Methods of statistical tests independence verification
Keywords:Pseudorandom sequences generator, pseudorandom sequence, pseudorandom sequence quality, statistic tests of pseudorandom sequence quality assessment, test independence.
The necessary condition for the cryptosystem security is the certain cryptographic properties of pseudorandom number generator used in it. Therefore, both the developer and the user of such system are faced with the quality checking issues of the generator or its individual sequences. The main modern methods for pseudorandom sequence quality testing are reduced to the statistical randomness tests use. At the moment there are several statistical test suites, among which the most widely used is NIST statistical randomness test suite. The statistical tests choice and the suite creation is a complex task, since the tests should not only verify propinquity of pseudorandom sequence to true random sequence, but also perform such task effectively. Unfortunately, a compromise is achieved quite hard in this case and modern suites also have statistical dependencies, which unreasonably increase such suites operating time. Thus, one of the main question of tests suite construction and the statistical tests using is statistical independence of tests from this suite. To create an effective suite, tests without statistical dependencies should be used and, at the same time, the tests set should remain sufficiently complete. However, modern questions of forming texts suite, its number determination, type I error value, etc. are solved intuitively and empirically. This article provides the existing evaluation methods overview of statistical randomness tests independence verification and proposes a new, mathematically grounded method, which can be applied to arbitrary tests number and arbitrary random sequences number. The proposed method has advantages in speed and implementation. The paper also presents the experimental research results of the new method application to the statistical randomness test suite.
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