The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of (2, Z) on projective line over the finite field (2 9 ) to construct proposed S-box. The vertices of the cost diagram are elements of (2 9 ) which can be represented by powers of , where is the root of irreducible polynomial ( ) = 9 + 4 + 1 over Z 2 . Let * (2 9 ) denote the elements of (2 9 ) which are of the form of even powers of . In the first step, we construct a 16 × 16 matrix with the elements of * (2 9 ) in a specific order, determined by the coset diagram. Next, we consider ℎ :2 ) = to destroy the structure of (2 8 ). In the last step, we apply a bijective map on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.

In the literature, different algebraic techniques have been applied on Galois field (2 8 ) to construct substitution boxes. In this paper, instead of Galois field (2 8 ), we use a cyclic group 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 of order 255 to generate 255 . Next, we adjoin 0 to 255 and write the elements of 255 ∪ {0} in 16 × 16 matrix to destroy the initial sequence 0, 1, 2, . . . , 255.In the 2 nd step, the randomness in the data is increased by applying certain permutations of the symmetric group 16 on rows and columns of the matrix. In the last step we consider the symmetric group 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.