Let f denote a given n-ary function, and suppose parties \(P_1,\ldots,P_n\) each hold an input value \(x_1,\ldots,x_n\), respectively. A secure multiparty computation for f is a joint protocol between parties \(P_1,\ldots,P_n\) for computing \(y=f (x_1,\ldots,x_n)\) securely. That is, even when a certain fraction of the parties is corrupted, (i) each party obtains the correct output value y and (ii) no information leaks on the input values of the honest parties beyond what is implied logically by the value of y and the values of the inputs of the corrupted parties.
Conceptually, a secure multiparty computation for function f can be viewed as an implementation of a trusted third party T, which, upon receipt of the input values \(x_1,\ldots,x_n\) from parties \(P_1,\ldots,P_n\), respectively, produces the output value \(y=f (x_1,\ldots,x_n)\). Party T is trusted for (i) providing the correct value for y and (ii) ot revealing any further information to parties \(P_1,\ldots,P_n\).
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Schoenmakers, B. (2005). Multiparty Computation. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_265
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