The concept is important in the field of cryptography and is closely related to the idea of zero-knowledgeness. 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— Secure computation was formally introduced in 1982 by A. Yao The millionaire problem and its solution gave way to a generalization to multi-party protocols. Like many cryptographic protocols, the security of an MPC protocol can rely on different assumptions: - It can be computational (i.e. based on some mathematical problem, like factoring) or unconditional (usually with some probability of error which can be made arbitrarily small).
- The model in which the scheme is described might assume that participants use a synchronized network (a message sent at a "tick" always arrives at the next "tick"), that a secure and reliable broadcast channel exists, that a secure communication channel exists between every pair of participants (an adversary cannot read, modify or generate messages in the channel), etc.
- The centrally controlled adversary considered can be passive (only allowed to read the data of a certain number of participants) or active (can corrupt the execution protocol or a certain number of participants).
- An adversary can be static (chooses its victims before the start of the multi-party computation) or dynamic (can choose its victims during the course of execution of the multiparty computation). Attaining security against a dynamic adversary is often much harder than security against a static adversary.
- An adversary can be defined as a threshold structure (meaning that it can corrupt or simply read the memory of a number of participants up to some threshold), or be defined as a more complex structure (it can affect certain predefined subsets of participants, modeling different possible collusions). These structures are commonly referred to as adversary structures. The opposite set consisting of the sets of honest parties that can still execute a computational task is related to the concept ofaccess structures.
An important primitive in MPC is oblivious transfer. Unconditionally or information-theoretically secure MPC is closely related to the problem of secret sharing, and more specifically verifiable secret sharing (VSS); many secure MPC protocols that protect against active adversaries use VSS. Secure MPC provides solutions to various real-life problems such as distributed voting, private bidding and auctions, sharing of signature or decryption functions, private information retrieval, etc. The first large-scale and practical application of multiparty computation took place in Denmark in January 2008, as described by Bogetoft et al.
## [edit]Two-party computationThe sub-problem of MPC that has received special attention by researchers because of its close relation to many cryptographic tasks is referred to as secure two-party computation (2PC) or just as Secure function evaluation (SFE). This area of research is concerned with the question: 'Can two party computation be achieved more efficiently and under weaker security assumptions than general MPC?' ## [edit]Virtual Party ProtocolVirtual Party Protocol is an SMC protocol which uses virtual parties and complex mathematics to hide the identity of the parties. |

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