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