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Fast Computation on Encrypted Polynomials and Applications

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Cryptology and Network Security (CANS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7092))

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Abstract

In this paper, we explore fast algorithms for computing on encrypted polynomials. More specifically, we describe efficient algorithms for computing the Discrete Fourier Transform, multiplication, division, and multipoint evaluation on encrypted polynomials. The encryption scheme we use needs to be additively homomorphic, with a plaintext domain that contains appropriate primitive roots of unity. We show that some modifications to the key generation setups and working with variants of the original hardness assumptions one can adapt the existing homomorphic encryption schemes to work in our algorithms.

The above set of algorithms on encrypted polynomials are useful building blocks for the design of secure computation protocols. We demonstrate their usefulness by utilizing them to solve two problems from the literature, namely the oblivious polynomial evaluation (OPE) and the private set intersection but expect the techniques to be applicable to other problems as well.

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Author information

Authors and Affiliations

  1. University of Calgary, Canada

    Payman Mohassel

Authors
  1. Payman Mohassel
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Editor information

Editors and Affiliations

  1. The State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, 100190, Beijing, China

    Dongdai Lin

  2. Computer Science Department, University of California, 92697-3435, Irvine, CA, USA

    Gene Tsudik

  3. Shandong University, China

    Xiaoyun Wang

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Mohassel, P. (2011). Fast Computation on Encrypted Polynomials and Applications. In: Lin, D., Tsudik, G., Wang, X. (eds) Cryptology and Network Security. CANS 2011. Lecture Notes in Computer Science, vol 7092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25513-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-25513-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25512-0

  • Online ISBN: 978-3-642-25513-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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