Linear random number generator with Collatz transformation function

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dc.citation.epage49
dc.citation.issue3
dc.citation.journalTitleКомп’ютерні системи проектування. Теорія і практика
dc.citation.spage41
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorВасилишин, Богдан
dc.contributor.authorКособуцький, Петро
dc.contributor.authorVasylyshyn, Bohdan
dc.contributor.authorKosobutskyy, Petro
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-12-16T08:41:07Z
dc.description.abstractУ роботі вперше побудовано та досліджено статистичну модель генератора псевдо- випадкових чисел (ГВЧ) із функцією перетворення Коллатца. Модель реалізовано в середовищі ста- тистичного програмування Python, а функцію отримано методом зворотного перетворення. Встанов- лено, що інтегральна функція ймовірностей набуває вигляду трансцендентного полінома квадратичної природи, в межах якого обґрунтовано діапазон значень ГВЧ.
dc.description.abstractFor the first time, a statistical model of a pseudo-random number generator (PRNG) with the Collatz transformation function is constructed and investigated in this paper. The PRNG is implemented in the Python statistical programming environment, and the function is obtained using the inverse transformation method. It is established that the probability integral function takes the form of a transcendental polynomial of quadratic nature, within which the range of PRNG values is justified.
dc.format.extent41-49
dc.format.pages9
dc.identifier.citationVasylyshyn B. Linear random number generator with Collatz transformation function / Bohdan Vasylyshyn, Petro Kosobutskyy // Computer Systems of Design. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 6. — No 3. — P. 41–49.
dc.identifier.citation2015Vasylyshyn B., Kosobutskyy P. Linear random number generator with Collatz transformation function // Computer Systems of Design. Theory and Practice, Lviv. 2024. Vol 6. No 3. P. 41–49.
dc.identifier.citationenAPAVasylyshyn, B., & Kosobutskyy, P. (2024). Linear random number generator with Collatz transformation function. Computer Systems of Design. Theory and Practice, 6(3), 41-49. Lviv Politechnic Publishing House..
dc.identifier.citationenCHICAGOVasylyshyn B., Kosobutskyy P. (2024) Linear random number generator with Collatz transformation function. Computer Systems of Design. Theory and Practice (Lviv), vol. 6, no 3, pp. 41-49.
dc.identifier.doihttps://doi.org/10.23939/cds2024.03.041
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/124100
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofКомп’ютерні системи проектування. Теорія і практика, 3 (6), 2024
dc.relation.ispartofComputer Systems of Design. Theory and Practice, 3 (6), 2024
dc.relation.references[1] Ballesteros, Dora, M., Peña, Jimmy, & Renza, Diego. (2018). A Novel Image Encryption Scheme Based on Collatz Conjecture. Entropy, 20(12), 901. https://doi.org/10.3390/e20120901
dc.relation.references[2] Isakov, O., & Voitusik, S. (2023). Comparative analysis of digital noise generated by addative Fobonacci generatos. Ukrainian Journal of Information Technology, 5(1), 67–76. https://doi.org/10.23939/ujit2023.01.067
dc.relation.references[3] NIST SP 800-22. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. https://csrc.nist.gov/publications/nistpubs//SP80022rev1a.pdf
dc.relation.references[4] Horbenko, I. D., Shapochka, N.V. ―Analysis of random bit generators according to ISO/IEC 18031 standard and recommendations for its application in Ukraine‖, International Symposium ―Issues of Computational Optimization‖. Katsiveli, 2009. Pp. 164–170.
