Design and Evaluation a new Pseudorandom Number Generator based on Chaotic Maps

Document Type : Original Article

Authors

1 PhD student, Department of Mathematics, Faculty of Basic Sciences, Khwarazmi University, Tehran, Iran

2 Associate Professor Imam Hossein University , Tehran, Iran

Abstract

In computer science and cyber security, random numbers play a prominent and effective role in some applications such as authentication, secret key generation, game theory, and simulation. Considering the difficult challenges of generating true random numbers, generating pseudorandom numbers is suitable  and cost-effective solution. In cryptography schemes, high quality pseudo-random number generators are seriously needed to make password keys. The better the quality of the encryption keys, the stronger and more secure the encryption algorithm will be. It can be said that almost all cryptographic systems are highly dependent on generating high-quality random numbers. In this paper, a new generator for generating pseudorandom numbers is first designed by combining several chaotic maps using ⨁ and transition operators. Then, by performing statistical tests of correlation coefficient, goodness of fit, and NIST standard tests, and the evaluation criteria presented in [1], the appropriate quality of the proposed new generator is evaluated for cryptographic applications in terms of independence, data uniformity, and the degree of randomness of the generator output. Finally, it is compared with several other generators.

Keywords

Main Subjects


  • [1] Gaeini A., Mirghadri A., Jandaghi G., “A General Evaluation Pattern for Pseudo Random Number Generators”, Trends in Applied Sciences Research, 10 (5), 2015, pp 231-244.
  • [2] Padányi V., Herendi T., “A study on comparison of pseudorandom number generator”, International Journal of Mathematics and Computer in Engineering, 1(1) , 2023, pp 25 –
  • [3] Hasted J., “Pseudo-random generators under uniform assumptions”, In 22nd ACM Symposium on Theory of Computing, 1880.
  • [4] Michael Pidd, “Computer Simulation in Management Science”, 4th Edition, John Wiley & Sons, (1998).
  • [5] L'Ecuyer P., ''Uniform Random Number Generation, Annuls of Operations Research'', Vol. 23 (1994).
  • [6] GomezGutierrezJ.,  Ibeas A., ''Cryptanalysis of the Quadratic Generator'', Progress in Cryptology – INDOCRYPT, 2005, pp 118–129.
  • [7] Moysis L., Kafetzis I., Baptista S., Volos C., ''Chaotification of One-Dimensional Maps Based on Remainder Operator Addition'', Mathematics, 10, 2801, 2022.
  • [8] Matthews, R.A.J., “On the Derivation of a “Chaotic” Encryption Algorithm”. Cryptologia, Vol. 13, Issue 1, 1989, pp. 29-42.
    http://dx.doi.org/10.1080/0161-118991863745
  • [9] Habutsu H., Nishio, I. Sasase and S. Mori, “A Secret Key Cryptosystem by Iterating a Chaotic Map”. Advances in Cryptology, Proceedings of EuroCrypt91,Vol .547,pp.127-140,1991.
  • [10] Stojanovski T., Kocarev L., ''Chaos-based random number generators – part 1: practical realization'', IEEE Transactions on circuits and systems I: Fundamental Theory and applications, vol. 48 (2001) 281-288.
  • [11] Stojanovski T., Pihl J., Kocarev L., ''Chaos-based random number generators – part 2: Practical realization'', IEEE Transactions on circuits and systems I: Fundamental Theory and applications, vol. 48 (2001) 382-385.
  • [12] Kocarev L., and Jakimoski G., ''Pseudorandom bits generated by chaotic maps'', IEEE Transactions on circuits and systems I: Fundamental Theory and applications, 50 (2003) 123-126.
  • [13] Fu S. , Chen Z. Y., and Zhou Y. A., ''Chaos-based random number generators'', Computer research and development, 41 (2004) 749-754.
  • [14] Liu J., ''Design of chaotic random sequence and its application'', Computer Engineering, 31 (2005) 150-152.
  • [15] Wang Y., Shen H., Yan X., ''Design of a chaotic random number generator'', Chinese Journal of Semiconductors, 26 (2005) 2433-2439.
  • [16] Wang L., Wang F.P., Wang Z.J., ''Novel chaos based pseudorandom number generator'', Acta Physical Sinica, 55 (2006) 3964-3968.
  • [17] Ergun S., and Ozoguz S., ''Truly random number generators based on a non-autonomous chaotic oscillator'', AEU-International J. Electronics & Communications, 62 (2007) 235-242.
  • [18] Hu Y., Liao X., Wong K.W., and Zhou Q., ''A true random number generator based on mouse movement and chaotic cryptography'', Chaos solitons and fractals, 40 (2009) 2286-2293.
  • [19] Firat Artuger, Fatih Ozkaynak, “A new chaotic system and its practical applications in substitution box and random number generator”, Multimedia Tools and Applications, 04 April 2024.
  • [20] Wenbo Zhao, and Caochuan Ma, ''Modification of intertwining logestic map and anovel Pseudo-Random Number Generator'', Symmetry, Vol. 16, Issue 2, 31 January 2024, 169. https://doi.org/10.3390/sym16020169
  • [21] Moysis L., Tutueva A., Volos C., Butusov D., Munoz-Pacheco J., Nistazakis H., ''A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation'', 12 (2020) 829.
  • [22] Huang X., Liu L., Li X., Yu M., Wu Z., “A New Pseudorandom Bit Generator Based on Mixing Three-Dimensional Chen Chaotic System with a Chaotic Tactics”, 6567198, Complexity (2019).
  • [23] Adhikari S., Karforma S., ''A novel audio encryption method using Henon –Tent chaotic pseudo random number sequence'', 13(4) (2021) pp1463–1471.
  • [24] Rasika B. Naik and Udayprakash Singh, “A Review on Applications of Chaotic Maps in Pseudo-Random Number Generators and Encryption”, Annals of  Data Science, 18 January 2022.
  • [25] Gaeini A., Mirghadri A., Jandaghi G., “Design and analysis of a new efficient Pseudo Random Number Generators for Cryptography”, Ph.D Thesis, Imam Hussein University, 2014 (In Persian).
Volume 13, Issue 3 - Serial Number 51
Autumn
November 2025
Pages 61-73
  • Receive Date: 09 July 2025
  • Revise Date: 29 August 2025
  • Accept Date: 14 October 2025
  • Publish Date: 23 October 2025