A Novel Technique for the Construction of Safe Substitution Boxes Based on Cyclic and Symmetric Groups. (4th October 2018) - Razaq, Abdul; Al-Olayan, Hanan A.; Ullah, Atta; Riaz, Arshad; Waheed, Adil
Abstract : In the literature, different algebraic techniques have been applied on Galois field G F ( 2 8 ) to construct substitution boxes. In this paper, instead of Galois field G F ( 2 8 ), we use a cyclic group C 255 in the formation of proposed substitution box. The construction proposed S-box involves three simple steps. In the first step, we introduce a special type of transformation T of order 255 to generate C 255 . Next, we adjoin 0 to C 255 and write the elements of C 255 ∪ 0 in 16 × 16 matrix to destroy the initial sequence 0, 1, 2, …, 255 . In the 2 n d step, the randomness in the data is increased by applying certain permutations of the symmetric group S 16 on rows and columns of the matrix. In the last step we consider the symmetric group S 256, and positions of the elements of the matrix obtained in step 2 are changed by its certain permutations to construct the suggested S-box. The strength of our S-box to work against cryptanalysis is checked through various tests. The results are then compared with the famous S-boxes. The comparison shows that the ability of our S-box to create confusion is better than most of the famous S-boxes.