Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications

Celal Erbay

doi:10.29130/dubited.1631332

EN TR

Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications

Abstract

Ensuring the security of multimedia data has become increasingly critical with the rapid expansion of digital applications. This study presents a security analysis of a chaotic system-based random number generator (RNG) designed for high-security multimedia encryption. The analyzed RNG is based on a ten-term chaotic system without equilibrium points and generates random bit sequences using the Runge-Kutta 4 algorithm. Although chaotic systems exhibit inherent unpredictability, the findings reveal significant security vulnerabilities. By employing the master-slave synchronization approach, the generated bit sequences exhibit deterministic behavior under specific conditions, making them susceptible to cryptanalytic attacks. The ability to predict both the next bit and the entire output stream undermines the RNG’s suitability for cryptographic applications such as image encryption and sound steganography. Simulation and numerical results confirm that attackers with partial knowledge of the system can reconstruct the RNG’s output. This study highlights the necessity of developing more robust chaotic RNGs with enhanced resistance to synchronization attacks, incorporating hybrid models and additional entropy sources to improve cryptographic security in multimedia applications.

Keywords

Security Analysis, Chaotic systems, random number generators

Multimedya Uygulamaları için On Terimli Kaotik Bir Sisteme Dayalı Rastgele Sayı Üretecinin Güvenlik Analizi

Abstract

Dijital uygulamaların hızla yaygınlaşmasıyla birlikte multimedya verilerinin güvenliğinin sağlanması giderek daha kritik hale gelmiştir. Bu çalışma, yüksek güvenlikli multimedya şifrelemesi için tasarlanmış kaotik sistem tabanlı bir rastgele sayı üretecinin (RNG) güvenlik analizini sunmaktadır. Analiz edilen RNG, denge noktaları olmayan on terimli kaotik bir sisteme dayanmaktadır ve Runge-Kutta 4 algoritmasını kullanarak rastgele bit dizileri üretmektedir. Kaotik sistemler doğal olarak öngörülemezlik gösterse de bulgular önemli güvenlik açıklarını ortaya koymaktadır. Ana-köle senkronizasyon yaklaşımının kullanılmasıyla, üretilen bit dizileri belirli koşullar altında deterministik davranış sergileyerek bunları kriptoanalitik saldırılara karşı hassas hale getirmektedir. Hem bir sonraki biti hem de tüm çıktı akışını tahmin etme yeteneği, RNG'nin görüntü şifreleme ve ses steganografisi gibi kriptografik uygulamalar için uygunluğunu zayıflatmaktadır. Simülasyon ve sayısal sonuçlar, sistem hakkında kısmi bilgiye sahip saldırganların RNG'nin çıktısını yeniden oluşturabileceğini doğrulamaktadır. Bu çalışma, multimedya uygulamalarında kriptografik güvenliği iyileştirmek için hibrit modeller ve ek entropi kaynakları içeren, senkronizasyon saldırılarına karşı geliştirilmiş dayanıklılığa sahip, daha sağlam kaotik RNG'lerin geliştirilmesinin gerekliliğini vurgulamaktadır.

