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

Year 2023, , 242 - 251, 31.12.2023

Fırat Artuğer

https://doi.org/10.54365/adyumbd.1334213

Abstract

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.

Keywords

Substitution box (s-box), Chaos, Chaotic maps

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

Abstract

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.

Keywords

Yer değiştirme kutusu (s-box), Kaos, Kaotik haritalar

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