A new spectral test for nonrandomness and the DES

A test for detecting the nonrandomness of finite binary strings is proposed. This test, based on an evaluation of the power spectrum of a finite string, extends and quantifies a similar test proposed by J. Gait (see ibid., vol.3, no.5, p.359-63, 1977). As an empirical measure of the sensitivity of the test, it was compared with a chi-square test for uniformity of distribution, which also measures nonrandomness. This comparison was performed by applying each of these tests to binary strings produced using short-round versions of the data encryption standard (DES) in output-feedback mode. By varying the number of DES rounds from 1 to 16, it was possible to gradually vary the degree of randomness of the resulting strings. The degree of randomness of the DES, including the 15 short-round versions, was also assessed. Only ensembles generated by one and two round versions were rejected as random.<
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