Efficient and secure chaotic PRNG for color image encryption

Abstract

Random number generation is considered a major problem for any digital color image cipher algorithm and secret communication protocol. Pseudo-random number generators (PRNGs) are used in many security applications because they afford both features, the randomness efficiency and quality of the PRNG. The paper proposes a new PRNG depending on a combination of the Secure Hash Algorithm (SHA-2(256)) with the results of three chaotic maps: the 2D Henon map, the 2D Kaplan-Yorke map, and the 2D Tinkerbell map. In the proposed chaotic generator, 6 initial floating-point numbers with 10−16 precision are inputs to SHA-2(256) for generating the initial values of the three chaotic maps. Then the chaotic maps are iterated to produce a binary sequence that is processed to enhance the sequence complexity based on binary XOR addition operation and 2D shifting scrambling method. The random binary sequences produced by the proposed PRNG algorithm were tested using several number of analyses like the national statistical test suite, correlation analyses, key space analyses, Sum of absolute analyses (SAD), key sensitivity analyses, and histogram analyses. The results proved that scrambling binary sequences have passed successfully the NIST tests where the ratio η of p-value concerns individual sequences between [0.9805, 0.9994], the correlation between the produced sequences is very small where the distributions of Pearson's correlation coefficients belong to [-0.03, 0.03] and the distributions of Hamming distance coefficients belonging to [0.49, 0.52], all the results of the SAD between [0.33237, 0.33451] which are almost close ideal values, and the key space of proposed PRNG is very large which is 2319. The proposed PRNG was applied as a random key generation algorithm on a new color image cipher algorithm, with strong permutation and substitution methods to encrypt and decrypt each image color channel. The practicableness of the algorithm was tested by different statistical and security analyses.