Optimizing Nonlinearity Value of Substitution Boxes

Öz

One of the most important requirements in encryption algorithms is called confusion. For this reason, the data to be encrypted must be effectively mixed. Substitution box (s-box) is one of the most important structures that meet this requirement. The higher the nonlinearity value, which is one of the most important features of this structure, the healthier the mixing will be. Many techniques are used to obtain substitution boxes. It is the most used optimization technique among these techniques. In this technique, an s-box is obtained initially, usually with the help of chaos. The positions of the elements are then changed using an optimization technique. The nonlinearity criterion is used as the fitness value. When the nonlinearity value increases after new positioning, the s-box structure is updated. In this study, first, explains how the nonlinearity value is optimized in s-box structures. Then an s-box is optimized using the sine cosine algorithm. The nonlinearity value of the obtained s-box structure was observed to be 108 at the end of 500 iterations. Other performance criteria of an s-box structure are also described.

Anahtar Kelimeler

• Substitution box (s-box)
• Chaos
• Nonlinearity
• Optimization

İkame Kutularının Lineer Olmama Değerini Optimize Etme

Öz

Şifreleme algoritmalarında en önemli gereksinimlerden bir tanesi karıştırma olarak adlandırılmaktadır. Bu nedenle şifrelenecek verinin etkin bir şekilde karıştırılması gerekmektedir. İkame kutusu (s-box), bu gereksinimi sağlayan en önemli yapılardan bir tanesidir. Bu yapının en önemli özelliklerinden biri olan lineer olmama değeri ne kadar yüksek olursa karıştırmayı o kadar sağlıklı bir şekilde yerine getirecektir. İkame kutularının elde edilmesinde birçok teknik kullanılmaktadır. Bu tekniklerden en çok kullanılan, optimizasyon tekniğidir. Bu teknikte, başlangıçta genellikle kaos yardımıyla bir s-box elde edilir. Daha sonra bir optimizasyon tekniği kullanılarak elemanların konumları değiştirilir. Uygunluk değeri olarak lineer olmama kriteri kullanılır. Yeni konumlandırmalardan sonra lineer olmama değeri arttığında s-box yapısı güncellenmektedir. Bu çalışmada öncelikle s-box yapılarında lineer olmama değerinin nasıl optimize edildiği açıklanmıştır. Daha sonra sinüs kosinüs algoritması kullanılarak bir s-box optimize edilmiştir. Elde edilen s-box yapısının, 500 iterasyon sonunda lineer olmama değeri 108 olarak gözlemlenmiştir. Ayrıca bir s-box yapısının diğer performans kriterleri de açıklanmıştır.

Anahtar Kelimeler

• İkame kutusu (s-box)
• Kaos
• Lineer olmama
• Optimizasyon

Kaynakça

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