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Method of Controlled Random Tests Generation

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Abstract
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This paper analyzes methods for constructing controlled random tests based on scaling initial templates representing tests with a small number of patterns and low bit size. The advantages and disadvantages of scalingbased approaches, which can significantly reduce the computational costs required to construct controlled random tests with specified characteristics, are highlighted. A general approach for constructing controlled random tests based on a scaling matrix is formulated, allowing the use of low-dimensional tests. The effectiveness of twodimensional scaling of both binary vectors and templates is demonstrated, increasing not only the bit size of test patterns but also their number. Dependencies for determining the resulting test metrics based on the characteristics of the scaling matrix and template are obtained.

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  • 10.37661/1816-0301-2025-22-2-63-80
Scaling controlled random tests based on Hadamard matrices
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Objectives. The problem of constructing controlled random tests is solved by two-dimensional scaling of initial templates using Hadamard matrices. The limitations of classical approaches to generating test patterns based on enumeration of candidates for test patterns are shown. With an increase in the threshold values of the difference measures of binary test patterns, the computational complexity of constructing such tests increases. The main goal of this article is to develop methods for constructing tests based on initial templates and their expansion to the required bit size based on the application of formal rules.Methods. For two-dimensional scaling of initial templates with specified Hamming distance thresholds, Hadamard matrices and the Sylvester recursive procedure for their construction are applied. The experimental research employed the method of statistical trials.Results. It is demonstrated that methods for constructing controlled random tests based on templates can be viewed as a procedure for scaling controlled random tests to the required bit size. Both templates characterized by the minimum bit size of patterns and any controlled random tests are used to construct the desired tests. The procedure itself is characterized as one-dimensional scaling, which increases the bit size of patterns while maintaining their quantity. To simultaneously increase the bit size and quantity of test sets, a method based on two-dimensional scaling of templates using Hadamard matrices is proposed. This allows for the construction of controlled random tests without the labor-intensive process of enumerating candidate test patterns and computing their difference measure values. It is shown that the unique orthogonality property of Hadamard matrices, as their order increases, enables achieving ratios of the average Hamming distance between test patterns to their bit size close to 1/2. It is noted that the characteristics of the initial templates do not significantly affect the characteristics of the resulting tests constructed using Hadamard matrices obtained through the Sylvester recursive procedure. The feasibility and efficiency of the proposed approach to constructing controlled random tests are evaluated for the case of testing memory devices. It is demonstrated that controlled random tests constructed using Hadamard matrices have significantly higher coverage capability compared to random tests.Conclusion. An approach for generating test patterns in the formation of controlled random tests using Hadamard matrices is considered. The proposed approach is based on two-dimensional scaling of initial templates using these matrices. It is shown that the use of various templates and their two-dimensional scaling allows for the construction of controlled random tests with the required bit size of test patterns and a larger number of them

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Random numbers are essential for communications security, as they are widely employed as secret keys and other critical parameters of cryptographic algorithms. The Linux random number generator (LRNG) is the most popular open-source software-based random number generator (RNG). The security of LRNG is influenced by the overall design, especially the quality of entropy sources. Therefore, it is necessary to assess and quantify the quality of the entropy sources which contribute the main randomness to RNGs. In this paper, we perform an empirical study on the quality of entropy sources in LRNG with Linux kernel 5.6, and provide the following two findings. We first analyze two important entropy sources: jiffies and cycles, and propose a method to predict jiffies by cycles with high accuracy. The results indicate that, the jiffies can be correctly predicted thus contain almost no entropy in the condition of knowing cycles. The other important finding is the failure of interrupt cycles during system boot. The lower bits of cycles caused by interrupts contain little entropy, which is contrary to our traditional cognition that lower bits have more entropy. We believe these findings are of great significance to improve the efficiency and security of the RNG design on software platforms.

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Evaluation of Test Metrics: Stuck-at, Bridge Coverage Estimate and Gate Exhaustive
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