Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences

Random sequences are widely used in many cryptographic applications and hence their generation is one of the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses or nonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statistical randomness tests and test suites, defined as a collection of tests. An efficient test suite should consist of a number of uncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated' is not a well-defined or well-understood concept in the literature. In this work, we apply Pearson's correlation test to measure the correlation between the tests.


Koçak, Onur Ozan; SULAK, FATİH; Doğanaksoy, Ali; Uğuz, Muhiddin (2018-01-01)
Generating random numbers and random sequences that are indistinguishable from truly random sequences is an important task for cryptography. To measure the randomness, statistical randomness tests are applied to the generated numbers and sequences. Knuth test suite is the one of the first statistical randomness suites. This suite, however, is mostly for real number sequences and the parameters of the tests are not given explicitly.
Alternative Approach to Maurer's Universal Statistical Test
Tezcan, Cihangir; Doğanaksoy, Ali (null; 2008-12-01)
Statistical tests for randomness play an important role in cryptography since many cryptographic applications require random or pseudorandom numbers. In this study, we introduce an alternative approach to Maurer’s Universal Test. This approach allows us to test short binary sequences as small as 66 bits and to choose slightly larger block sizes. Moreover, it does not have an initialization part and requires less time to test a binary sequence.
On the independence of statistical randomness tests included in the NIST test suite
SULAK, FATİH; Uğuz, Muhiddin; Koçak, Onur Ozan; Doğanaksoy, Ali (2017-01-01)
Random numbers and random sequences are used to produce vital parts of cryptographic algorithms such as encryption keys and therefore the generation and evaluation of random sequences in terms of randomness are vital. Test suites consisting of a number of statistical randomness tests are used to detect the nonrandom characteristics of the sequences. Construction of a test suite is not an easy task. On one hand, the coverage of a suite should be wide; that is, it should compare the sequence under considerati...
Analyzes of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber
Aksoy, Berkin; Cenk, Murat; Department of Cryptography (2022-2-28)
Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptography (PQC) Standardization Process, efficient implementations of lattice-based algorithms have been studied extensively. Lattice-based NIST PQC finalists use polynomial or matrix-vector multiplications on the ring with type {Z}_{q}[x] / f(x). For convenient ring types, Number Theoretic Transform (NTT) can be used to perform multiplications as done in Crystals-KYBER among the finalists of the NIST PQC S...
Mutual correlation of randomness test and analysis of test outputs of transformed and biased sequences
Akcengiz, Ziya; Doğanaksoy, Ali; Department of Cryptography (2014)
Randomness is one of the most important parts of the cryptography because key generation and key itself depend on random values. In literature, there exist statistical randomness tests and test suites to evaluate randomness of the cryptographic algorithm. Although there exist randomness tests, there is no mathematical evidence to prove that a sequence or a number is random. Therefore, it is vital to choose tests in the test suites due to independency and coverage of the tests used in the suites. Sensitivity...
Citation Formats
A. Doğanaksoy, M. Uğuz, and Z. Akcengiz, “Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences,” TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES, pp. 655–665, 2017, Accessed: 00, 2020. [Online]. Available: