Secure multi-party computation

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Secure multi-party computation (also known as secure computation or multi-party computation (MPC)) is a subfield of cryptography with the goal to create methods for parties to jointly compute a function over their inputs, and keeping these inputs private.


In an MPC, a given number of participants p1, p2, ..., pN each have private data, respectively d1, d2, ..., dN. Participants want to compute the value of a public function F on N variables at the point (d1, d2, ..., dN). An MPC protocol is secure, if no participant can learn more from the description of the public function and the result of the global calculation than what he/she can learn from his/her own entry — under particular conditions depending on the model used.[citation needed]


The concept is closely related to the idea of zero knowledge. For example, two millionaires can compute which one is richer without revealing their net worth. This very example was used by Andrew C. Yao in a 1982 paper,[1] which was later named the millionaire problem.[2]

In general it refers to computational systems in which multiple parties wish to jointly compute some value, based on individually held secret bits of information, but do not wish to reveal their secrets to one another in the process. For example, two individuals who each possess some secret information—x and y, respectively—may wish to jointly compute some function f(x,y) without revealing any information about x and y other than what can be reasonably deduced by knowing the actual value of f(x,y), where "reasonably deduced" is often interpreted as equivalent to computation within polynomial time. The primary motivation for studying methods of secure computation is to design systems that allow for maximum utility of information without compromising user privacy.[citation needed]

Unconditionally or information-theoretically secure MPC is closely related to the problem of secret sharing, and more specifically verifiable secret sharing (VSS), which many secure MPC protocols that protect against active adversaries use.

Performing a computation using MPC protocols is still orders of magnitude slower than performing the computation using a trusted third party.[citation needed] Increasingly efficient protocols for MPC have been proposed, and MPC can be now used as a practical solution to various real-life problems such as distributed voting, private bidding and auctions, sharing of signature or decryption functions and private information retrieval.[3] The first large-scale and practical application of multiparty computation took place in Denmark in January 2008.[4]


Secure computation was formally introduced as secure two-party computation (2PC) in 1982 by Andrew Yao,[5] the first recipient of the Knuth Prize. It is also referred to as Secure function evaluation (SFE), and is concerned with the question: 'Can two party computation be achieved more efficiently and under weaker security assumptions than general MPC?'[citation needed]

The millionaire problem solution gave way to a generalization to multi-party protocols.[6]

Security assumptions[edit]

Like many cryptographic protocols, the security of an MPC protocol can rely on different assumptions:

The set of honest parties that can execute a computational task is related to the concept of access structure. In contrast, "adversary structures" can consist of the following:

Protocols used[edit]

An important primitive used in MPC is oblivious transfer.[citation needed]

Virtual Party Protocol is a protocol which uses virtual parties and complex mathematics to hide the identity of the parties.[7]

Secure sum protocols allow multiple cooperating parties to compute sum function of their individual data without revealing the data to one another.[8]

In 2014 a "model of fairness in secure computation in which an adversarial party that aborts on receiving output is forced to pay a mutually predefined monetary penalty" has been described for the Bitcoin network or for fair lottery.[9]

See also[edit]


  1. ^ Andrew Chi-Chih Yao: Protocols for Secure Computations (Extended Abstract) FOCS 1982: 160-164
  2. ^ Sheikh, R., Mishra, D. K. & Kumar, B. (2011). Secure Multiparty Computation: From Millionaires Problem to Anonymizer. Information Security Journal: A Global Perspective, 20, 25-33.
  3. ^ Claudio Orlandi: Is multiparty computation any good in practice?, ICASSP 2011
  4. ^ Peter Bogetoft, Dan Lund Christensen, Ivan Damgård, Martin Geisler, Thomas Jakobsen, Mikkel Krøigaard, Janus Dam Nielsen, Jesper Buus Nielsen, Kurt Nielse, Jakob Pagter, Michael Schwartzbach and Tomas Toft (2008). "Multiparty Computation Goes Live". Cryptology ePrint Archive (Report 2008/068). 
  5. ^ Andrew C. Yao, Protocols for secure computations (extended abstract)
  6. ^ O. Goldreich, S. Micali, and A. Wigderson. How to play ANY mental game. In Proceedings of the nineteenth annual ACM conference on Theory of computing, pages 218-229. ACM Press, 1987.
  7. ^ Pathak Rohit, Joshi Satyadhar, Advances in Information Security and Assurance, Springer Berlin / Heidelberg, ISSN 0302-9743 (Print) 1611-3349 (Online), ISBN 978-3-642-02616-4, DOI 10.1007/978-3-642-02617-1
  8. ^ Rashid Sheikh, Brijesh Kumar and Durgesh Kumar Mishra, Privacy Preserving k-secure sum protocols, International Journal of Computer Science and Information Security, ISSN 1947-5500 (Online),Vol.6, No.2, Nov. 2009
  9. ^ Iddo Bentov, Ranjit Kumaresan (2014). "How to Use Bitcoin to Design Fair Protocols". Cryptology e print (International Association for Cryptologic Research (IACR)) (129): 1–38. Retrieved 9 October 2014. 

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