First, by analyzing the previous fault analysis on RSA using square and multiply algorithm because these attacks require quite precise fault injections like a bit flip and the fault injection can’t be used effectively, this paper builds a new fault analysis model on RSA using square and multiply algorithm based on non-invasive fault, including the square operation fault and the multiply operation fault; Next, an improved fault analysis algorithm based on recovering key segment and a random fault analysis algorithm on RSA using SPA-FA resistant are proposed separately, these proposed fault analysis algorithms are proved in theory and the method of controlling the opportunity in fault injection is suggested; Finally, a fault attack is implemented on RSA in a Protues simulation environment, using the computer program simulation to inject the fault. Experimental results show that the proposed fault analysis algorithm based on recovering key segment can reduce the accuracy requirements of fault injection, and number of fault injection is reduced by about 80%; and the random fault analysis algorithm based on the multiply operation fault can cancel the dependence between the each key bit recover, further improve the feasibility of fault analysis.