{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:19:22Z","timestamp":1760231962821,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T00:00:00Z","timestamp":1665532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100014538","name":"Lembaga Pengelola Dana Pendidikan (LPDP) through the Riset Inovatif Produktif (RISPRO) program","doi-asserted-by":"publisher","award":["PRJ- 7\/LPDP\/2020","99\/PKS\/WR III\/UI\/2020"],"award-info":[{"award-number":["PRJ- 7\/LPDP\/2020","99\/PKS\/WR III\/UI\/2020"]}],"id":[{"id":"10.13039\/501100014538","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was \u22122 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206.<\/jats:p>","DOI":"10.3390\/sym14102122","type":"journal-article","created":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T22:45:29Z","timestamp":1665614729000},"page":"2122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel Discrete-Time Chaos-Function-Based Random-Number Generator: Design and Variability Analysis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9915-6966","authenticated-orcid":false,"given":"Magfirawaty","family":"Magfirawaty","sequence":"first","affiliation":[{"name":"Cryptographic Hardware Engineering Programme, Politeknik Siber dan Sandi Negara, Bogor 16120, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6613-4114","authenticated-orcid":false,"given":"Andriani Adi","family":"Lestari","sequence":"additional","affiliation":[{"name":"Cryptographic Hardware Engineering Programme, Politeknik Siber dan Sandi Negara, Bogor 16120, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8049-7605","authenticated-orcid":false,"given":"Agus Reza Aristiadi","family":"Nurwa","sequence":"additional","affiliation":[{"name":"Cryptographic Hardware Engineering Programme, Politeknik Siber dan Sandi Negara, Bogor 16120, Indonesia"}]},{"given":"Suryadi","family":"MT","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0374-4465","authenticated-orcid":false,"given":"Kalamullah","family":"Ramli","sequence":"additional","affiliation":[{"name":"Department Electrical of Engineering, Universitas Indonesia, Depok 16424, Indonesia"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Menezes, A.J., Van Oorschot, P.C., and Vanstone, S.A. (2018). Handbook of Applied Cryptography, CRC Press.","DOI":"10.1201\/9781439821916"},{"key":"ref_2","unstructured":"Bruce, S. (1996). Applied Cryptography: Protocols, Algorithms, and Source Code in C, Wiley."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Booz-Allen and Hamilton Inc Mclean va. Technical Report.","DOI":"10.6028\/NIST.SP.800-22"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kocarev, L., and Lian, S. (2011). Chaos-Based Cryptography: Theory, Algorithms and Applications, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-20542-2"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ci\u00e7ek, I., Pusane, A.E., and D\u00fcndar, G. (2013, January 28\u201330). A novel dual entropy core true random number generator. Proceedings of the 2013 8th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey.","DOI":"10.1109\/ELECO.2013.6713856"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.vlsi.2013.06.003","article-title":"A novel design method for discrete time chaos based true random number generators","volume":"47","author":"Cicek","year":"2014","journal-title":"Integration"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pareschi, F., Setti, G., and Rovatti, R. (2006, January 19\u201321). A fast chaos-based true random number generator for cryptographic applications. Proceedings of the 2006 32nd European Solid-State Circuits Conference, Montreaux, Switzerland.","DOI":"10.1109\/ESSCIR.2006.307548"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1109\/TSP.2004.839924","article-title":"Embeddable ADC-based true random number generator for cryptographic applications exploiting nonlinear signal processing and chaos","volume":"53","author":"Callegari","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s10470-012-9893-9","article-title":"Discrete-time chaotic-map truly random number generators: Design, implementation, and variability analysis of the zigzag map","volume":"73","author":"Nejati","year":"2012","journal-title":"Analog Integr. Circuits Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Moysis, L., Volos, C., Jafari, S., Munoz-Pacheco, J.M., Kengne, J., Rajagopal, K., and Stouboulos, I. (2020). Modification of the logistic map using fuzzy numbers with application to pseudorandom number generation and image encryption. Entropy, 22.","DOI":"10.3390\/e22040474"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Moysis, L., Tutueva, A., Volos, C., Butusov, D., Munoz-Pacheco, J.M., and Nistazakis, H. (2020). A two-parameter modified logistic map and its application to random bit generation. Symmetry, 12.","DOI":"10.3390\/sym12050829"},{"key":"ref_12","unstructured":"Suryadi, M.T., and Ramli, K. (2017, January 18\u201320). Performance analysis of zigzag map and hash function to generate random number. Proceedings of the 2017 International Conference on Electrical Engineering and Informatics (ICELTICs), Banda Aceh, Indonesia."