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A New S-box Generation Algorithm Based on Selective Chaotic Permutations for Cryptographic Structures

Yıl 2023, Cilt: 10 Sayı: 21, 242 - 251, 31.12.2023
https://doi.org/10.54365/adyumbd.1334213

Öz

Cryptography aims to design algorithms for the protection of data transmitted over unsecured networks. These algorithms encrypt the data and render it incomprehensible even if it is intercepted by third parties. S-box satisfies one of the basic requirements in the algorithm, called confusion. An s-box structure with a high nonlinearity value greatly increases the security against various attacks. Therefore, s-box is of vital importance in an encryption algorithm. When we look at the literature, chaos-based s-box structures are frequently used. However, the non-linearity value of s-boxes produced with chaos is low. In this article, a new algorithm is proposed to overcome this problem In the proposed method, an s-box is first generated with the help of any chaotic map. Then, in this s-box, the nonlinearity value is checked by changing the location of the two selected elements with the same chaotic map. When this value increases, the s-box is updated. In this way, an s-box with a nonlinearity value of 107.5 was produced after only 100 iterations. This value surpasses many studies in the literature.

Kaynakça

  • Van Oorschot, P. C., Menezes, A. J., Vanstone, S. A. Handbook of applied cryptography. CRC press, 1996.
  • J. Daemen and V. Rijmen, AES proposal: Rijndael, in Proc. 1st Adv. Encryption Conf., CA, USA, pp. 1–45, 1998.
  • Standard, D. E. Data encryption standard. Federal Information Processing Standards Publication, 112, 1999.
  • Artuğer, F., Özkaynak, F. SBOX-CGA: substitution box generator based on chaos and genetic algorithm. Neural Computing and Applications, 1-9, 2022.
  • Artuğer, F., Özkaynak, F. An effective method to improve lineer olmama değer of substitution boxes based on random selection. Information Sciences, 576, 577-588, 2021.
  • Ahmad, M., Khaja, I. A., Baz, A., Alhakami, H. Alhakami, W. Particle swarm optimization based highly nonlinear substitution-boxes generation for security applications. IEEE Access, 8, 116132-116147, 2020.
  • Alhadawi, H. S., Lambić, D., Zolkipli, M. F., Ahmad, M. Globalized firefly algorithm and chaos for designing substitution box. Journal of Information Security and Applications, 55, 102671, 2020.
  • Ahmad, M., Al-Solami, E. Evolving dynamic S-boxes using fractional-order hopfield neural network based scheme. Entropy, 22(7), 717, 2020.
  • Alzaidi, A. A., Ahmad, M., Ahmed, H. S., Solami, E. A. Sine-cosine optimization-based bijective substitution-boxes construction using enhanced dynamics of chaotic map. Complexity, 2018, 2018.
  • Farah, T., Rhouma, R., Belghith, S. A novel method for designing S-box based on chaotic map and teaching–learning-based optimization. Nonlinear dynamics, 88(2), 1059-1074, 2017.
  • Tian, Y., Lu, Z. Chaotic S-box: Intertwining logistic map and bacterial foraging optimization. Mathematical Problems in Engineering, 2017, 2017.
  • Ahmad, M., Bhatia, D., Hassan, Y. A novel ant colony optimization based scheme for substitution box design. Procedia Computer Science, 57, 572-580, 2015.
  • Chen, G. A novel heuristic method for obtaining S-boxes. Chaos, Solitons & Fractals, 36(4), 1028-1036, 2008.
  • Zamli, K. Z., Kader, A., Din, F., Alhadawi, H. S. Selective chaotic maps Tiki-Taka algorithm for the S-box generation and optimization. Neural Computing and Applications, 1-18, 2021.
  • Zamli, K. Z. Optimizing S-box Generation based on the Adaptive Agent Heroes and Cowards Algorithm. Expert Systems with Applications, 115305, 2021.
  • Alhadawi, H. S., Majid, M. A., Lambić, D., Ahmad, M. A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm. Multimedia Tools and Applications, 80(5), 7333-7350, 2021.
  • Wei, Y., Pasalic, E., Zhang, F., Hodžić, S. Efficient probabilistic algorithm for estimating the algebraic properties of Boolean functions for large n. Information Sciences, 402, 91-104, 2017.
  • Örs, S. B., Preneel, B., Verbauwhede, I. Side-channel analysis attacks on hardware implementations of cryptographic algorithms. Wireless Security and Cryptography-Specifications and Implementations, 213-247, 2007.
