On the Relativity of Binary Derivation and Autocorrelation Randomness Test

Randomness test plays an important role in the application of cryptography. There exists a lot of randomness test now, but it is impossible to choose all of them in practical test. It is significant to study the relativities among these test items. In this paper, the relativity of two important randomness tests, which are autocorrelation test and binary derivation test, is studied. The test procedures of these two randomness tests are analyzed based on their statistical theory. And a conclusion of the study is that binary derivation test equals to autocorrelation test while the parameter k equals 2\+t according to an attribute of Yang Hui triangle. So it is redundant to implement these two randomness tests for the same sequence synchronously. This conclusion is also proved through experimentation. Otherwise, another conclusion of this paper is that each bit of the derivation sequence is relevant to all the correlative bits of initial sequence when the test parameter k equals to 2\+t-1 in binary derivation test. The work of this paper is helpful to select reasonable and scientific parameters in practical randomness test.