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Threshold Homomorphic Cryptosystems

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Encyclopedia of Cryptography and Security

Related Concepts

Homomorphic Encryption; Threshold Cryptography

Definition

A threshold homomorphic cryptosystem is an asymmetric cryptosystem which combines the use of threshold cryptography and homomorphic encryption. A key pair is generated jointly between multiple parties, and whereas the public key is used for encryption as in ordinary asymmetric cryptosystems, the private key will only exist as a shared secret throughout its lifetime.

Background

Threshold homomorphic cryptosystems are used in many constructions of privacy-protecting protocols. Early use of the combination of homomorphic encryption and threshold decryption was made in Benaloh et al.’s voting schemes (see, e.g., [2]), and this approach became standard after the efficient voting scheme of [4]. More generally, in a series of papers [3,  7,  8,  11] it has been shown how threshold homomorphic cryptosystems can be used as a basic building block for achieving secure multiparty computation.

Theory

A threshold homomorphic...

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Recommended Reading

  1. Algesheimer J, Camenisch J, Shoup V (2002) Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. In: Advances in cryptology—CRYPTO ’02. Lecture notes in computer science, vol 2442. Springer, Berlin, pp 417–432

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  2. Benaloh J, Yung M (1986) Distributing the power of a government to enhance the privacy of voters. In: Proceedings of the 5th ACM symposium on principles of distributed computing (PODC ’86), ACM, New York, pp 52–62

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  8. Franklin M, Haber S (1996) Joint encryption and message-efficient secure computation. J Cryptol 9(4):217–232

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  10. Pedersen T (1991) A threshold cryptosystem without a trusted party. In: Advances in cryptology—EUROCRYPT ’91. Lecture notes in computer science, vol 547. Springer, Berlin, pp 522–526

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  11. Schoenmakers B, Tuyls P (2004) Practical two-party computation based on the conditional gate. In: Advances in cryptology—ASIACRYPT ’04. Lecture notes in computer science, vol 3329. Springer, Berlin, pp 119–136

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Den Dolech 2, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Berry Schoenmakers Professor

Authors
  1. Berry Schoenmakers Professor
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Schoenmakers, B. (2011). Threshold Homomorphic Cryptosystems. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_13

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