A new pseudorandom number generator based on chaos in digital filters for image encryption

Pseudorandom number generators (PRNGs) are an essential tool in cryptography; they produce secret keys to encrypt messages or mask the content by combining it with a random sequence. This study introduces an efficient pseudorandom number generator for a new cryptographic application. The PRNG structure comprises two chaotic digital IIR filters of the second and third order and a 4D hyperchaotic system. In this system, the first chaotic sequence is used as the input to the filters, and the second chaotic sequence is used to select the values of the pseudorandom sequence from the outputs of filters. The cryptosystem algorithm utilizes the pseudorandom sequence produced by the proposed PRNG to create a matrix mask and XOR it with a source image after being permuted with a new technique. The permutation method involves shuffling the positions of the original image using a matrix derived from two mathematical operations (modulo and division) and the final chaotic sequence. For heightened security, the shuffled image is subsequently divided into blocks and mixed using the third chaotic sequence. Statistical and frequency tests demonstrate that the proposed PRNG has strong randomness, high uncertainty, and an absence of discernible statistical patterns. Furthermore, simulation, experimental results, and performance analysis confirm that the new cryptosystem exhibits high security and resilience against various attacks, including differential and statistical attacks.