A novel method to generate key-dependent s-boxes with identical algebraic properties
Ahmad Yousef Al-Dweik, Iqtadar Hussain, Moutaz Saleh, M. T. Mustafa Β· Journal of Information Security and Applications Β· 2021
The s-box plays the vital role of creating confusion between the ciphertext and secret key in any cryptosystem , and is the only nonlinear component in many block ciphers . Dynamic s-boxes, as compared to static, improve entropy of the system, hence leading to better resistance against linear and differential attacks. It was shown in Easttom (2018) that while incorporating dynamic s-boxes in cryptosystems is sufficiently secure, they do not keep non-linearity invariant. This work provides an algorithmic scheme to generate key-dependent dynamic π Γ π clone s-boxes having the same algebraic properties namely bijection, nonlinearity, the strict avalanche criterion (SAC), the output bits independence criterion (BIC) as of the initial seed s-box. The method is based on group action of symmetric group π π and a subgroup π 2 π respectively on columns and rows of Boolean functions ( πΊ β‘ πΉ β‘ ( 2 π ) β πΊ β‘ πΉ β‘ ( 2 ) ) of s-box. Invariance of the bijection, nonlinearity, SAC, and BIC for the generated clone copies is proved. As illustration, examples are provided for π = 8 and π = 4 along with comparison of the algebraic properties of the clone and initial seed s-box. The proposed method is an extension of Hussain et al. (2012); Hussain et al. (2012); Hussain et al. (2018); Anees and Chen (2020) which involved group action of π 8 only on columns of Boolean functions ( πΊ β‘ πΉ β‘ ( 2 8 ) β πΊ β‘ πΉ β‘ ( 2 ) ) of s-box. For π = 4 , we have used an initial 4 Γ 4 s-box constructed by Carlisle Adams and Stafford Tavares (Adams and Tavares, 1990) to generated ( 4 ! ) 2 clone copies. For π = 8 , it can be seen (Hussain et al. (2012); Hussain et al. (2012); Hussain et al. (2018); Anees and Chen (2020)) that the number of clone copies that can be constructed by permuting the columns is 8 ! . For each column permutation, the proposed method enables to generate 8 ! clone copies by permuting the rows.