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

Abstract : This paper discusses some aspects of selecting and testing random and pseudorandom number generators. The outputs of such generators may he 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 he 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 he useful as a first step in determining whether or not a generator is suitable for a particular cryptographic application. The design and cryptanalysis of generators is outside the scope of this paper.

[1]  I. Good The serial test for sampling numbers and other tests for randomness , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[3]  Igor N. Kovalenko,et al.  Distribution of the Linear Rank of a Random Matrix , 1973 .

[4]  K. Chung,et al.  Elementary Probability Theory with Stochastic Processes. , 1975 .

[5]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[6]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[7]  G. Marsaglia,et al.  Matrices and the structure of random number sequences , 1985 .

[8]  L. R. Moore,et al.  An Exhaustive Analysis of Multiplicative Congruential Random Number Generators with Modulus $2^{31} - 1$ , 1986 .

[9]  Manuel Blum,et al.  A Simple Unpredictable Pseudo-Random Number Generator , 1986, SIAM J. Comput..

[10]  M. Kimberley Comparison of two statistical tests for keystream sequences , 1987 .

[11]  O. Chrysaphinou,et al.  A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials , 1988 .

[12]  D. Aldous,et al.  A diffusion limit for a class of randomly-growing binary trees , 1988 .

[13]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[14]  J. Ziv Compression, tests for randomness and estimating the statistical model of an individual sequence , 1990 .

[15]  Pál Révész,et al.  Random walk in random and non-random environments , 1990 .

[16]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[17]  Helmut Prodinger,et al.  Digital Search Trees Again Revisited: The Internal Path Length Perspective , 1994, SIAM J. Comput..

[18]  Ed Dawson,et al.  A computer package for measuring the strength of encryption algorithms , 1994, Comput. Secur..

[19]  Anant P. Godbole,et al.  Runs and patterns in probability : selected papers , 1996 .

[20]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[21]  S. Pincus,et al.  Randomness and degrees of irregularity. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[22]  R E Kalman,et al.  Not all (possibly) "random" sequences are created equal. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Jean-Sébastien Coron,et al.  An Accurate Evaluation of Maurer's Universal Test , 1998, Selected Areas in Cryptography.

[24]  Andrew L. Rukhin,et al.  Distribution of the number of visits of a random walk , 1999 .

[25]  Brent B Welch,et al.  Practical Programming in Tcl and Tk , 1999 .

[26]  David Thomas,et al.  The Art in Computer Programming , 2001 .