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A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications



Lawrence E. Bassham, Andrew L. Rukhin, Juan Soto, James R. Nechvatal, Miles E. Smid, Stefan D. Leigh, M Levenson, M Vangel, Nathanael A. Heckert, D L. Banks


This paper discusses some aspects of selecting and testing random and pseudorandom number generators. The outputs of such generators may be used in many cryptographic applications, such as the generation of key material. Generators suitable for use in cryptographic applications may need to meet stronger requirements than for other applications. In particular, their outputs must be unpredictable in the absence of knowledge of the inputs. Some criteria for characterizing and selecting appropriate generators are discussed in this document. The subject of statistical testing and its relation to cryptanalysis is also discussed, and some recommended statistical tests are provided. These tests may be useful as a first step in determining whether or not a generator is suitable for a particular cryptographic application. However, no set of statistical tests can absolutely certify a generator as appropriate for usage in a particular application, i.e., statistical testing cannot serve as a substitute for cryptanalysis. The design and cryptanalysis of generators is outside the scope of this paper. [Supersedes SP 800-22 (May 15, 2001):]
Special Publication (NIST SP) - 800-22 Rev 1a
Report Number
800-22 Rev 1a


hypothesis test, P-value, random number generator, statistical tests


Bassham, L. , Rukhin, A. , Soto, J. , Nechvatal, J. , Smid, M. , Leigh, S. , Levenson, M. , Vangel, M. , Heckert, N. and Banks, D. (2010), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Special Publication (NIST SP), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 29, 2024)


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Created September 16, 2010, Updated February 19, 2017