Güçlü Yer Değiştirme Kutuları Üretmek İçin Yeni Bir Yaklaşım

Yıl 2023, Cilt: 39 Sayı: 1, 70 - 78, 02.05.2023

Fırat Artuğer

Öz

Yer değiştirme kutusu (s-box), kriptografik yapılar için hayati öneme sahiptir. Çünkü bir simetrik şifreleme algoritmasında karıştırma olarak adlandırdığımız gereksinimi yerine getirmektedir. Bu yüzden geliştirilecek olan simetrik şifreleme algoritmasının başarımı önemli ölçüde s-box yapısına bağlı olacaktır. Bir s-box yapısı olabildiğince lineer bir yapıya sahip olmamalıdır. Yani bir s-box yapısının bakılması gereken en önemli kriteri yüksek lineer olmama değeridir. Lineer olmama değeri ne kadar yüksek olursa algoritmanın kırılması o kadar zor olacaktır. Bir s-box elde etmek için genellikle kaotik yöntemler kullanılmaktadır. Ancak bu şekilde elde edilen s-box yapılarında lineer olmama değeri düşüktür. Bu çalışmada özellikle bu şekilde üretilen s-box ‘ların lineer olmama değerini hızlı bir şekilde arttıran bir yöntem önerilmektedir. Bu yöntemde rastgele elde edilmiş bir s-box yapısında ilk değer sırasıyla diğer tüm elemanlarla yer değiştirilir. Bu şekilde s-box yapısının lineer olmama değeri artar veya eşit kalırsa s-box güncellenir. Bu şekilde sadece 255 iterasyon ile lineer olmama değeri 102.25 ‘den 107.5 ‘e kadar arttırılmıştır. Bir diğer s-box ‘da ise lineer olmama değeri 103.75 ‘den 107.25 ‘e çıkmıştır.

