Software for testing small-length bit sequences for randomness

Abstract

This article dedicated to systematization of scientific positions about the static testing of sequences, widely used in cryptographic systems of information protection for the production of key and additional information (random numbers, vectors of initialization etc.) In this paper, randomness and the best-known test suite for detecting it is examined. Testing a bit sequence for randomness is not a new problem. Now there are a large number of test packages that solve this problem. Particular attention is paid to the statistical study of bit sequences. However, the specificity of subject areas, testing systems and problems of existing methods indicate the relevance of this issue and the need to improve existing testing methods. The available test suites show low flexibility and versatility in finding hidden patterns in small data lengths (up to 100 bits). To solve this problem, it is proposed to use algorithms based on multivariate statistics. Tests for multivariate statistics allow you to better explore a sequence by using multiple sequence characteristics simultaneously. They are based on examining patterns of length two and / or three and help to uncover hidden dependencies between data. These algorithms combine all the advantages of statistical methods and are the only alternative for analyzing short and medium length sequences. In this paper, static testing of sequences using multivariate statistics is considered. The paper provides formulas for testing bit sequences for randomness, using two-dimensional or three-dimensional statistics, which can be used to test short and medium sequences. To implement the proposed technique, a software tool was developed to test the bit sequence for randomness. This tool includes NIST tests as well as tests using multivariate statistics, which have worked well for testing short bit sequences. As a result of using the developed tool, it is possible to analyze a bit sequence and select the highest quality pseudo-random sequence for use in a particular subject area.