Image Encryption Based on Fourier-DNA Coding for Hyperchaotic Chen System, Chen-Based Binary Quantization S-Box, and Variable-Base Modulo Operation

Abstract

This research work extends the hyperchaotic 4D Chen system into the fractional-order domain to carry out image encryption over 3 stages. For the first encryption stage, the discrete Fourier transform (DFT) of the numerical solution of the fractional-order Chen system is obtained, quantized, and employed in carrying out DNA coding. For the second stage, a robust S-box is constructed from the DFT-quantized solution of the Chen system and applied. For the third stage, a Mersenne Twister encryption key is converted to base- $\phi $ , and a modulo operation is applied. The proposed technique is shown to be efficient, secure, and robust, performing comparably to its counterparts in the literature. Average computed values include an MSE of 9610, a PSNR of 8.33 dB, an MAE of 80.22, an information entropy of 7.999, correlation coefficients of zero, an NPCR of $99.62\%$ , and a UACI of $31.46\%$ . It also passes all the NIST SP 800 suite of tests. The main advantages of the proposed technique are its superior key space of 21754 and encryption rate of 72.6 Mbps.

Keywords

• Chen hyperchaotic system
• discrete Fourier transform
• encryption key
• fractional-order circuits and systems
• image encryption
• Mersenne Twister