Keywords

Güvenlik Analizi, Kaotik Sistemler, rastgele sayı üreteçleri

References

[1] H.S. Kwok, K. S. Tang Wallace, "A fast image encryption system based on chaotic maps with finite precision representation", Chaos Solitons and Fractals, vol. 3, no. 2, pp. 1518-1529, 2007.
[2] Rhouma Rhouma, Soumaya Meherzi, Safya Belghith, "OCML-based colour image encryption", Chaos Solitons and Fractals, vol. 40, pp. 309-318, 2009.
[3] Xiaojun Tong, Minggen Cui, "Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator", Signal Processing, vol. 89, pp. 480-491, 2009.
[4] C.K. Huang, H.H. Nien, "Multi chaotic systems based pixel shuffle for image encryption", Optics Communications, vol. 282, pp. 2123-2127, 2009.
[5] Haojiang Gao, Yisheng Zhang, Shuyun Liang, Dequn Li, "A new chaotic algorithm for image encryption", Chaos Solitons and Fractals, vol. 29, pp. 393-399, 2009.
[6] Min Long, Li Tan. A chaos-based data encryption algorithm for image/video. 2010 Second International Conference on MultiMedia and Information Technology. Kaifeng, Chia, no.2, pp.172-175, 2010.
[7] Guodong Ye, Kaixin Jiao, Chen Pan, and Xiaoling Huang, “An Effective Framework for Chaotic Image Encryption Based on 3D Logistic Map,” Security and Communication Networks, vol. 2018, 11 pages, 2018.
[8] Shuguo Yang, Shenghe Sun, “A video encryption method based on chaotic maps in DCT domain,” Progress in Natural Science, Volume 18, Issue 10, 2008, Pages 1299-1304.
[9] Zhenjun Tang, Ye Yang, Shijie Xu, Chunqiang Yu, and Xianquan Zhang, “Image Encryption with Double Spiral Scans and Chaotic Maps,” Security and Communication Networks, vol. 2019, Article ID 8694678, 15 pages, 2019.
[10] Guodong Ye, Image scrambling encryption algorithm of pixel bit based on chaos map, Pattern Recognition Letters, Volume 31, Issue 5, 2010, Pages 347-354.

[11] Yushu Zhang, Di Xiao, “Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform,” Optics and Lasers in Engineering, Volume 51, Issue 4, 2013, Pages 472-480.
[12] Ünal Çavuşoğlu, Sezgin Kaçar, Ihsan Pehlivan, Ahmet Zengin, Secure image encryption algorithm design using a novel chaos based S-Box, Chaos, Solitons & Fractals, Volume 95, 2017, Pages 92-101.
[13] Shujun Li, Xuan Zheng, Xuanqin Mou, Yuanlong Cai, "Chaotic encryption scheme for real-time digital video," Proc. SPIE 4666, Real-Time Imaging VI, (27 February 2002).
[14] H. Kezia and G. F. Sudha, “Encryption of digital video based on Lorenz Chaotic system,” in Proc. 16th Int. Conf. Advanced Computing and Communications (ADCOM 2008), 2008, pp. 40–45.
[15] H. Liu, A. Kadir, and Y. Li, “Audio encryption scheme by confusion and diffusion based on multi-scroll chaotic system and one-time keys,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 19, pp. 7431–7438, 2016.
[16] S. H. M. Kwok and E. Y. Lam, "FPGA-based High-speed True Random Number Generator for Cryptographic Applications," TENCON 2006 - 2006 IEEE Region 10 Conference, Hong Kong, 2006, pp. 1-4.
[17] C. S. Petrie and J. A. Connelly, "A noise-based IC random number generator for applications in cryptography," in IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 47, no. 5, pp. 615-621, May 2000.
[18] V. Bagini and M. Bucci, “A design of reliable true random number generator for cryptographic applications”, in Proc. Workshop Cryptographic Hardware and Embedded Systems (CHES'99), 1999, pp. 204-218.
[19] Ü. Güler and S. Ergün, “A high speed, fully digital IC random number generator,” AEU—Int. J. Electron. Commun., vol. 66, no. 2, pp. 143–149, Feb. 2012.
[20] S. Ergün, "Cryptanalysis of a random number generator based on a double scroll chaotic oscillator," International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS), 2016, pp. 1-4.
[21] Xiong Wang, Akif Akgul, Sezgin Kacar, and Viet-Thanh Pham, “Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium,” Complexity, vol. 2017.
[22] M. S. Baptista, "Cryptography with chaos," Physics Letters A, vol. 240, no. 1-2, pp. 50–54, 1998.
[23] G. Álvarez and S. Li, "Some basic cryptographic requirements for chaos-based cryptosystems," International Journal of Bifurcation and Chaos, vol. 16, no. 08, pp. 2129–2151, 2006.
[24] C. Li, S. Li, G. Alvarez, G. Chen, and K.-T. Lo, "Cryptanalysis of a chaotic block cipher with external key and its improved version," Chaos, Solitons & Fractals, vol. 37, no. 1, pp. 299–307, 2008.
[25] J.S. Armand Eyebe Fouda, J. Yves Effa, Samrat L. Sabat, Maaruf Ali, "A fast chaotic block cipher for image encryption," Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 3, pp. 578–588, 2014.
[26] S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, "A novel algorithm for image encryption based on mixture of chaotic maps," Chaos, Solitons & Fractals, vol. 35, no. 2, pp. 408–419, 2008.
[27] M. T. Gençoğlu, Ö. Karaduman, and F. Özkaynak, "Chaotic Real Number Generator with Quantum Wave Equation," Symmetry, vol. 17, no. 3, 2025.
[28] S. Behnia, A. Akhshani, H. Mahmodi, and A. Akhavan, "A Bias-Free Quantum Random Number Generation Using Photon Arrival Time Selectively," IEEE Photonics Journal, vol. 7, no. 2, pp. 1–8, 2015.
[29] Richard Taylor, "LOGISTIC MAPS AND SYNCHRONIZATION," Brigham Young University thesis, 2007.
[30] Teh-Lu Liao, Sheng-Hung Lin, "Adaptive control and synchronization of Lorenz systems," Journal of the Franklin Institute, vol. 336, no. 6, pp. 925–937, 1999.
[31] Behrouz Kharabian, Hossein Mirinejad, "Synchronization of Rossler chaotic systems via hybrid adaptive backstepping/sliding mode control,” Results in Control and Optimization, vol. 4, 100020, 2021.
[32] Guanghui Cheng, Dan Li, Yuangen Yao, Rong Gui, "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells,” Chaos, Solitons & Fractals, vol. 174, 113837, 2023.

