Study On Image Encryption On Galois Finite Field GF(2~n)

There is little work on GF(2n) for Image processing so far. Nev-ertheless we have obtained some great results in this field and issued a paper (see Liebin Yan and Ruisong Ye. Image encryption using novel mappings over GF(2n)) on this work published by Studies in Mathemat-ical Sciences. Two image encryptions are proposed based on two map-pingsφandψrespectively. By making use of Frobenius automorphism, mappingφ, which acts upon 2-dimensional vector space over GF(2n), is given naturally. And by taking the advantage ofpolynomial base of 2n-dimensional vector space over GF(2n) and thanks to the virtue of Kro-necker product, we expand the space up to 22n-dimensional and conse-quently we construct a polynomial base with two parameters. As a result, incorporating with 0, a base that involves variant parameters is obtained. With the help of inner product, mappingψis deduced, which is most important in our work. We keep working on these two mappings and have a discussion about Arnold cat map over GF(2n). To evaluate our algorithms, we invoke three recommended tests:NPCR, UACI and Cor-relation of Two Adjacent Pixels. As the results shown, our schemes for image encryption are as great as other famous schemes. Our schemes for image encryption are featured with huge key space, high diffusion and confusion, such features are valuable to practical applications.