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A New Spectral Test for Nonrandomness and the DES
March 1990 (vol. 16 no. 3)
pp. 261-267

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. 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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Index Terms:
spectral test; nonrandomness; finite binary strings; power spectrum; empirical measure; chi-square test; short-round versions; data encryption standard; output-feedback mode; DES rounds; cryptography; program testing; standards; statistical analysis; word processing.
F.A. Feldman, "A New Spectral Test for Nonrandomness and the DES," IEEE Transactions on Software Engineering, vol. 16, no. 3, pp. 261-267, March 1990, doi:10.1109/32.48934
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