Image encryption scheme with key sequences based on Chaotic functions

摘要

The current information age demands enormous opportunities, where, the sensitive data and information is being exchanged, analyzed and made use of. It has led to several concerns and challenges, mainly in the areas of information privacy, authentication and integrity. This concern, attracted cryptographers to device more effective methodologies and algorithms to ensure better protection to sensitive information. In this context, the application of chaotic based systems is considered to design a pseudorandom sequence generator, which is used as a key stream generator in the additive Stream Cipher system. Chaotic map is a mathematic function that generates highly nonlinear and random real sequence which is very sensitive to initial conditions. In this view, this work focusses on the study of Logistic map, considered from a bunch of various Chaotic functions available [1], [2]. Chaotic real sequence is binarized using a new binarization algorithm using Linear Feedback Shift Register (LFSR), which is designed in such a way that the randomness of Chaotic real sequence is not affected as far as possible. Using Logistic map, about 50 sequences are generated each of length ≥ 10. To ensure the randomness of binary sequences, NIST(National Institute of Standards and Technology) test is used. It is observed that, all the sequences have strictly passed most of the NIST tests with an average passing proportion ≥ 0.87. These sequences are used as key sequences in image encryption and decryption. It is interesting to observe that, encrypted image does not contain any residual information. This result is cross verified by plotting the Histogram, computing the Correlation coefficient and Entropy of the output images. It is observed that, Histograms are almost flat indicating the equiprobable distribution of pixels. Also, Entropy of the encrypted image is close to 8 and Correlation coefficient value is very negligible indicating that neighboring pixels ar- heavily uncorrelated. As the key sequence based on Chaotic functions is sensitive to initial conditions, the sequence generated will be highly nonlinear and random which encourages one to use in cryptographic applications.