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 ℤ_n 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.

有限域的算术特性对对称和非对称密码系统的安全性具有显着影响。以往，在现代对称密钥密码系统，这取决于一个8度不可约原始多项式超过256个元件伽罗瓦域ℤ ₂用于设计的S-box，在AES的主要非线性分量。与基于混沌系统的方法相比，基于S-box的图像加密方案的经验并不明显。在这项研究中，我们改进通过在所有16个不同的程度8次原始不可约多项式的使用基于S盒图像加密算法ℤ ₂并通过引入所述环的一个新的角色ℤ _Ñ整数模Ñ在排列步骤中。通过一些统计分析评估了这种新颖的基于2代数结构的图像加密方案的强度，并获得了显着的性能水平。给出了加密质量与最近一些基于混沌的图像加密算法的比较，显然，新推出的方案具有很高的性能。因此，图像加密方法的这一新发展可以为依赖混沌的图像加密提供替代方法。