Construction of S-box over Galois Ring and its Application in Color Image Encryption

Abstract

The fundamental building block of symmetric cryptography systems, Boolean functions provide the basis of an S-box. Since they are nonlinear components, Boolean functions are utilised in block cyphers for S-box designing.The substitution boxes are used in block ciphers with the purpose to induce confusion in data. The design of a substitution box determines the confusion ability of the cipher,therefore, many different types of boxes have been proposed by various authors in literature.Customarily, an 8 × 8 S-box is a 16 × 16 look up table over Galois field GF(28), algebra over the binary field Z2.A 24×24 S-box over Galois field GF(224) is not viable as computer memory does not support it.In this we used a scheme of Galois Ring,In the first step we construct a Galois Field GF(28),then we construct a 8 × 8 S-box having non-linearity is 112, In this S-box each element is of 8-bits,in the next and last step we convert each element of 8-bits into 24-bits by using isomorphic property between Galois Field and Maximal Cyclic Subgroups elements. The newly constructed S-box has much higher confusion capability than any of 8 × 8 S-boxes. To judge the impact of this new 24 × 24 S-box, an RGB color image encryption application is demonstrated.Initially, in the proposed encryption scheme we use 24 × 24 S-box for confusion in RGB channels of plain image.We apply Permutation on Galois Field S-box and Subsitution apply on newly constructed S-box over Galois Ring and finaly apply XORonS-box of Galois Ring. Thus, we introduce a novel technique by which 24 binary bits are divided into 3 bytes and each one deals R, G and B channel of the color image separately.Hence this 24 × 24 S-box dependent encryption method replaces8 × 8 S-box based RGB color image encryption scheme. This thesis is arranged in a way that the definitions and introductory ideas introduced in Chapter 1,the overall argument of the thesis. Chapter 2, contains the research behind the construction of S-boxes using Galois Field, Chapter 3, explained proposed scheme for the construction of S-box using Galois Ring,Lastly, Chapter 4, contains proposed color image encryption scheme by using Galois Ring and detailed comparison of the new S-boxes to various already-in-place schemes and conducts a thorough security study of their design