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Message Expansion of Homomorphic Encryption Using Product Pairing

  • Eom, Soo Kyung (Department of Mathematics, Ewha Womans University) ;
  • Lee, Hyang-Sook (Department of Mathematics, Ewha Womans University) ;
  • Lim, Seongan (Institute of Mathematical Sciences, Ewha Womans University)
  • Received : 2015.07.08
  • Accepted : 2015.09.25
  • Published : 2016.02.01

Abstract

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 BGN-type 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.

Acknowledgement

Supported by : Ministry of Education of Korea

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