  • Hussain, I. True-chaotic substitution box based on Boolean functions. The European Physical Journal Plus, 135(8), 1-17, 2020.
  • Malik, M. S. M., Ali, M. A., Khan, M. A., Ehatisham-Ul-Haq, M., Shah, S. N. M., Rehman, M., Ahmad, W. Generation of highly nonlinear and dynamic AES substitution-boxes (S-boxes) using chaos-based rotational matrices. IEEE Access, 8, 35682-35695, 2020.
  • Arshad, B., Siddiqui, N., Hussain, Z., Ehatisham-ul-Haq, M. A Novel Scheme for Designing Secure Substitution Boxes (S-Boxes) Based on Mobius Group and Finite Field. Wireless Personal Communications, 1-22, 2022.
  • Razaq, A., Ullah, A., Alolaiyan, H., Yousaf, A. A novel group theoretic and graphical approach for designing cryptographically strong nonlinear components of block ciphers. Wireless Personal Communications, 116(4), 3165-3190, 2021.
  • Ahmad, M., Al-Solami, E. Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation. Complexity, 2020.
  • Khan, M., Shah, T. A novel image encryption technique based on Hénon chaotic map and S8 symmetric group. Neural Computing and Applications, 25(7), 1717-1722, 2014.
  • Siddiqui, N., Yousaf, F., Murtaza, F., Ehatisham-ul-Haq, M., Ashraf, M. U., Alghamdi, A. M., Alfakeeh, A. S. 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, 2020.
  • Razaq, A., Ahmad, M., Yousaf, A., Alawida, M., Ullah, A., Shuaib, U. A group theoretic construction of large number of AES-like substitution-boxes. Wireless Personal Communications, 122(3), 2057-2080, 2022.
  • Artuğer, F., Özkaynak, F. A novel method for performance improvement of chaos-based substitution boxes. Symmetry, 12(4), 571, 2020.
  • Artuğer, F., Özkaynak, F. A method for generation of substitution box based on random selection. Egyptian Informatics Journal, 23(1), 127-135, 2022.
  • Tang, G., Liao, X. A method for designing dynamical S-boxes based on discretized chaotic map. Chaos, solitons & fractals, 23(5), 1901-1909, 2005.
  • Tang, G., Liao, X., Chen, Y. A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals, 23(2), 413-419, 2005.
  • Lambić, D. S-box design method based on improved one-dimensional discrete chaotic map. Journal of Information and Telecommunication, 2(2), 181-191, 2018.
  • Lambić, D. 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, 2020.
  • Özkaynak, F. 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, 2020.
  • Belazi, A., Abd El-Latif, A. A. A simple yet efficient S-box method based on chaotic sine map. Optik, 130, 1438-1444, 2017.
  • Ye, T., Zhimao, L. Chaotic S-box: Six-dimensional fractional Lorenz–Duffing chaotic system and O-shaped path scrambling. Nonlinear Dynamics, 94(3), 2115-2126, 2018.
  • Özkaynak, F. On the effect of chaotic system in performance characteristics of chaos based s-box designs. Physica A: Statistical Mechanics and its Applications, 550, 124072, 2020.
  • Khan, M., Shah, T., Gondal, M. A. An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dynamics, 73(3), 1795-1801, 2013.
  • Çavuşoğlu, Ü., Zengin, A., Pehlivan, I., Kaçar, S. A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear dynamics, 87(2), 1081-1094, 2017.
  • Liu, G. Designing S-box based on 4D-4wing hyperchaotic system. 3D Research, 8(1), 1-9, 2017.
  • Özkaynak, F., Özer, A. B. A method for designing strong S-Boxes based on chaotic Lorenz system. Physics Letters A, 374(36), 3733-3738, 2010.
  • Khan, M., Shah, T. An efficient construction of substitution box with fractional chaotic system. Signal, Image and Video Processing, 9(6), 1335-1338, 2015.
  • Özkaynak, F., Çelik, V., Özer, A. B. A new S-box construction method based on the fractional-order chaotic Chen system. Signal, Image and Video Processing, 11(4), 659-664, 2017.
  • Tanyildizi, E., Özkaynak, F. A new chaotic S-box generation method using parameter optimization of one dimensional chaotic maps. IEEE Access, 7, 117829-117838, 2019.
  • Biham, E., Shamir, ADifferential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 4(1), 3-72, 1991.
  • Webster, A. F., Tavares, S. E. On the design of S-boxes. In Conference on the theory and application of cryptographic techniques (pp. 523-534). Springer, Berlin, Heidelberg, 1985.

Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması

Yıl 2023, Cilt: 10 Sayı: 21, 242 - 251, 31.12.2023
https://doi.org/10.54365/adyumbd.1334213

Öz

Kriptografi, güvenli olmayan ağlar üzerinden iletilen verilerin korunması için algoritmalar tasarlamayı amaçlamaktadır. Bu algoritmalar, verileri şifreler ve üçüncü kişiler tarafından ele geçirilse bile, veriyi anlaşılmaz hale getirir. S-box, algoritmada karıştırma adı verilen temel gereksinimlerden birini sağlamaktadır. Lineer olmama değeri yüksek bir s-box yapısı, çeşitli saldırılarına karşı güvenliği oldukça arttırmaktadır. Bu nedenle, bir şifreleme algoritmasında s-box oldukça hayati bir önem taşımaktadır. Literatüre bakıldığında kaos tabanlı s-box yapıları sıklıkla kullanılmaktadır. Ancak kaos ile üretilen s-box ‘ların lineer olmama değeri düşüktür. Bu makalede, bu problemin üstesinden gelmek için yeni bir algoritma önerilmiştir. Önerilen yöntemde öncelikle herhangi bir kaotik harita yardımıyla bir s-box üretilir. Daha sonra bu s-box ‘da yine aynı kaotik harita ile seçilmiş iki elemanın yeri değiştirilerek lineer olmama değeri kontrol edilir. Bu değer arttığında s-box güncellenir. Bu şekilde sadece 100 yineleme sonucunda lineer olmama değeri 107.5 olan bir s-box üretilmiştir. Bu değer literatürdeki birçok çalışmayı geride bırakmaktadır.

