Pseudorandom sequences generated by linear feedback shift registers with some nonlinear combining functions have been proposed for cryptographic applications as a running key genarators in some stream ciphers. In this correspondence it will be shown that the number of trails to break these types of ciphers can be significantly reduced by using correlation methods. By comperison of computer simulations and theoretical result based on a statistical model, the validitiy of this analysis is demonstrated. Furthermore, a fast corelation attack will be proposed based on this idea. Then, to prevent such attacts, properties of a good choices of nonlinear functions will be proposed and the construction of such function will be described. 

Key words :  Cryptanalysis, Stream cipher, Linear feedback shitf register (LFSR), Correlation, Correlation immunity.