A Novel Image Encryption Technique Based on Mobius Transformation

The nonlinear transformation concedes as S-box which is responsible for the certainty of contemporary block ciphers. Many kinds of S-boxes are planned by various authors in the literature. Construction of S-box with a powerful cryptographic analysis is the vital step in scheming block cipher. Through this paper, we give more powerful and worthy S-boxes and compare their characteristics with some previous S-boxes employed in cryptography. The algorithm program planned in this paper applies the action of projective general linear group P G L 2 , G F 2 8 on Galois field G F 2 8 . The proposed S-boxes are constructed by using Mobius transformation and elements of Galois field. By using this approach, we will encrypt an image which is the preeminent application of S-boxes. These S-boxes offer a strong algebraic quality and powerful confusion capability. We have tested the strength of the proposed S-boxes by using different tests, BIC, SAC, DP, LP, and nonlinearity. Furthermore, we have applied these S-boxes in image encryption scheme. To check the strength of image encryption scheme, we have calculated contrast, entropy, correlation, energy, and homogeneity. The results assured that the proposed scheme is better. The advantage of this scheme is that we can secure our confidential image data during transmission.

A simple group of order 168 is isomorphic to PGL(2,7)

We present a sketch on a problem related to the isomorphism between the simple group of order 168 and the projective general linear group.

BOUNDEDNESS PROPERTIES OF AUTOMORPHISM GROUPS OF FORMS OF FLAG VARIETIES

We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let K be a field of characteristic 0, containing all roots of unity. Let the K-variety X be a form of an admissible flag variety. We prove that X is either ruled, or the automorphism group of X is bounded, meaning that there exists a constant C ∈ ℕ such that if G is a finite subgroup of AutK(X), then the cardinality of G is smaller than C.