Abstract:

Secure multi-party computation protocol allows a set of -parties to evaluate a joint function of their inputs such that the function is calculated correctly and furthermore no information about their inputs is revealed by the output of the function. Based on the determinate-commutative cryptosystem and under the semi-honest model hypothesis, secure two-party computation protocols for determine whether an element is belong to a certain finite set, whether two finite sets are equal, and whether two equivalence relations are equal are considered. A mathematic method, relates to kernel, image and kernel-classes of mapping, to determine whether two mappings are equal is introduced. Furthermore, two-party computation protocol for determine whether two mappings are equal is given. Correctness, security, and efficiency of our protocols are analyzed.

Key words: cryptography, secure two-party computation, equivalent relation, mapping, finite full transformation semigroup