Use of Entropy Pools Obtained from Optimisation Based Random Number Generators in S-Box Generation and Performance Analysis of Image Encryption

Abstract

This study analyzes how optimization algorithms and random number generators jointly produce random numbers (the entropy pool) used to generate S-boxes for image encryption. As a result of running the Bat Algorithm (BA), Golden Sine Search Algorithm - 2 (GoldSA-2) and Particle Swarm Optimization (PSO) algorithms together with Linear Feedback Shift Register (LFSR) and Delayed Fibonacci Generators (LFG), initial configurations suitable for generator structures and successfully passing the NIST SP 800-22 test functions, which is our objective function, were determined. Random number sequences that pass 15/15 of the NIST tests accepted in the literature are transferred to the entropy pool. Chi-square and autocorrelation analyses of the random numbers taken from the entropy pool, which are other test methods, are evaluated, and the success of the random numbers obtained with successful results in the areas of S-boxing and image encryption applications is shown. The effectiveness of random numbers in practical applications is investigated by using S-box analysis and image encryption analysis metrics. The findings show that high-quality entropy pools, obtained from optimization-based random number generators, exhibit superior cryptographic properties compared to conventional methods in S-box generation and image encryption applications.

Keywords

• Optimization Algorithms
• Entropy Pool
• S-box
• Image Encryption

Optimizasyon Tabanlı Rastgele Sayı Üreteçlerinden Elde Edilen Entropi Havuzlarının S-Box Üretiminde Kullanımı ve Görüntü Şifreleme Performans Analizi

Abstract

Bu çalışma, optimizasyon algoritmalarının ve rastgele sayı üreteçlerinin birlikte görüntü şifreleme için S-kutuları oluşturmada kullanılan rastgele sayıları (entropi havuzu) nasıl ürettiğini analiz etmektedir. Yarasa Algoritması (BA), Altın Sinüs Arama Algoritması - 2 (GoldSA-2) ve Parçacık Sürü Optimizasyonu (PSO) algoritmalarının Doğrusal Geri Beslemeli Kaydırmalı Kaydedici (LFSR) ve Gecikmeli Fibonacci Üreteçleri (LFG) ile birlikte çalıştırılması sonucunda üreteç yapılarına uygun ve amaç fonksiyonumuz olan NIST SP 800-22 test fonksiyonlarını başarıyla geçen başlangıç konfigürasyonları belirlenmiştir. Literatürde kabul gören NIST testlerinin 15/15'inden geçen rastgele sayı dizileri entropi havuzuna aktarılmıştır. Entropi havuzundan alınan rastgele sayıların diğer test yöntemleri olan ki-kare ve otokorelasyon analizleri değerlendirilmiş, başarılı sonuçlar ile elde edilen rastgele sayıların S-kutusu üretimi ve görüntü şifreleme alanlarındaki başarısı gösterilmiştir. Rastgele sayıların pratik uygulamalardaki etkinliği S-kutusu analizi ve görüntü şifreleme analizi metrikleri kullanılarak araştırılmıştır. Elde edilen bulgular, optimizasyon tabanlı rastgele sayı üreteçlerinden elde edilen yüksek kaliteli entropi havuzlarının, S-kutusu üretimi ve görüntü şifreleme uygulamalarında geleneksel yöntemlere kıyasla daha üstün kriptografik özellikler sergilediğini göstermektedir.

