Evaluation of a Random Number Generator based on an Internal Linear Feedback Shift Register

Abstract

A previous study presented a random number generator based on the fluctuation in the sampling interval of an internal linear feedback shift register (LFSR). They reported that the derived random numbers passed the Diehard test; however, the design guidelines were not specified. The previous study examined two configurations of LFSR, which are far from satisfactory to determine the appropriate length and feedback polynomial. Moreover, the minimal sampling period was not known. The present study focuses on these aspects and elucidates the requirements of LFSRs to generate high-quality random numbers. Extensive experiments were conducted, and the following results were derived. (1) The selection of the characteristic polynomial of an LFSR affects the quality of random numbers. (2) The length of an LFSR should be 48 bits or greater with a constant sampling period. (3) The sampling period should be 32 cycles or larger. (4) The quality of random number sequence is considerably improved by a fluctuating sampling period. (5) The properly designed random number generator passes the NIST test.