A Non-empirical Test on the Second to the Sixth Least Significant Bits of Pseudorandom Number Generators

Abstract

Lagged Fibonacci generators are widely used random number generators. Some implementations discard the least significant bit of their outputs, because their weight distribution has a strong deviation. But the degree of the improvement is unclear. In this paper, we give a method to compute the weight distribution of the n-th least significant bit of several pseudo random number generators for arbitrary n, generalizing the weight discrepancy test which was possible only for n D 1. The method is based on the MacWilliams identity over Z=2n, and predicts the sample size for which the bit stream fails in a statistical test. These tests are effective to lagged Fibonacci generators such as random() in BSD-C library. For example, we show that the second least significant bit of random() will be rejected if the sample size is of order 104, while the sixth bit will be rejected for the sample size around 107. © Springer-Verlag Berlin Heidelberg 2013.