Details

Primary Language

English

Subjects

Machine Learning (Other), Electronics, Sensors and Digital Hardware (Other)

Journal Section

Research Article

Authors

Celal Erbay ^*
0000-0001-8501-3908
Türkiye

Publication Date

July 31, 2025

Submission Date

February 2, 2025

Acceptance Date

April 17, 2025

Published in Issue

Year 2025 Volume: 13 Number: 3

DOI

https://doi.org/10.29130/dubited.1631332

IZ

https://izlik.org/JA93BA62GM

APA

Erbay, C. (2025). Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications. Duzce University Journal of Science and Technology, 13(3), 1098-1111. https://doi.org/10.29130/dubited.1631332

AMA

1.Erbay C. Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications. DUBİTED. 2025;13(3):1098-1111. doi:10.29130/dubited.1631332

Chicago

Erbay, Celal. 2025. “Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications”. Duzce University Journal of Science and Technology 13 (3): 1098-1111. https://doi.org/10.29130/dubited.1631332.

EndNote

Erbay C (July 1, 2025) Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications. Duzce University Journal of Science and Technology 13 3 1098–1111.

IEEE

[1]C. Erbay, “Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications”, DUBİTED, vol. 13, no. 3, pp. 1098–1111, July 2025, doi: 10.29130/dubited.1631332.

ISNAD

Erbay, Celal. “Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications”. Duzce University Journal of Science and Technology 13/3 (July 1, 2025): 1098-1111. https://doi.org/10.29130/dubited.1631332.

JAMA

1.Erbay C. Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications. DUBİTED. 2025;13:1098–1111.

MLA

Erbay, Celal. “Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications”. Duzce University Journal of Science and Technology, vol. 13, no. 3, July 2025, pp. 1098-11, doi:10.29130/dubited.1631332.

Vancouver

1.Celal Erbay. Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications. DUBİTED. 2025 Jul. 1;13(3):1098-111. doi:10.29130/dubited.1631332

Security Analysis of a Random Number Generator Based on a Ten-Term Chaotic System for Multimedia Applications

Abstract

Keywords

Multimedya Uygulamaları için On Terimli Kaotik Bir Sisteme Dayalı Rastgele Sayı Üretecinin Güvenlik Analizi

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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