Correlation test for code sequence randomness with almost linear computational complexity

• Published in: Известия высших учебных заведений. Поволжский регион:Технические науки no. 3
• Main Authors: Volchikhin, V.I., Ivanov, A.I., Ivanov, A.P., Strokov, A.V.
• Format: Journal Article
• Language: English
• Published: Penza State University Publishing House 01-12-2021
• Subjects: evaluation of white noise quality; low computational complexity; statistical criteria for testing the hypothesis of independence
• ISSN: 2072-3059
• DOI: 10.21685/2072-3059-2021-3-3

Background. The purpose of this article is to create and study a new test of random code sequence quality with low computational complexity. Materials and methods. It is proposed, by analogy with the classical calculation of the autocorrelation function of noise with continual samples, to use the autocorrelation function for discrete noise. It is proposed to receive almost “white” noise from a software pseudo-random number generator. Samples of “colored” noise are proposed to be obtained by a sliding convolution of eight adjacent readings of “white” noise without weighing them. Results. The sum of the modules of the first 7 samples of the autocorrelation function of the analyzed noise is a powerful criterion for testing the hypothesis of independence of discrete data with a sample of 256 bits. This criterion has a low almost linear computational complexity and at the same time gives a high level of linear separability of dependent and independent data. The power of this new statistical test is higher than the power of similar statistical tests based on calculating Hamming distances. Conclusions. The proposed statistical criterion can be used when testing biometric authentication codes in a small-sized trusted computing environment with low bit depth, low power consumption, and a small amount of long-term and random access memory.