Kaynakça

  • Van Oorschot, P. C., Menezes, A. J., Vanstone, S. A. Handbook of applied cryptography. CRC press, 1996.
  • J. Daemen and V. Rijmen, AES proposal: Rijndael, in Proc. 1st Adv. Encryption Conf., CA, USA, pp. 1–45, 1998.
  • Standard, D. E. Data encryption standard. Federal Information Processing Standards Publication, 112, 1999.
  • Artuğer, F., Özkaynak, F. SBOX-CGA: substitution box generator based on chaos and genetic algorithm. Neural Computing and Applications, 1-9, 2022.
  • Artuğer, F., Özkaynak, F. An effective method to improve lineer olmama değer of substitution boxes based on random selection. Information Sciences, 576, 577-588, 2021.
  • Ahmad, M., Khaja, I. A., Baz, A., Alhakami, H. Alhakami, W. Particle swarm optimization based highly nonlinear substitution-boxes generation for security applications. IEEE Access, 8, 116132-116147, 2020.
  • Alhadawi, H. S., Lambić, D., Zolkipli, M. F., Ahmad, M. Globalized firefly algorithm and chaos for designing substitution box. Journal of Information Security and Applications, 55, 102671, 2020.
  • Ahmad, M., Al-Solami, E. Evolving dynamic S-boxes using fractional-order hopfield neural network based scheme. Entropy, 22(7), 717, 2020.
  • Alzaidi, A. A., Ahmad, M., Ahmed, H. S., Solami, E. A. Sine-cosine optimization-based bijective substitution-boxes construction using enhanced dynamics of chaotic map. Complexity, 2018, 2018.
  • Farah, T., Rhouma, R., Belghith, S. A novel method for designing S-box based on chaotic map and teaching–learning-based optimization. Nonlinear dynamics, 88(2), 1059-1074, 2017.
  • Tian, Y., Lu, Z. Chaotic S-box: Intertwining logistic map and bacterial foraging optimization. Mathematical Problems in Engineering, 2017, 2017.
  • Ahmad, M., Bhatia, D., Hassan, Y. A novel ant colony optimization based scheme for substitution box design. Procedia Computer Science, 57, 572-580, 2015.
  • Chen, G. A novel heuristic method for obtaining S-boxes. Chaos, Solitons & Fractals, 36(4), 1028-1036, 2008.
  • Zamli, K. Z., Kader, A., Din, F., Alhadawi, H. S. Selective chaotic maps Tiki-Taka algorithm for the S-box generation and optimization. Neural Computing and Applications, 1-18, 2021.
  • Zamli, K. Z. Optimizing S-box Generation based on the Adaptive Agent Heroes and Cowards Algorithm. Expert Systems with Applications, 115305, 2021.
  • Alhadawi, H. S., Majid, M. A., Lambić, D., Ahmad, M. A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm. Multimedia Tools and Applications, 80(5), 7333-7350, 2021.
  • Wei, Y., Pasalic, E., Zhang, F., Hodžić, S. Efficient probabilistic algorithm for estimating the algebraic properties of Boolean functions for large n. Information Sciences, 402, 91-104, 2017.
  • Örs, S. B., Preneel, B., Verbauwhede, I. Side-channel analysis attacks on hardware implementations of cryptographic algorithms. Wireless Security and Cryptography-Specifications and Implementations, 213-247, 2007.
  • Hussain, I. True-chaotic substitution box based on Boolean functions. The European Physical Journal Plus, 135(8), 1-17, 2020.
  • Malik, M. S. M., Ali, M. A., Khan, M. A., Ehatisham-Ul-Haq, M., Shah, S. N. M., Rehman, M., Ahmad, W. Generation of highly nonlinear and dynamic AES substitution-boxes (S-boxes) using chaos-based rotational matrices. IEEE Access, 8, 35682-35695, 2020.
  • Arshad, B., Siddiqui, N., Hussain, Z., Ehatisham-ul-Haq, M. A Novel Scheme for Designing Secure Substitution Boxes (S-Boxes) Based on Mobius Group and Finite Field. Wireless Personal Communications, 1-22, 2022.
  • Razaq, A., Ullah, A., Alolaiyan, H., Yousaf, A. A novel group theoretic and graphical approach for designing cryptographically strong nonlinear components of block ciphers. Wireless Personal Communications, 116(4), 3165-3190, 2021.
  • Ahmad, M., Al-Solami, E. Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation. Complexity, 2020.
  • Khan, M., Shah, T. A novel image encryption technique based on Hénon chaotic map and S8 symmetric group. Neural Computing and Applications, 25(7), 1717-1722, 2014.
  • Siddiqui, N., Yousaf, F., Murtaza, F., Ehatisham-ul-Haq, M., Ashraf, M. U., Alghamdi, A. M., Alfakeeh, A. S. 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, 2020.
  • Razaq, A., Ahmad, M., Yousaf, A., Alawida, M., Ullah, A., Shuaib, U. A group theoretic construction of large number of AES-like substitution-boxes. Wireless Personal Communications, 122(3), 2057-2080, 2022.
  • Artuğer, F., Özkaynak, F. A novel method for performance improvement of chaos-based substitution boxes. Symmetry, 12(4), 571, 2020.
  • Artuğer, F., Özkaynak, F. A method for generation of substitution box based on random selection. Egyptian Informatics Journal, 23(1), 127-135, 2022.
  • Tang, G., Liao, X. A method for designing dynamical S-boxes based on discretized chaotic map. Chaos, solitons & fractals, 23(5), 1901-1909, 2005.
  • Tang, G., Liao, X., Chen, Y. A novel method for designing S-boxes based on chaotic maps. Chaos, Solitons & Fractals, 23(2), 413-419, 2005.
  • Lambić, D. S-box design method based on improved one-dimensional discrete chaotic map. Journal of Information and Telecommunication, 2(2), 181-191, 2018.
  • Lambić, D. 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, 2020.
  • Özkaynak, F. 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, 2020.
  • Belazi, A., Abd El-Latif, A. A. A simple yet efficient S-box method based on chaotic sine map. Optik, 130, 1438-1444, 2017.
  • Ye, T., Zhimao, L. Chaotic S-box: Six-dimensional fractional Lorenz–Duffing chaotic system and O-shaped path scrambling. Nonlinear Dynamics, 94(3), 2115-2126, 2018.
  • Özkaynak, F. On the effect of chaotic system in performance characteristics of chaos based s-box designs. Physica A: Statistical Mechanics and its Applications, 550, 124072, 2020.
  • Khan, M., Shah, T., Gondal, M. A. An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dynamics, 73(3), 1795-1801, 2013.
  • Çavuşoğlu, Ü., Zengin, A., Pehlivan, I., Kaçar, S. A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear dynamics, 87(2), 1081-1094, 2017.
  • Liu, G. Designing S-box based on 4D-4wing hyperchaotic system. 3D Research, 8(1), 1-9, 2017.
  • Özkaynak, F., Özer, A. B. A method for designing strong S-Boxes based on chaotic Lorenz system. Physics Letters A, 374(36), 3733-3738, 2010.
  • Khan, M., Shah, T. An efficient construction of substitution box with fractional chaotic system. Signal, Image and Video Processing, 9(6), 1335-1338, 2015.
  • Özkaynak, F., Çelik, V., Özer, A. B. A new S-box construction method based on the fractional-order chaotic Chen system. Signal, Image and Video Processing, 11(4), 659-664, 2017.
  • Tanyildizi, E., Özkaynak, F. A new chaotic S-box generation method using parameter optimization of one dimensional chaotic maps. IEEE Access, 7, 117829-117838, 2019.
  • Biham, E., Shamir, ADifferential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 4(1), 3-72, 1991.
  • Webster, A. F., Tavares, S. E. On the design of S-boxes. In Conference on the theory and application of cryptographic techniques (pp. 523-534). Springer, Berlin, Heidelberg, 1985.
Toplam 45 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Bilgi Güvenliği Yönetimi
Bölüm Makaleler
Yazarlar

