Generation of S-Boxes Using Hippopotamus Optimization Algorithm and Logistic Chaotic Map

Abstract

Cryptographically strong substitution boxes (S-boxes) is a crucial issue in block cipher cryptographic design. In this paper, we propose the design of a new method to create 16x16 S-boxes by using the Hippopotamus Optimization Algorithm, or HOA and the Logistic Chaotic Map. We introduce a hybrid architecture of the HOA considering dynamic equilibrium among HOA's exploration and exploitation balance with the sensitivity and unpredictability of chaotic systems for this purpose. The chaotic sequences created by the Logistic Map are employed in the first stage to establish a candidate S-box population with diverse structures. Moving on in the optimization stage, the HOA automatically updates the S-box configuration with nonlinearity-based fitness functions. Experimental evaluations are performed against established cryptographic metrics. The results show that our proposed HOA-Logistic-based 16x16 S-boxes perform more satisfactorily than some of the chaotic, or metaheuristic models, when randomness, key sensitivity, and robustness are included. It is quite apparent that the non-linearity criterion value of 109.5 indicates that this method is quite competitive. The large key space obtained by using the Logistic map can be used to improve security against brute-force and statistical attacks. Taken together, the proposed implementation offers an effective and safe means of large-scale S-box generation as is applied today in symmetric cryptosystems.

Keywords

• Substitution box
• Logistic map
• Optimization
• Cryptography

Hippopotamus Optimizasyon Algoritması ve Logistic Kaotik Haritası Kullanılarak İkame Kutusu Üretilmesi

Öz

Kriptografik olarak güçlü ikame kutuları (S-kutuları), blok şifreli kriptografik tasarımda önemli bir konudur. Bu makalede, Hipopotam Optimizasyon Algoritması veya HOA ve Lojistik Kaotik Harita kullanılarak 16x16 S-kutuları oluşturmak için yeni bir yöntem tasarımı öneriyoruz. Bu amaçla, HOA'nın keşif ve sömürü dengesi ile kaotik sistemlerin duyarlılığı ve öngörülemezliği arasındaki dinamik dengeyi göz önünde bulunduran hibrit bir HOA mimarisi sunuyoruz. Lojistik Harita tarafından oluşturulan kaotik diziler, ilk aşamada çeşitli yapılara sahip bir aday S-kutusu popülasyonu oluşturmak için kullanılır. Optimizasyon aşamasında, HOA, S-kutu yapılandırmasını doğrusal olmayanlığa dayalı uygunluk fonksiyonlarıyla otomatik olarak günceller. Deneysel değerlendirmeler, yerleşik kriptografik metriklere göre gerçekleştirilir. Sonuçlar, önerdiğimiz HOA-Lojistik tabanlı 16x16 S-kutularının, rastgelelik, anahtar duyarlılığı ve sağlamlık dahil edildiğinde bazı kaotik veya metasezgisel modellerden daha iyi performans gösterdiğini göstermektedir. 109,5'lik doğrusal olmayanlık kriteri değerinin, bu yöntemin oldukça rekabetçi olduğunu gösterdiği oldukça açıktır. Lojistik haritası kullanılarak elde edilen geniş anahtar alanı, kaba kuvvet ve istatistiksel saldırılara karşı güvenliği artırmak için kullanılabilir. Önerilen uygulama, bir bütün olarak ele alındığında, günümüzde simetrik kripto sistemlerinde uygulandığı gibi, büyük ölçekli S-kutusu üretimi için etkili ve güvenli bir yol sunmaktadır.

Anahtar Kelimeler

• İkame kutusu
• Logistic haritası
• Optimization
• Kriptografi

Kaynakça

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