externally given parameters in the random number generation system which sequentially generates the random numbers by the predetermined conversion and the feedback based on the given initial value and more particularly the change of the parameter which controls the conversion system before a number of random number sequences required for determining the conversion system are outputted to change the conversion system from the above it should be understood that the random number generation system is not limited to the linear and non linear feedback registers but various other systems may be used as to the conversion system in the feedback conversion the control by the externally given parameter has been described alternatively a combined parameter of the externally given parameter and an internally generated parameter may be used for the control in fig7 no shift register is used in the procedure for generating the random number in the present embodiment s registers r 1 r s which are operated by the same clock and m non linear conversion circuits t 1 t m which effect the non linear conversion by the outputs from the respective registers and the final register r s and output it to the next register are used as the random number generation circuit by the system a and a parameter calculation circuit 61 by the system b.