Fırat Artuğer 0000-0002-4096-0458

Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 28 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 10 Sayı: 21

Kaynak Göster

APA Artuğer, F. (2023). Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, 10(21), 242-251. https://doi.org/10.54365/adyumbd.1334213
AMA Artuğer F. Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. Aralık 2023;10(21):242-251. doi:10.54365/adyumbd.1334213
Chicago Artuğer, Fırat. “Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni Bir S-Box Üretme Algoritması”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 10, sy. 21 (Aralık 2023): 242-51. https://doi.org/10.54365/adyumbd.1334213.
EndNote Artuğer F (01 Aralık 2023) Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 10 21 242–251.
IEEE F. Artuğer, “Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması”, Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 10, sy. 21, ss. 242–251, 2023, doi: 10.54365/adyumbd.1334213.
ISNAD Artuğer, Fırat. “Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni Bir S-Box Üretme Algoritması”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 10/21 (Aralık 2023), 242-251. https://doi.org/10.54365/adyumbd.1334213.
JAMA Artuğer F. Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2023;10:242–251.
MLA Artuğer, Fırat. “Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni Bir S-Box Üretme Algoritması”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 10, sy. 21, 2023, ss. 242-51, doi:10.54365/adyumbd.1334213.
Vancouver Artuğer F. Kriptografik Yapılar için Seçmeli Kaotik Permütasyonlar Tabanlı Yeni bir S-box Üretme Algoritması. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2023;10(21):242-51.