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.ijleo.2018.12.178","article-title":"An image encryption algorithm based on modified logistic chaotic map","volume":"181","author":"Han","year":"2019","journal-title":"Optik"},{"key":"ref_14","first-page":"608","article-title":"A low-cost low-power ring oscillator-based truly random number generator for encryption on smart cards","volume":"63","author":"Liu","year":"2016","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1007\/s11071-018-4403-y","article-title":"Chaotic behavior of logistic map in superior orbit and an improved chaos-based traffic control model","volume":"94","author":"Cao","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"150609","DOI":"10.1109\/ACCESS.2019.2947561","article-title":"Digital cosine chaotic map for cryptographic applications","volume":"7","author":"Alawida","year":"2019","journal-title":"IEEE Access"},{"key":"ref_17","first-page":"1533","article-title":"A chaos-based probabilistic block cipher for image encryption","volume":"34","author":"Dhall","year":"2018","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kod\u1ef3tek, F., and L\u00f3rencz, R. (2015, January 22\u201324). A design of ring oscillator based PUF on FPGA. Proceedings of the 2015 IEEE 18th International Symposium on Design and Diagnostics of Electronic Circuits & Systems, Belgrade, Serbia.","DOI":"10.1109\/DDECS.2015.21"},{"key":"ref_19","unstructured":"Lestari, A.A., Suryadi, M., and Ramli, K. (2018, January 2\u20134). Modified logistic maps for discrete time chaos based random number generator. Proceedings of the 2018 International Conference on Electrical Engineering and Computer Science (ICECOS), Pangkal Pinang, Indonesia."},{"key":"ref_20","first-page":"3","article-title":"13. various techniques used in connection with random digits","volume":"12","year":"1951","journal-title":"Appl. Math. Ser."},{"key":"ref_21","unstructured":"Dang, Q. (2022, September 16). Recommendation for Applications Using Approved Hash Algorithms, Available online: https:\/\/tsapps.nist.gov\/publication\/getpdf.cfm?pubid=911479."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"88997","DOI":"10.1109\/ACCESS.2021.3089913","article-title":"A New and Efficient Scheme for Improving the Digitized Chaotic Systems from Dynamical Degradation","volume":"9","author":"Merah","year":"2021","journal-title":"IEEE Access"},{"key":"ref_23","first-page":"329","article-title":"An integrated dual entropy core true random number generator","volume":"64","author":"Cicek","year":"2016","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_24","unstructured":"Jessa, M., and Jaworski, M. (2010, January 7\u201310). Randomness of a combined TRNG based on the ring oscillator sampling method. Proceedings of the ICSES 2010 International Conference on Signals and Electronic Circuits, Gliwice, Poland."},{"key":"ref_25","first-page":"441","article-title":"A pseudo random bit generator based on chaotic logistic map and its statistical testing","volume":"33","author":"Patidar","year":"2009","journal-title":"Informatica"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"773","DOI":"10.4236\/am.2015.65073","article-title":"Modified logistic maps for cryptographic application","volume":"6","author":"Borujeni","year":"2015","journal-title":"Appl. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1088\/0951-7715\/18\/3\/022","article-title":"Constructing an opposite map to a specified chaotic map","volume":"18","author":"Huang","year":"2005","journal-title":"Nonlinearity"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Beirami, A., Nejati, H., and Massoud, Y. (2008, January 10\u201313). A performance metric for discrete-time chaos-based truly random number generators. Proceedings of the 2008 51st Midwest Symposium on Circuits and Systems, Knoxville, TN, USA.","DOI":"10.1109\/MWSCAS.2008.4616754"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1142\/S0218127406015970","article-title":"Some basic cryptographic requirements for chaos-based cryptosystems","volume":"16","author":"Alvarez","year":"2006","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_30","first-page":"11","article-title":"IEEE standard 754 for binary floating-point arithmetic","volume":"754","author":"Kahan","year":"1996","journal-title":"Lect. Notes Status IEEE"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Irfan, M., Ali, A., Khan, M.A., Ehatisham-ul Haq, M., Mehmood Shah, S.N., Saboor, A., and Ahmad, W. (2020). Pseudorandom number generator (PRNG) design using hyper-chaotic modified robust logistic map (HC-MRLM). Electronics, 9.","DOI":"10.3390\/electronics9010104"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2373","DOI":"10.1007\/s11071-015-2488-0","article-title":"A pseudorandom number generator based on piecewise logistic map","volume":"83","author":"Wang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wang, L., and Cheng, H. (2019). Pseudo-random number generator based on logistic chaotic system. Entropy, 21.","DOI":"10.3390\/e21100960"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s11071-016-3051-3","article-title":"A novel pseudorandom number generator based on pseudorandomly enhanced logistic map","volume":"87","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3455","DOI":"10.1016\/j.cam.2011.02.006","article-title":"A novel dynamic model of pseudo random number generator","volume":"235","author":"Behnia","year":"2011","journal-title":"J. Comput. Appl. Math."},{"key":"ref_36","unstructured":"Lasota, A., and Mackey, M.C. (1998). Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, Springer Science & Business Media."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"062327","DOI":"10.1103\/PhysRevA.87.062327","article-title":"Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction","volume":"87","author":"Ma","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_39","unstructured":"Marsaglia, G. (2022, September 16). The Marsaglia Random Number CDROM Including the Diehard Battery of Tests of Randomness. Available online: https:\/\/web.archive.org\/web\/20160125103112\/http:\/stat.fsu.edu\/pub\/diehard\/."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1007\/s11071-017-3755-z","article-title":"Hardware implementation of pseudo-random number generators based on chaotic maps","volume":"90","year":"2017","journal-title":"Nonlinear Dyn."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:52:37Z","timestamp":1760143957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,12]]},"references-count":40,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14102122"],"URL":"https:\/\/doi.org\/10.3390\/sym14102122","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,10,12]]}}}