International Conference on Security and Privacy in Communication Networks. 10th International ICST Conference, SecureComm 2014, Beijing, China, September 24-26, 2014, Revised Selected Papers, Part I

Research Article

# TST: A New Randomness Test Method Based on Coupon Collector’s Problem

• ```@INPROCEEDINGS{10.1007/978-3-319-23829-6_25,
author={Qinglong Zhang and Zongbin Liu and Quanwei Cai and Ji Xiang},
title={TST: A New Randomness Test Method Based on Coupon Collector’s Problem},
proceedings={International Conference on Security and Privacy in Communication Networks. 10th International ICST Conference, SecureComm 2014, Beijing, China, September 24-26, 2014, Revised Selected Papers, Part I},
proceedings_a={SECURECOMM},
year={2015},
month={11},
keywords={Randomness tests Cryptography Golden section ratio Coefficient of variation},
doi={10.1007/978-3-319-23829-6_25}
}
```
• Qinglong Zhang
Zongbin Liu
Quanwei Cai
Ji Xiang
Year: 2015
TST: A New Randomness Test Method Based on Coupon Collector’s Problem
SECURECOMM
Springer
DOI: 10.1007/978-3-319-23829-6_25
Qinglong Zhang,*, Zongbin Liu,*, Quanwei Cai,*, Ji Xiang,*
*Contact email: qlzhang@is.ac.cn, zbliu@is.ac.cn, qwcai@is.ac.cn, jixiang@is.ac.cn

## Abstract

In this paper we find that a random sequence is expected to obey a new interesting distribution, and the coefficient of variation of this distribution approximates the value of , the difference between these two numbers is only 0.000797. As this interesting property, this newfound distribution is derived from Coupon Collector’s Problem and founded by the uniformity of frequency. Based on this distribution a new method is proposed to evaluate the randomness of a given sequence. Through the new method, the binary and decimal expansions of e, , , and the bits generated by Matlab are concluded to be random. These sequences can pass NIST tests and also pass our test. At the same time, we test some sequences generated by a physical random number generator WNG8. However, these sequences can pass the NIST tests but cannot pass our test. In particular, the new test is easy to be implemented, very fast and thus well suited for practical applications. We hope this test method could be a supplement of other test methods.