Statistical independence properties of pseudorandom vectors produced by matrix generators

Abstract

The uniformity test and the serial test are standard statistical tests for equidistribution and statistical independence, respectively, in sequences of uniform pseudorandom numbers. We introduce analogues of these tests for sequences of uniform pseudorandom vectors and we apply these tests to matrix generators for uniform pseudorandom vector generation. The results show that these generators behave well under these tests provided that the matrix in the generation algorithm is chosen carefully. The essential condition is that a certain figure of merit attached to the matrix be large. We also prove a general theorem which guarantees the existence of matrices with large figure of merit.