dc.relation.references[5] Andrea Rock. Pseudorandom Number Generators for Cryptographic Applications. Diplomarbeit zur Erlangung des Magistergrades an der Naturwissenschaftlichen Fakultat der Paris-Lodron-Universitat Salzburg. Salzburg, 2005
dc.relation.references[6] Application Notes and Interpretation of the Scheme (AIS) 31. Functionality classes and evaluation methodology for physical random number generators. Certification body of the BSI in context of certification scheme. BSI, 2001
dc.relation.references[7] ISO/IEC 18031:2005(E). Information technology – Security techniques – Random bit generation
dc.relation.references[8] P. Kosobutskyy. The Collatz problem as a reverse problem on a graph tree formed from Q×2:n(Q=1,3,5,7,…) Jacobsthal-type numbers. arXiv:2306.14635v1
dc.relation.references[9] X. Henderson. Rapsody in Numbers. https://yozh.org/
dc.relation.references[10] Smith, J.K., & Johnson, L. (2020). ―A study on the implementation of linear random number generators using the Collatz transformation function‖. Proceedings of the IEEE International Conference on Computational Intelligence and Computing Research, 78–83.
dc.relation.referencesen[1] Ballesteros, Dora, M., Peña, Jimmy, & Renza, Diego. (2018). A Novel Image Encryption Scheme Based on Collatz Conjecture. Entropy, 20(12), 901. https://doi.org/10.3390/e20120901
dc.relation.referencesen[2] Isakov, O., & Voitusik, S. (2023). Comparative analysis of digital noise generated by addative Fobonacci generatos. Ukrainian Journal of Information Technology, 5(1), 67–76. https://doi.org/10.23939/ujit2023.01.067
dc.relation.referencesen[3] NIST SP 800-22. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. https://csrc.nist.gov/publications/nistpubs//SP80022rev1a.pdf
dc.relation.referencesen[4] Horbenko, I. D., Shapochka, N.V. ―Analysis of random bit generators according to ISO/IEC 18031 standard and recommendations for its application in Ukraine‖, International Symposium ―Issues of Computational Optimization‖. Katsiveli, 2009. Pp. 164–170.
dc.relation.referencesen[5] Andrea Rock. Pseudorandom Number Generators for Cryptographic Applications. Diplomarbeit zur Erlangung des Magistergrades an der Naturwissenschaftlichen Fakultat der Paris-Lodron-Universitat Salzburg. Salzburg, 2005
dc.relation.referencesen[6] Application Notes and Interpretation of the Scheme (AIS) 31. Functionality classes and evaluation methodology for physical random number generators. Certification body of the BSI in context of certification scheme. BSI, 2001
dc.relation.referencesen[7] ISO/IEC 18031:2005(E). Information technology – Security techniques – Random bit generation
dc.relation.referencesen[8] P. Kosobutskyy. The Collatz problem as a reverse problem on a graph tree formed from Q×2:n(Q=1,3,5,7,…) Jacobsthal-type numbers. arXiv:2306.14635v1
dc.relation.referencesen[9] X. Henderson. Rapsody in Numbers. https://yozh.org/
dc.relation.referencesen[10] Smith, J.K., & Johnson, L. (2020). ―A study on the implementation of linear random number generators using the Collatz transformation function‖. Proceedings of the IEEE International Conference on Computational Intelligence and Computing Research, 78–83.
dc.relation.urihttps://doi.org/10.3390/e20120901
dc.relation.urihttps://doi.org/10.23939/ujit2023.01.067
dc.relation.urihttps://csrc.nist.gov/publications/nistpubs//SP80022rev1a.pdf
dc.relation.urihttps://yozh.org/
dc.rights.holder© Національний університет „Львівська політехніка“, 2024
dc.rights.holder© Vasylyshyn B., Kosobutskyy P., 2024
dc.subjectгенератор випадкових чисел (ГВЧ)
dc.subjectлогістична модель Коллатца
dc.subjectстатистична мова програмування Python
dc.subjectмодель Якобсталя – Коллатца
dc.subjectнатуральні числа
dc.subjectгенератор на основі Коллатца
dc.subjectrandom number generator (RNG)
dc.subjectlogistic Collatz model
dc.subjectPython statistical programming language
dc.subjectJacobsthal-Collatz model
dc.subjectnatural numbers
dc.subjectThe Collatz-based generator
dc.titleLinear random number generator with Collatz transformation function
dc.title.alternativeЛінійний генератор випадкових чисел з функцією перетворення Коллатца
dc.typeArticle

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Комп'ютерні системи проектування теорія і практика. – 2024. – Том 6, № 3