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Message Expansion of Homomorphic Encryption Using Product Pairing
Authors:Soo Kyung Eom  Hyang‐Sook Lee  Seongan Lim
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.
Keywords:BGN cryptosystem  pairing  product pairing  homomorphic encryption  decisional Diffie–  Hellman problem
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