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Homomorphic Encryption

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Encyclopedia of Database Systems

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Definition

Homomorphic encryption is a form of public-key encryption where one can perform a specific algebraic operation on the plaintext by performing an (possibly different) algebraic operation on the ciphertext. For example, knowing only C 1 = (x) and C 2 = (y), but not x, y, one may be able to get (x + y) by calculating C 1 × C 2. A homomorphic encryption scheme allows a third party to operate on encrypted values without knowing the plaintext.

Key Points

Depending on the intended application, the homomorphic property can be seen as a positive or negative attribute of the cryptosystem. Homomorphic encryption schemes are malleable by design. On the other hand, the ability to enable manipulating ciphertexts without being able to decrypt can be very useful in some applications.

A fully homomorphic encryption scheme enables one to perform operations on the ciphertext to achieve both addition and multiplication on the enclosed plaintext. This enables one to compute arbitrary functions...

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Recommended Reading

  1. Gentry C. Fully homomorphic encryption using ideal lattices. In: STOC’09 Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, Bethesda. ACM Press; 2009. p. 169–78.

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  2. Paillier P. Public-key cryptosystems based on composite degree residuosity classes. In: Advances in Cryptology: EUROCRYPT’99, Prague. LNCS, vol. 1592. Springer; 1999. p. 223–38.

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  3. van Dijk M, Gentry C, Halevi S, Vaikuntanathan V. Fully homomorphic encryption over the integers. In: Advances in Cryptology: EUROCRYPT’10, Nice. LNCS, vol. 6110. Springer; 2010. p. 24–43.

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Author information

Authors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Ninghui Li

Authors
  1. Ninghui Li
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Correspondence to Ninghui Li .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, Georgia, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, Ontario, Canada

    M. Tamer Özsu

Section Editor information

  1. DiSTA, University of Insubria, Via Mazzini, 5, 21100, Varese, Italy

    Elena Ferrari

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Li, N. (2017). Homomorphic Encryption. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_1486-3

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  • DOI: https://doi.org/10.1007/978-1-4899-7993-3_1486-3

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4899-7993-3

  • Online ISBN: 978-1-4899-7993-3

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