STATISTICAL PROPERTIES OF THE PSEUDORANDOM SEQUENCE GENERATION ALGORITHM

Abstract

One of the most important issues in the design of cryptographic algorithms is studying their cryptographic strength. Among the factors determining the reliability of cryptographic algorithms, a good pseudorandom sequence generator, which is used for key generation, holds particular significance. The main goal of this work is to verify the normal distribution of pseudorandom sequences obtained using the generation algorithm and demonstrate that there is no mutual statistical correlation between the values of the resulting sequence. If these requirements are met, we will consider such a generator reliable. This article describes the pseudorandom sequence generation algorithm and outlines the steps for each operation involved in this algorithm. To verify the properties of the pseudorandom sequence generated by the proposed algorithm, it was programmatically implemented in the Microsoft Visual C++ integrated development environment. To assess the statistical security of the pseudorandom sequence generation algorithm, 1000 files with a block length of 10000 bits and an initial data length of 256 bits were selected. Statistical analysis was conducted using tests by D. Knuth and NIST. As shown in the works of researchers, the pseudorandom sequence generation algorithm, verified by these tests, can be considered among the reliable algorithms. The results of each graphical test by D. Knuth are presented separately. The graphical tests were evaluated using values obtained from each test, while the chi-squared criterion with degrees of freedom was used to analyze the evaluation tests. The success or failure of the test was determined using a program developed by the Information Security Laboratory. Analysis of the data from the D. Knuth tests showed good results. In the NIST tests, the P-value for the selected sequence was calculated, and corresponding evaluations were made. The output data obtained from the NIST tests also showed very good results. The proposed pseudorandom sequence generation algorithm allows generating and selecting a high-quality pseudorandom sequence of a specified length for use in the field of information security.

Keywords

• cryptography; algorithms; random sequence; pseudorandom sequence; statistical testing.