随着分布式计算的发展，分布式计算环境中的安全性问题变得越来越突出。基于RSA算法的分布式认证和分布式数据加密等安全性机制也取得了长足的发展。不过，这些机制中大部分是基于传统密码协议中参与者类型的假设：半诚实或恶意的。本文从假设参与者是理性的这一视角出发，设计了基于RSA欧拉函数秘密分享的RSA私钥的分布式计算协议。协议中所有的参与者均是理性的，他们以自我利益为驱动。所有的参与者均采取遵守协议的执行这一策略形成了纳什均衡,并且该策略是不能严格劣势剔除的。

Along with the distributed computation becoming more and more popular,security mechanisms of the  distributed RSA key computation to enhance the strength of distributed authentication and data privacy have been developed quite a lot. However,most of them are the solutions for parties with traditional types like being semihonest or malicious. We propose a rational approach to dealing with the distributed computation of the RSA private key based on the secret sharing of the Euler totient function over polynomials,in which each player evolved is selfish and motivated to gain interest as mush as possible. The achievement is that it is a Nash equilibrium that each player follows the execution of the prescribed protocol. And the strategy survives the  iterated deletion of weakly dominated strategies