No. 970

Title:

Physical Random Number Generator for Personal Computers

Author(s):

Niki, Naoto (The Institute of Statistical Mathematics)

Key words:

random number; Zener diode noise; personal computer

Abstract:

    A physical random number generator has been designed, made and tasted by the author. The structure of the generator is very simple so that it may be assembled on a small PC board. The source of a random process is the noise of a Zener diode in a proper bias condition. After being amplified and passed through a high-pass-filter, the noise is applied to a voltage comparator to generate the random pulse procsee. The number of random pulses (very thin pulse are eliminated) occuring during 125 micro seconds has a distribution closely approximated by the normal distribution with mean between 430 and 470 and variance between 100 and 120. Therefore, the distribution of the least significant digit of the number of pulses in hexadecimal (decimal) represen- tation is very close to the discrete rectangular distribution on [0, 15] ([0, 9]). The maximum relative error of approximatetion may be estimated at 0.0009( ),theoretically, which may suffice for use on personal computers. The least significant digit of the number of pulses is extracted by use of a hexadecimal (decimal) counter,a Schmitt- trigger gate, a clock circuit and a set of interface circuits between the computer and the generator. The time interval of clock-triggers is selectable between 125 and 250 micro seconds. When the clock is set at 250 micro seconds, the approximation error to the discrete rectangular distribution may become less than for hexadecimal random numbers or for decimal ones. Tests for checking the deviation of the empirical distribution from uniformity and the dependence between neighbouring numbers have been made. The tests were applied to the even-odd ratio for each group of hexadecimal numbers of size 4,096, the even-odd independence and the uniformity. The empirical distributions of 's, each of 30,000 in size, were compared with the distributions under the hypothesis. The second and third theoretical distributions are well approximated by the distributions of degrees of freedom 3 and 15 respectively. The first may be directly calculated. The tests of goodness of fit have shown that the observed numbers have good properties towards true randomness. The numbers derived from m-sequences and the numbers generated by RND function in BASIC have, however, been unfavourable to the hypothesis that they are equidistributed.