中文摘要：

随机性检测在密码学中发挥着重要的作用，目前，已有多种不同的随机性检测算法．但是，实际应用申选择所有的检测算法进行检测不现实，选择哪些算法能够使检测充分且无冗余，这需要研究检测算法之间可能存在的关系．对两种重要的随机性检测算法二元推导和自相关进行了研究．从二者的基本原理出发，对其检测的推导过程进行了分析，结合杨辉三角的性质证明了在参数k选择为2^t时，二元推导与自相关是等价的．若同时进行参数为2^t的二元推导检测和自相关检测则存在冗余．同时对这个结论进行了实验验证．另外，研究还发现，在参数k选择为2‘一1时，二元推导检测中推导序列的每一个比特包含初始序列的所有相关比特信息．所研究工作为实际应用中随机性检测项目和检测参数的选择提供了理论的指导．

英文摘要：

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＇ according to an attribute of gang 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.