12×12 S-box Design and its Application to RGB Image Encryption

Abstract

Customarily, 8×8 S-box is a 16×16 look up table over Galois field GF28, algebra over the binary field F2. A 12×12 S-box over GF212 is not workable as the computer memory does not manage it. The finite chain ring F2[x]<x12> is fundamentally an algebra over the binary field F2. In this paper we considered the advantage and devise a novel method of 12×12 S-box design over the unit elements of finite chain ring F2[x]<x12>. The newly obtained S-box has greatly higher confusion ability than any of 8×8 S-box. To observe this effect, an RGB image encryption application is given. In the proposed encryption scheme, we doubled the bits of 12×12 S-box from 12 to 24 for creating confusion in the data. Consequently, a new method of color image encryption is designed by which 24 binary bits are utilized at the place of byte. Whereas for diffusion we apply the linear permutation P=i×32 mod 257 and finally bitwise Exclusive-or operation is operationalized. Analysis reveals that the proposed image encryption approach might switch many 8×8 S-box based color image encryption schemes.