Cryptographic Key Generation Using Burning Ship Fractal

Abstract

The study introduces a key generation scheme using a burning ship fractal function, Hilbert transformation and an external key. The burning ship function is a modified version of a well-known Mandelbrot set function in which absolute value of a complex variable is considered. The process starts with the scrambling of the fractal image pixels by applying a Hilbert curve scanning. To enhance the randomness and complexity, an external key is obtained using a pseudo random number generator (PRNG), whose length depends on the size of the used fractal image. Further, a covering module is applied in which eight different types of operations are performed recursively to cover the scrambled fractal image pixels using eight different keys. At each iteration, a modified external key was used to perform the respective operation to the remaining image pixels. Moreover, to ensure the robustness of the proposed scheme, each block of tempkey (created in previous step) permuted using the sorting indexes of the modified tempkey blocks. The performance analysis of the given method is carried out in terms of the key space, key sensitivity, key generation time, histogram, and correlation coefficient. The results indicate that the proposed method is reliable and secure with great potential to be further use in the image encryption applications.