Message expansion of homomorphic encryption using product pairing

Soo Kyung Eom, Hyang Sook Lee, Seongan Lim

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The Boneh, Goh, and Nissim (BGN) cryptosytem is the first homomorphic encryption scheme that allows additions and multiplications of plaintexts on encrypted data. BGN-type cryptosystems permit very small plaintext sizes. The best-known approach for the expansion of a message size by t times is one that requires t implementations of an initial scheme; however, such an approach becomes impractical when t is large. In this paper, we present a method of message expansion of BGNtype homomorphic encryption using composite product pairing, which is practical for relatively large t. In addition, we prove that the indistinguishability under chosen plaintext attack security of our construction relies on the decisional Diffie-Hellman assumption for all subgroups of prime order of the underlying composite pairing group.

Original languageEnglish
Pages (from-to)123-132
Number of pages10
JournalETRI Journal
Issue number1
StatePublished - Feb 2016

Bibliographical note

Publisher Copyright:
© 2016 ETRI.


  • BGN cryptosystem
  • Decisional Diffie-Hellman problem
  • Homomorphic encryption
  • Pairing
  • Product pairing


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