Keywords

• Optimizasyon Algoritmaları
• Entropi Havuzu
• S-kutusu
• Görüntü Şifreleme

References

1. Robshaw M, Billet O. New Stream Cipher Designs. vol. 4986. Springer Berlin Heidelberg; 2008. https://doi.org/10.1007/978-3-540-68351-3.
2. Garipcan AM, Erdem E. Implementation and Performance Analysis of True Random Number Generator on FPGA Environment by Using Non-periodic Chaotic Signals Obtained from Chaotic Maps. Arab J Sci Eng 2019;44:9427–41. https://doi.org/10.1007/s13369-019-04027-x.
3. Garipcan AM, Erdem E. A TRNG using chaotic entropy pool as a post-processing technique: analysis, design and FPGA implementation. Analog Integr Circuits Signal Process 2020;103:391–410. https://doi.org/10.1007/s10470-020-01605-0.
4. Sheveleva AM, Belyaev SA. Development of the Software for Solving the Knapsack Problem by Solving the Traveling Salesman Problem. 2021 IEEE Conf. Russ. Young Res. Electr. Electron. Eng., IEEE; 2021, p. 652–6. https://doi.org/10.1109/ElConRus51938.2021.9396448.
5. Asif M, Baig R. Solving NP-complete problem using ACO algorithm. 2009 Int. Conf. Emerg. Technol., IEEE; 2009, p. 13–6. https://doi.org/10.1109/ICET.2009.5353209.
6. Eroz E, Tanyildizi E, Ozkaynak F. Determination of Suitable Configuration Parameters for Linear Feedback Shift Register using Binary Bat Optimization Algorithm. IEEE EUROCON 2021 - 19th Int. Conf. Smart Technol., IEEE; 2021, p. 348–51. https://doi.org/10.1109/EUROCON52738.2021.9535616.
7. Zhao M, Yuan Z, Li L, Chen X-B. A novel efficient S-box design algorithm based on a new chaotic map and permutation. Multimed Tools Appl 2024;83:64899–918. https://doi.org/10.1007/s11042-023-17720-9.
8. Podder D, Deb S, Banik D, Kar N, Sahu AK. Robust medical and color image cryptosystem using array index and chaotic S-box. Cluster Comput 2024;27:4321–46. https://doi.org/10.1007/s10586-024-04584-3.

9. Duong P-P, Nguyen HM, Dao B-A, Kieu-Do-Nguyen B, Tran T-H, Hoang T-T, et al. Construction of Robust Lightweight S-Boxes Using Enhanced Logistic and Enhanced Sine Maps. IEEE Access 2024;12:63976–94. https://doi.org/10.1109/ACCESS.2024.3396452.
10. Zhu H, Tong X, Wang Z, Ma J. A novel method of dynamic S-box design based on combined chaotic map and fitness function. Multimed Tools Appl 2020;79:12329–47. https://doi.org/10.1007/s11042-019-08478-0.
11. Khan M, Asghar Z. A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation. Neural Comput Appl 2018;29:993–9. https://doi.org/10.1007/s00521-016-2511-5.
12. Nasry H, Abdallah AA, Farhan AK, Ahmed HE, Sobky WIE. Multi Chaotic System to Generate Novel S-Box for Image Encryption. J Phys Conf Ser 2022;2304:12007. https://doi.org/10.1088/1742-6596/2304/1/012007.
13. Cassal-Quiroga BB, Campos-Cantón E. Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map. Math Probl Eng 2020;2020:1–12. https://doi.org/10.1155/2020/2702653.
14. Eroz E, Tanyildizi E, Ozkaynak F. COLFSR - A Hybrid Random Number Generator Based on Chaos Optimisation and Linear Feedback Shift Register. Elektron Ir Elektrotechnika 2025;31:30–8. https://doi.org/10.5755/j02.eie.38291.
15. Ozkaynak F. A Novel Random Number Generator Based on Fractional Order Chaotic Chua System. Elektron Ir Elektrotechnika 2020;26:52–7. https://doi.org/10.5755/j01.eie.26.1.25310.
16. Knuth DE. Art of Computer Programming, The, Volumes 1-3 Boxed Set (3rd Edition). 3rd ed. Addison-Wesley Professional; 1998.
17. Soto J, Rukhin A. Statistical Testing of Random Number Generators 1999.
18. Field AP. Discovering statistics using IBM SPSS statistics 2024:1110.
19. Özkaynak F, Yavuz S. Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn 2013;74:551–7. https://doi.org/10.1007/s11071-013-0987-4.