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How to play ANY mental game

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Abstract

We present a polynomial-time algorithm that, given as a input the description of a game with incomplete information and any number of players, produces a protocol for playing the game that leaks no partial information, provided the majority of the players is honest. Our algorithm automatically solves all the multi-party protocol problems addressed in complexity-based cryptography during the last 10 years. It actually is a completeness theorem for the class of distributed protocols with honest majority. Such completeness theorem is optimal in the sense that, if the majority of the players is not honest, some protocol problems have no efficient solution [C].
... SMC protocols are usually built over some form of Secret Sharing (e.g. Shamir's Secret Sharing [18], GMW [19], BGW [20]), or Garbled Circuits (e.g., Yao's GCs [21], BMR [22]), and are often combined with cryptographic primitives like public-key encryption, symmetric encryption, Homomorphic Encryption (HE) or Oblivious Transfers (OTs) to perform specific functionalities, each lending different levels of security, computational and communication costs [23]. Our approach for the private extraction of x-vectors relies on two forms of secret sharing briefly described below. ...
... The above-mentioned schemes are described with regard to arithmetic operations, but also hold for binary computations, with minor modifications [19]. This is important, as performing operations in each of these domains may prove to be more efficient for different operations, or may even allow performing different functionalities. ...
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