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

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International Conference on Security and Privacy in Communication Networks (SecureComm 2014)

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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 golden section ratio, 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, \(\pi \), \(\sqrt{2}\), \(\sqrt{3}\) 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.

Z. Liu—The work is supported by a grant from the National High Technology Research and Development Program of China (863 Program, No. 2013AA01A214) and the National Basic Research Program of China (973 Program, No. 2013CB338001).

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Authors and Affiliations

  1. Data Assurance and Communication Security Research Center, Beijing, China

    Qinglong Zhang, Zongbin Liu, Quanwei Cai & Ji Xiang

  2. State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, China

    Qinglong Zhang, Zongbin Liu, Quanwei Cai & Ji Xiang

  3. University of Chinese Academy of Sciences, Beijing, China

    Qinglong Zhang & Quanwei Cai

Authors
  1. Qinglong Zhang
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  2. Zongbin Liu
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  3. Quanwei Cai
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  4. Ji Xiang
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Corresponding author

Correspondence to Zongbin Liu .

Editor information

Editors and Affiliations

  1. CAS, Institute of Information Engineering CAS, Beijing, China

    Jing Tian

  2. Institute of Information Engineering, CAS, Beijing, China

    Jiwu Jing

  3. IBM Thomas J. Watson Research Center, New York, New York, USA

    Mudhakar Srivatsa

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© 2015 Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Zhang, Q., Liu, Z., Cai, Q., Xiang, J. (2015). TST: A New Randomness Test Method Based on Coupon Collector’s Problem. In: Tian, J., Jing, J., Srivatsa, M. (eds) International Conference on Security and Privacy in Communication Networks. SecureComm 2014. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 152. Springer, Cham. https://doi.org/10.1007/978-3-319-23829-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-23829-6_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23828-9

  • Online ISBN: 978-3-319-23829-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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