Walsh − Hadamard randomness testand new methods of test results integration

Abstract

We present a new statistical randomness test based on the Walsh-Hadamard transform. This test is an extension of frequency and autocorrelation tests and can detect a general class of defects that can appear in (pseudo)random generators. The test is based on the probability distribution of the Walsh-Hadamard transform. NIST Special Publication 800-22 [10] present two methods of integrating the results of one or more tests based on the proportion of passing tests and uniformity of the corresponding P−values. This paper will introduce another two methods of integration of test results based on maximum test statistics and sum of squares test statistics. The integration of test results is independent of the proposed test and may be used by all statistical tests based on confidence intervals. Some of the applications of the Walsh-Hadamard statistical test and decision procedures are in the following areas: (pseudo)randomness testing, cryptanalytic area, and steganographic detection.