda \) is the security parameter. We also extend our FHE scheme to a batch FHE scheme.


Fully homomorphic encryption Non-binary message 


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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)TsukubaJapan
  2. 2.Japan Science and Technology Agency (JST) PRESTO ResearcherNagoyaJapan
  3. 3.Ibaraki UniversityHitachiJapan

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