物理学报2026，Vol.75Issue(6)：1-20,20.DOI:10.7498/aps.75.20251657
基于Caputo算子的四维忆阻神经网络构建及其在双重生物加密中的应用
Construction of four-dimensional memristive neural network based on Caputo operator and its application in dual biological encryption
摘要
Abstract
To address traditional image encryption's drawbacks of high computational complexity,insufficient key space,and weak anti-attack capability,this study proposes a novel encryption system integrating fractional-order chaos and dual biological encoding,i.e.a four-dimensional fractional-order discrete-time hopfield neural network(F-DHNN)embedded with locally active memristors,which is constructed using the Caputo fractional difference operator to enhance nonlinear complexity and long-memory characteristics.The systematic dynamic analyses via Lyapunov exponent spectra,bifurcation diagrams,and phase portraits focused on key parameters w22,q,and k1 reveal pronounced hyperchaotic behavior at w22=2.2,q=0.6,and k1=2.75(with multiple positive Lyapunov exponents),whereas the locally active memristor,validated by hysteresis loops and DC V-I characteristics,contributes nonvolatility and local activity to the network's rich dynamics.The encryption mechanism integrates RNA dynamic transcription(three rounds of pairing,mutation,insertion/deletion)and DNA encoding(8 dynamic rules,base XOR),combined with 16 rounds of triple hybrid diffusion and global cyclic shifting.The security tests show that the encrypted images have information entropy of 7.9991(near the theoretical maximum 8),NPCR of 99.6033％,and UACI of 33.4540％,which are close to their corresponding ideal values,with adjacent pixel correlation approaching zero,enabling resistance to 25％cropping and 10％salt-and-pepper noise attacks;hardware implementation on an ARM(STM32)platform confirms consistency with simulations,and this system that features linear time complexity(O(M×N)),outperforms single-mechanism schemes,providing high security and engineering feasibility for sensitive image transmission.关键词
分数阶离散时间/局部有源忆阻器/RNA动态转录/DNA编码Key words
fractional-order discrete time/local active memristor/RNA dynamic transcription/DNA encoding引用本文复制引用
张力,李中意,杨宗立,刘丹..基于Caputo算子的四维忆阻神经网络构建及其在双重生物加密中的应用[J].物理学报,2026,75(6):1-20,20.基金项目
盐城市重点研发计划(批准号:BE2023002)资助的课题. Project supported by the Yancheng Key R&D Program,China(Grant No.BE2023002). （批准号:BE2023002）
