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Since Gentry’s breakthrough result was introduced in the year 2009, the homomorphic encryption has become a very popular topic. The main contribution of Gentry’s thesis [5] was, that it has proven, that it actually is possible to design a fully homomorphic encryption scheme. However ground-breaking Gentry’s result was, the designs, that employ the bootstrapping technique suffer from terrible performance both in key generation and homomorphic evaluation of circuits. Some authors tried to design schemes, that could evaluate homomorphic circuits of arbitrarily many inputs without need of bootstrapping. This paper introduces the notion of symmetric homomorphic encryption, and analyses the security of four such proposals, published in three different papers ([2], [7], [10]). Our result is a known plaintext key-recovery attack on every one of these schemes.

  • [1]

    Brakerski, Zvika and Vaikuntanathan, Vinod, Fully homomorphic encryption from ring-lwe and security for key dependent messages, in: Proceedings of the31st annual conference on Advances in cryptology, CRYPTO′11, pages 505524, Berlin, Heidelberg, 2011. Springer-Verlag.

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  • [2]

    Chan, Aldar C-F. , Symmetric-key homomorphic encryption for encrypted data processing, in: Proceedings of the 2009 IEEE international conference on Communications, ICC′09, pages 774778, Piscataway, NJ, USA, 2009. IEEE Press.

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  • [3]

    Coppersmith, Don , Small solutions to polynomial equations, and low exponent rsa vulnerabilities, J. Cryptology, 10(4) (1997), 233260.

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  • [4]

    Fan, Junfeng and Vercauteren, Frederik, Somewhat practical fully homomorphic encryption, IACR Cryptology ePrint Archive, 2012 (2012), 144.

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  • [5]

    Gentry, Craig , A fully homomorphic encryption scheme, PhD thesis, Stanford, CA, USA, 2009. AAI3382729.

  • [6]

    Gentry, Craig and Halevi, Shai, Implementing gentry’s fully-homomorphic encryption scheme, Cryptology ePrint Archive, Report 2010/520, 2010.

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  • [7]

    Kipnis, Aviad and Hibshoosh, Eliphaz, Efficient methods for practical fully homomorphic symmetric-key encrypton, randomization and verification, IACRCryptology ePrint Archive, 2012 (2012), 637.

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  • [8]

    Rivest, R. L. , Adleman, L. and Dertouzos, M. L., On data banks and privacy homomorphisms, Foundations of Secure Computation, Academia Press, pages 169179, 1978.

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  • [9]

    van Dijk, Marten, Gentry, Craig, Halevi, Shai and Vaikuntanathan, Vinod, Fully homomorphic encryption over the integers, in: EUROCRYPT, pages 2443, 2010.

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  • [10]

    Xiao, Liangliang , Bastani, Osbert and Yen, I-Ling, An efficient homomorphic encryption protocol for multi-user systems, IACR Cryptology ePrint Archive, 2012 (2012), 193. Informal publication.

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  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

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