A Normalized Exponential Piecewise Chaotic System (NEPCS) and DNA Image Cryptography Using SHA-256

One-dimensional (1D) chaotic systems are crucial in cryptography to encrypt digital images effectively by transforming them into noise. Despite their simplicity and computational efficiency, 1D chaotic systems often struggle with short periodicity, narrow control parameter ranges, less complex phase space attractors, and regularity in their output, which limit their applicability in cryptography. A novel 1D piecewise chaotic map, called Normalized Exponential Piecewise Chaotic System (NEPCS), is proposed with an extensive range of control parameters λ and prime number p. It has a high score for Lyapunov exponent (> 7.88) , sample entropy score of 2.2137 and correlation dimension score exceeding 1.1. The NEPCS is evaluated using the SP800-22 test suite recommended by the National Institute of Standards and Technology (NIST). The qualifying rate for the NIST test is > 0.49, proving its high quality of randomness. To validate the efficacy of the NEPCS, an image encryption technique is introduced, leveraging the SHA-256 hash function used iteratively on keyboard inputs and plain images to derive initial seeds for NEPCS. The encryption process begins by permuting the pixels of a color image and converting them into DNA bases. The cipher block chaining mode (CBC) of substitution is sandwiched between the keyless transpositions. The exclusive-or and addition operations are alternately applied to substitute the DNA bases. The presented image cipher has NPCR > 99.59%, UACI exceeding 33.40%, χ² < 285.60, and entropy ≈ 7.9999 scores while resisting communication noises.