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Information Security Practice and Experience

Volume 7232 of the series Lecture Notes in Computer Science pp 353-368

On the CCA-1 Security of Somewhat Homomorphic Encryption over the Integers

  • Zhenfei ZhangAffiliated withCentre for Computer and Information Security Research, School of Computer Science & Software Engineering (SCSSE), University Of Wollongong
  • , Thomas PlantardAffiliated withCentre for Computer and Information Security Research, School of Computer Science & Software Engineering (SCSSE), University Of Wollongong
  • , Willy SusiloAffiliated withCentre for Computer and Information Security Research, School of Computer Science & Software Engineering (SCSSE), University Of Wollongong

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Abstract

The notion of fully homomorphic encryption is very important since it enables many important applications, such as the cloud computing scenario. In EUROCRYPT 2010, van Dijk, Gentry, Halevi and Vaikuntanathan proposed an interesting fully homomorphic encryption scheme based on a somewhat homomorphic encryption scheme using integers. In this paper, we demonstrate a very practical CCA-1 attack against this somewhat homomorphic encryption scheme. Given a decryption oracle, we show that within O(λ 2) queries, we can recover the secret key successfully, where λ is the security parameter for the system.

Keywords

Fully Homomorphic Encryption Somewhat Homomorphic Encryption CCA-1 attack Approximate GCD