The discrete multiple-parameter fractional Fourier transform SCIENCE CHINA Information Sciences 53, 2287 (2010); Two modified discrete chirp Fourier transform schemes Science in China Series F-Information Sciences 44, 329 (2001);
Runs distribution test is an important statistical test based on Golomb's randomness postulates. It is an important randomness test included in some famous evaluation standards and statistical test suites such as Application Notes and Interpretation of the Scheme (AIS20), the Federal Information Processing Standards (FIPS140), CryptX, and so on. However, when it is applied on some well-known good Deterministic Random Bit Generators (DRBGs), the test results show apparent bias from randomness. This shows that there exist some inaccuracies in the runs distribution test. The problem is solved and the runs distribution test through two ways is corrected. First, the degree of freedom of statistical value V is adjusted. Secondly, the expected number of different lengths runs is modified. The experiment results show that the corrected runs distribution test is more accurate under two-level evaluation approach proposed by National Institute of Standards and Technology (NIST) Special Publication (SP) 800-22.
It is important to study the correlation of randomness statistical tests The correlation of templates in non-overlapping template matching test is studied. The correlation degree between templates is defined and a correlation theorem is presented. For two different m-bit templates, when the last m−1 bits of one are equal to the first m−1 bits of the other one, correlation degree of them reaches the maximum value. Correlation experiments are also carried out and the results agree with the theorem. Finally, an effective selection strategy is proposed and the number of templates can be reduced about 50%.
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