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

Rukhin, Andrew; Soto, Juan; Nechvatal, James; Smid, Miles; Barker, Elaine; Leigh, Stefan; Levenson, Mark; Vangel, Mark; Banks, David; Heckert, N.; Dray, James; Vo, San; Bassham, Lawrence

doi:https://doi.org/10.6028/NIST.SP.800-22r1a

SP 800-22 Rev. 1a

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

Documentation Topics

Date Published: April 2010

Supersedes: SP 800-22 Rev. 1 (08/01/2008)

Planning Note (4/19/2022): This publication has been reviewed, and NIST has decided to REVISE it. See the full announcement and Crypto Publication Review Project for more details.

Author(s)

Andrew Rukhin (NIST), Juan Soto (NIST), James Nechvatal (NIST), Miles Smid (NIST), Elaine Barker (NIST), Stefan Leigh (NIST), Mark Levenson (NIST), Mark Vangel (NIST), David Banks (NIST), N. Heckert (NIST), James Dray (NIST), San Vo (NIST), Lawrence Bassham (NIST)

Abstract

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.

Keywords

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

Control Families

Assessment, Authorization and Monitoring; System and Communications Protection

Documentation

Publication:
SP 800-22 Rev. 1a (DOI)
Local Download

Supplemental Material:
None available

Document History:
04/30/10: SP 800-22 Rev. 1a (Final)

Topics

Security and Privacy
random number generation; testing & validation