Anahtar Kelimeler

Yer değiştirme kutusu (s-box), lineer olmama, simetrik şifreleme, kaotik harita

Kaynakça

• Van Oorschot, P. C., Menezes, A. J., & Vanstone, S. A. (1996). Handbook of applied cryptography. CRC press.
• J. Daemen and V. Rijmen, ‘‘AES proposal: Rijndael,’’ in Proc. 1st Adv. Encryption Conf., CA, USA, 1998, pp. 1–45.
• Standard, D. E. (1999). Data encryption standard. Federal Information Processing Standards Publication, 112.
• Artuğer, F., & Özkaynak, F. (2020). A novel method for performance improvement of chaos-based substitution boxes. Symmetry, 12(4), 571.
• Artuğer, F., & Özkaynak, F. (2022). A method for generation of substitution box based on random selection. Egyptian Informatics Journal, 23(1), 127-135.
• Özkaynak, F., Çelik, V., & Özer, A. B. (2017). A new S-box construction method based on the fractionalorder chaotic Chen system. Signal, Image and Video Processing, 11(4), 659-664.
• Khan, M., Shah, T., & Gondal, M. A. (2013). An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dynamics, 73(3), 1795-1801.
• Özkaynak, F. (2020). On the effect of chaotic system in performance characteristics of chaos based s-box designs. Physica A: Statistical Mechanics and its Applications, 550, 124072.
• Lambić, D. (2020). A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design. Nonlinear Dynamics, 100(1), 699-711.
• Lambić, D. (2018). S-box design method based on improved one-dimensional discrete chaotic map. Journal of Information and Telecommunication, 2(2), 181-191.
• Tang, G., Liao, X., & Chen, Y. (2005). A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals, 23(2), 413-419.
• Tang, G., & Liao, X. (2005). A method for designing dynamical S-boxes based on discretized chaotic map. Chaos, solitons & fractals, 23(5), 1901-1909.
• Khan, M., Shah, T., Mahmood, H., Gondal, M. A., & Hussain, I. (2012). A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dynamics, 70(3), 2303-2311.
• Özkaynak, F. (2020). An analysis and generation toolbox for chaotic substitution boxes: A case study based on chaotic labyrinth rene thomas system. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 44(1), 89-98.
• Ye, T., & Zhimao, L. (2018). Chaotic S-box: Six-dimensional fractional Lorenz–Duffing chaotic system and O-shaped path scrambling. Nonlinear Dynamics, 94(3), 2115-2126.
• Çavuşoğlu, Ü., Zengin, A., Pehlivan, I., & Kaçar, S. (2017). A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear dynamics, 87(2), 1081-1094.
• Belazi, A., & Abd El-Latif, A. A. (2017). A simple yet efficient S-box method based on chaotic sine map. Optik, 130, 1438-1444.
• Hematpour, N., & Ahadpour, S. (2021). Execution examination of chaotic S-box dependent on improved PSO algorithm. Neural Computing and Applications, 33(10), 5111-5133.
• Tian, Y., & Lu, Z. (2017). Chaotic S-box: Intertwining logistic map and bacterial foraging optimization. Mathematical Problems in Engineering, 2017.
• Artuğer, F., & Özkaynak, F. (2022). SBOX-CGA: substitution box generator based on chaos and genetic algorithm. Neural Computing and Applications, 34(22), 20203-20211.
• Kang, M., & Wang, M. (2022). New Genetic Operators for Developing S-Boxes With Low Boomerang Uniformity. IEEE Access, 10, 10898-10906.
• Chen, G. (2008). A novel heuristic method for obtaining S-boxes. Chaos, Solitons & Fractals, 36(4), 1028- 1036.
• Farah, T., Rhouma, R., & Belghith, S. (2017). A novel method for designing S-box based on chaotic map and teaching–learning-based optimization. Nonlinear dynamics, 88(2), 1059-1074.
• Alhadawi, H. S., Lambić, D., Zolkipli, M. F., & Ahmad, M. (2020). Globalized firefly algorithm and chaos for designing substitution box. Journal of Information Security and Applications, 55, 102671.
• Ahmad, M., Bhatia, D., & Hassan, Y. (2015). A novel ant colony optimization based scheme for substitution box design. Procedia Computer Science, 57, 572-580.
• Zamli, K. Z., Din, F., & Alhadawi, H. S. (2023). Exploring a Q-learning-based chaotic naked mole rat algorithm for S-box construction and optimization. Neural Computing and Applications, 1-23.
• Khan, H., Hazzazi, M. M., Jamal, S. S., Hussain, I., & Khan, M. (2023). New color image encryption technique based on three-dimensional logistic map and Grey wolf optimization based generated substitution boxes. Multimedia Tools and Applications, 82(5), 6943-6964.
• Örs, S. B., Preneel, B., & Verbauwhede, I. (2007). Side-channel analysis attacks on hardware implementations of cryptographic algorithms. Wireless Security and Cryptography-Specifications and Implementations, 213-247.
• Arshad, B., Siddiqui, N., Hussain, Z., & Ehatisham-ul-Haq, M. (2022). A Novel Scheme for Designing Secure Substitution Boxes (S-Boxes) Based on Mobius Group and Finite Field. Wireless Personal Communications, 1-22.
• Malik, M. S. M., Ali, M. A., Khan, M. A., Ehatisham-Ul-Haq, M., Shah, S. N. M., Rehman, M., & Ahmad, W. (2020). Generation of highly nonlinear and dynamic AES substitution-boxes (S-boxes) using chaos-based rotational matrices. IEEE Access, 8, 35682-35695.
• Siddiqui, N., Yousaf, F., Murtaza, F., Ehatisham-ul-Haq, M., Ashraf, M. U., Alghamdi, A. M., & Alfakeeh, A. S. (2020). A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field. Plos one, 15(11), e0241890.
• Khan, M., & Shah, T. (2014). A novel image encryption technique based on Hénon chaotic map and S8 symmetric group. Neural Computing and Applications, 25(7), 1717-1722.
• Bakunina, E. V., & Dykyi, O. V. (2022). Synthesis method for S-boxes satisfying the criterion of correlation immunity of Boolean and 4-functions. Journal of Discrete Mathematical Sciences and Cryptography, 1-13.
• Sokolov, A. V., & Radush, V. V. (2022). A method for synthesis of S-boxes with good avalanche characteristics of component Boolean and quaternary functions. Journal of Discrete Mathematical Sciences and Cryptography, 1-12.
• Artuğer, F., & Özkaynak, F. (2021). An effective method to improve lineer olmama value of substitution boxes based on random selection. Information Sciences, 576, 577-588.
• Webster, A. F., & Tavares, S. E. (1985, August). On the design of S-boxes. In Conference on the theory and application of cryptographic techniques (pp. 523-534). Springer, Berlin, Heidelberg.
• Biham, E., & Shamir, A. (1991). Differential cryptanalysis of DES-like cryptosystems. Journal of CRYPTOLOGY, 4(1), 3-72.