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

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Information Security Practice and Experience (ISPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7232))

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.

This work is supported by ARC Future Fellowship FT0991397.

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Author information

Authors and Affiliations

  1. Centre for Computer and Information Security Research, School of Computer Science & Software Engineering (SCSSE), University Of Wollongong, Australia

    Zhenfei Zhang, Thomas Plantard & Willy Susilo

Authors
  1. Zhenfei Zhang
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  2. Thomas Plantard
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  3. Willy Susilo
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, UK

    Mark D. Ryan

  2. Toshiba Corporation, 1, Komukai-Toshiba–Cho, 212-8582, Saiwai-ku, Kawasaki, Japan

    Ben Smyth

  3. School of Computer Science & Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Guilin Wang

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Zhang, Z., Plantard, T., Susilo, W. (2012). On the CCA-1 Security of Somewhat Homomorphic Encryption over the Integers. In: Ryan, M.D., Smyth, B., Wang, G. (eds) Information Security Practice and Experience. ISPEC 2012. Lecture Notes in Computer Science, vol 7232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29101-2_24

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  • DOI: https://doi.org/10.1007/978-3-642-29101-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29100-5

  • Online ISBN: 978-3-642-29101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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