TY - JOUR

T1 - Asymptotically most powerful tests for random number generators

AU - Ryabko, Boris

N1 - Funding Information:
Research was supported by Russian Foundation for Basic Research (grant no. 18-29-03005 ).
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2022/3

Y1 - 2022/3

N2 - The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

AB - The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

KW - p-value

KW - Random number generators

KW - Randomness testing

KW - Shannon entropy

KW - Statistical test

UR - http://www.scopus.com/inward/record.url?scp=85111049750&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2021.07.007

DO - 10.1016/j.jspi.2021.07.007

M3 - Article

AN - SCOPUS:85111049750

VL - 217

SP - 1

EP - 7

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -