A Chaotic Cryptosystem using Conjugate Transcendental Fractal Function

Abstract

A cryptosystem designed by using the combined features of fractal function and chaotic map, provides a secure and real time encryption environment. In this paper, a 2D-chaotic map is employed to create a chaotic key sequence to comply with the requirement of the key sensitivity. The set of initial values of the chaotic map has derived by iterating a conjugate transcendental fractal function (CTFF) i.e. +1 = (sin(2)) +. The fractal function produced three sets of initial values after iterating it using Picard, Mann, and Ishikawa iteration methods. Resultantly, three chaotic key sequences will be generated by executing 2D Sine Tent composite map (2D-STCM) for each set of initial values. Afterwards, perform zigzag scanning to each key stream to decorrelate the adjacent image pixels and combined them using XOR operation. By using a different summation of plain image pixels for each pixel encryption, improves the cryptosystem resistant against known/chosen-plaintext attack. Moreover, an encryption of a plain image pixel achieved using corresponding key sequence pixel and a previously ciphered pixel value. The proposed encryption/decryption scheme is evaluated using key space analysis, key sensitivity analysis, differential analysis and other statistical analyses. The performance result indicates the given scheme is efficient and reliable to be used with great potential for a secure image transmission application.

A New Composite Fractal Function and Its Application in Image Encryption

“…The author suggested an image encryption method in which an H-fractal was utilized to diffuse the scrambled image pixels [ 22 , 41 ]. The author in [ 42 ] proposed a fractal function-based cryptosystem, in which three sets of initial values are derived by iterating a conjugate transcendental fractal function using Picard, Mann, and Ishikawa iteration methods. An image encryption algorithm was proposed by utilizing the RSA algorithm elements with the fractal quadratic transformation system, best suited to the images that allow clearly distinguishing the contours [ 40 ].…”