  Rational secure multi-party computation (RSMC) means two or more rational
parties to complete a function on private inputs. In the process, the rational
parties choose strategies to maximize utility, which will cause players to
maliciously execute the protocol and undermine the fairness and correctness of
the protocol. To solve this problem, we leverage game theory to propose the
direction entropy-based solution. First, we utilize the direction vector of the
direction entropy to examine the player's strategy uncertainty and quantify its
strategy from different dimensions. Specifically, when parties choose a
cooperation strategy, the direction vector is positive, and the information
transmitted is positive, conversely, it is negative information. Then, we
provide mutual information to construct new utility functions for the players.
What's more, we measure the mutual information of players to appraise their
strategies. Finally, we prove in detail the protocol we gave, and the result
show that the fairness problem in rational secure two-party computation. We
also prove that the proposed protocol reaches the Nash equilibrium.
Furthermore, we conduct experiments using mutual information to construct
utility, and the results show that the utility obtained when the player is
honest will be higher.
