A novel discrete image encryption algorithm based on finite algebraic structures

Abstract

The arithmetic properties of a finite field have a remarkable impact on the security features of symmetric and asymmetric cryptosystems. Conventionally, in modern symmetric-key cryptosystems, a 256 elements Galois field depending on a single 8 degree primitive irreducible polynomial over ℤ2 is used for designing an S-box, the main nonlinear component in AES. The experience of S-box based image encryption schemes is not appreciable than chaotic systems based methods. In this study, we improve the S-box based image encryption algorithms by the usage of all 16 distinct degree 8 primitive irreducible polynomials over ℤ2 and by introducing a new role of the ring ℤn of integers modulo n in the permutation steps. The strength of this novel 2-algebraic structures based image encryption scheme is evaluated by some statistical analyses and a significant performance level is achieved. A comparison of encryption quality with some of the recent chaos-based image encryption algorithms is given and evidently the newly launched scheme spectacles high performance. Thus this new development in image encryption methods may provide an alternative to chaos dependent image encryption.