On Statistical Tests for Randomness Included in the NIST SP800-22 Test Suite and Based on the Binomial Distribution

Abstract

In this paper we review some statistical tests included in the NIST SP 800-22 suite, which is a collection of tests for the evaluation of both true-random (physical) and pseudorandom (algorithmic) number generators for cryptographic applications. The output of these tests is the so-called p-value which is a random variable whose distribution converges to the uniform distribution in the interval [0, 1] when testing an increasing number of samples from an ideal generator. Here, we compute the exact non-asymptotic distribution of p-values produced by few of the tests in the suite, and propose some computation-friendly approximations. This allows us to explain why intensive testing produces false-positives with a probability much higher than the expected one when considering asymptotic distribution instead of the true one. We also propose a new approximation for the Spectral Test reference distribution, which is more coherent with experimental results.

Checking the quality of approximation of p-values in statistical tests for random number generators by using a three-level test

“…We check the quality of the approximation of the 76 tests (90 statistics), whose statistics have continuous distributions, ignoring those whose statistics are discrete, namely the smarsa_CollisionOver test (No.3-10), the smarsa_BirthdaySpacings test (No. [11][12][13][14][15][16][17], the snpair_ClosePairs test (No. [18][19][20], the snpair_ClosePairsBitMatch test (No.21-22), and one of the test statistics of the sknuth_CollisionPermut test (No.39-40), where the numbers correspond to the enumeration of the tests in the user's guidebook [12].…”

Deriving the Variance of the Discrete Fourier Transform Test Using Parseval’s Theorem

“…To address the second problem, Kim et al also proposed to use (0.95)(0.05) n 4 as an estimate of the variance of N 1 [2]. In other words, because the variable d should follow a standard normal distribution, they proposed to change the computation of d to 3.8 as that [5]. These proposed values were experimentally derived but the theoretical value of this variance has not been derived.…”

An Improve Image Encryption Algorithm Based on Multi-level of Chaotic Maps and Lagrange Interpolation

“…So accordingly and depending on the proposed key size (size of keyimage) it is easy to conclude that the proposed encryption method has a sufficiently large key space to withstand versus to various types of brute-force attacks. Also series of statistical tests suite provided by the National Institute of Standards and Technology (NIST) special publication is used to detect variation of a binary sequence from true randomness [3].in this experimental we used 10 tests which are list in Table-2 [29] when the P-value larger than 0.01 this means that a sequence which passed the test is considered as random with 99% confidence. Thus, the new key are suitable for image encryption.…”