New Statistical Randomness Tests Based on Length of Runs

Doğanaksoy, Ali
Uğuz, Muhiddin
Seker, Okan
Akcengiz, Ziya
Random sequences and random numbers constitute a necessary part of cryptography. Many cryptographic protocols depend on random values. Randomness is measured by statistical tests and hence security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this work we focus on statistical distributions of runs of lengths one, two, and three. Using these distributions we state three new statistical randomness tests. New tests use chi(2) distribution and, therefore, exact values of probabilities are needed. Probabilities associated runs of lengths one, two, and three are stated. Corresponding probabilities are divided into five subintervals of equal probabilities. Accordingly, three new statistical tests are defined and pseudocodes for these new statistical tests are given. New statistical tests are designed to detect the deviations in the number of runs of various lengths from a random sequence. Together with some other statistical tests, we analyse our tests' results on outputs of well-known encryption algorithms and on binary expansions of e, pi, and root 2. Experimental results show the performance and sensitivity of our 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.
Statistical iid tests of integer sequences
Yılmaz, Sena; Doğanaksoy, Ali; Department of Mathematics (2019)
In order that an algorithm is cryptographically secure, the encryption keys must be random. To achieve this randomness, a number of random number generators are used. Since pseudo-random number generators can never provide true randomness, there is a need to measure the obtained pseudo-randomness. To obtain information about randomness, the entropy value of the output can be calculated. In order to measure the entropy of a sequence, it can be examined whether it is an IID (independent and identical distribu...
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...
Yeniaras, Esra; Cenk, Murat; Department of Cryptography (2022-1-21)
Some of the post-quantum cryptographic protocols require polynomial multiplication in characteristic three fields, thus the efficiency of such multiplication algorithms gain more importance recently. In this thesis, we propose four new polynomial multiplication algorithms in characteristic three fields and we show that they are more efficient than the current state-of-the-art methods. We first analyze the well-known algorithms such as the schoolbook method, Karatsuba 2-way and 3-way split methods, Bernstein...
Citation Formats
A. Doğanaksoy, F. SULAK, M. Uğuz, O. Seker, and Z. Akcengiz, “New Statistical Randomness Tests Based on Length of Runs,” MATHEMATICAL PROBLEMS IN ENGINEERING, pp. 0–0, 2015, Accessed: 00, 2020. [Online]. Available: