Design of a Multiple Pseudorandom Number Generator Combined Chaotic System With RNS and Its Application to Secure Image Processing

Abstract

This paper presents a novel approach to designing a multiple pseudorandom number generator (MPNG) through the integration of several key techniques. Specifically, the method leverages the chaotic dynamics of the 2D Tinkerbell system, a residue number system (RNS), and XOR operations to generate multiple sets of pseudorandom number sequences. The MPNG offers several advantages, including a simple design and low hardware resource requirements. Implemented using a field-programmable gate array (FPGA), it applies each chaotic system state to produce three sets of random number sequences, achieving a generation rate three times higher. The generated sequences are rigorously evaluated using the NIST SP800-22 and Diehard test suites, along with Shannon entropy and histogram analyses, all of which confirm their randomness. The results pass all NIST SP800-22 and Diehard test items, demonstrating the properties of random numbers. Additionally, this paper proposes a synchronization controller to achieve state synchronization between the master system and the slave system, enabling symmetric encryption and decryption applications for secure image processing.

Keywords

• Multiple pseudorandom number generator
• chaotic system
• residue number system
• field-programmable gate array