References
- Kolmogorov A.N., On tables of random numbers, Theoretical Computer Science, 207(2), 387-395, 1998.
- Kolmogorov A.N., Three approaches to the quantitative definition of information, Problems of Information Transmission, 1(1), 1-7, 1965.
- Chaitin G.J., On the simplicity and speed of programs for computing infinite sets of natural numbers, Journal of the ACM, 16(3), 407-422, 1969.
- Solomono R., A formal theory of inductive inference: Part I and Part II, Information and Control, 7(1) and (2), 1-22 and 224-254, 1964.
- Niederreiter H., Random Number Generation and Quasi-Monte Carlo Methods, Society for Industrial and Applied Mathematics (SIAM), USA, 1992.
- Mauduit C., Sárközy A., On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arithmetica, 82(4), 365-377, 1997.
- Weyl H., Üeber die Gleichverteilung von Zahlen mod. eins, Mathematische Annalen, 77, 313-352, 1916.
- Van Der Corput J.G., Verteilungsfunktionen (erste mitteilung), Proceedings of the Koninklijke Akademie van Wetenschappen te Amsterdam, 38, 813-821, 1935.
- Herendi T., Construction of uniformly distributed linear recurring sequences modulo powers of 2, Uniform Distribution Theory, 13(1), 109-129, 2018.
- Borel M.E., Les probabilités dénombrables et leurs applications arithmétiques, Rendiconti del Circolo Matematico di Palermo, 27, 247-271, 1909.
- Bruijn N.G., A combinatorial problem, Koninklijke Nederlandse Akademie v. Wetenschappen, 49, 758-764, 1946.
- Knuth D.E., The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison Wesley, 1981.
- Lehmer D.H., Mathematical methods in large-scale computing units, Proceedings of a Second Symposium on Large-Scale Digital Calculating, 26, 141-146, 1951.
- Lewis T.G., Payne W.H., Generalized Feedback Shift Register Pseudorandom Number Algorithm, Journal of the ACM, 20(3), 456-468, 1973.
- Kurita Y., Matsumoto M., Twisted GFSR generators, ACM Transactions on Modeling and Computer Simulation, 2(3), 179-194, 1992.
- Kurita Y., Matsumoto M., Twisted GFSR generators II. ACM Transactions on Modeling and Computer Simulation, 4(3), 245-466, 1994.
- Thomson W.E., A Modified Congruence Method of Generating Pseudo-random Numbers, The Computer Journal, 1(2), 83, 1958.
- Rotenberg A., A New Pseudo-Random Number Generator, Journal of the ACM, 7(1), 75-77, 1960.
- Matsumoto M., Nishimura T., Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions on Modeling and Computer Simulation, 8(1), 3-30, 1998.
- Panneton F., LEcuyer P., Matsumoto M., Improved long-period generators based on linear recurrences modulo 2, ACM Transactions on Mathematical Software, 32(1), 1-16, 2006.
- Wichmann B.A., Hill I.D., Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator, Journal of the Royal Statistical Society: Series C (Applied Statistics), 30(2), 188-190, 1982.
- Wichmann B.A., Hill I.D., Generating good pseudo-random numbers, Computational Statistics Data Analysis, 51(3), 1614-1622, 2006.
- Wikramaratna R.S., ACORN-A new method for generating sequences of uniformly distributed Pseudo-Random Numbers, Journal of Computational Physics, 83(1), 16-31, 1989.
- ONeill M.E., PCG: A family of simple fast space-efficient statistically good algorithms for random number generation, Harvey Mudd College, HMC-CS-2014-0905, 2014.
- Blum L., Blum M., Shub M., A Simple Unpredictable Pseudo-Random Number Generator, SIAM Journal on Computing, 15(2), 364-383, 1986.
- Eichenauer J., Lehn J., A non-linear congruential pseudo random number generator, Statistische Hefte, 27, 315-326, 1986.
- Neumann J.V., Various techniques used in connection with random digits, Applied Mathematics Series, Notes by G.E. Forsythe, in National Bureau of Standards, 12, 36-38, 1951.
- Padányi V., Herendi T., Generalized Middle-Square Method, Annales Mathematicae et Informaticae, 56, 95-108, 2022.
- Widynski B., Middle-Square weyl sequence RNG, arXiv:1704.00358 [cs.CR], 2022.
- Schneier B., Applied Cryptography: Second Edition: Protocols, Algorithms and Source Code in C (Cloth), John Wiley Sons, 1996.
- Marsaglia G., Xorshift RNGs, Journal of Statistical Software, 8(14), 1-6, 2003.
- Damgård I.B., On the randomness of legendre and jacobi sequences, Conference on the Theory and Application of Cryptography CRYPTO 1988: Advances in Cryptology CRYPTO 88, 163-172, Part of the Lecture Notes in Computer Science, 403, 163-172, 1990.
- FIPS-81. DES Modes of Operation. https://csrc.nist.gov/csrc/media/publications/fips/81/archive/1980-12-02/documents/fips81.pdf, 1980.
- Akopov N.Z., Martirosyan N.H., The optimal approach for Kolmogorov-Smirnov test calculation in high dimensional space, Mathematical Problems of Computer Science, 44, 138-144, 2021.
- Dieharder.https://webhome.phy.duke.edu/rgb/General/dieharder.php. Website.
- Lecuyer P., Simard R., TestU01: A C library for empirical testing of random number generators, ACM Transactions on Mathematical Software, 33(4), 1-40, 2007.
- National Institute of Standards and Technology. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications: NIST SP 800-822, 2012.
- Rukhin A.L., Soto J., Nechvatal J.R., Smid M.E., Barker E.B., Leigh S.D., Levenson M., Vangel M., Banks D.L., Heck-ert N.A., Dray J.F., Vo S.C., A statistical test suite for random and pseudorandom number generators for cryptographic applications, NIST Special Publication, 800-822, 2001.