In a keyless entry system, a CPU in an ECU and a CPU in a remote control key each have an associated memory for storing respective function formulas, which are specified by primary function formula data. With this structure, function formulas used in the remote control key and the ECU can be changed to respective new function formulas. This technique makes it difficult to predict the function formulas used in the remote control key and the ECU, thereby further reducing any regularity of rolling codes generated by the function formulas.