Abstract: In response to the strong correlation between the chaotic system state and initial state and parameters in traditional chaotic encryption algorithms, which may lead to periodicity in chaotic sequences, the chaos long short-term memory (Chaos-LSTM) model is constructed by combining chaotic systems with LSTM neural networks. The chaos sequence proliferation (CSP) algorithm is constructed to address the problem that the limited computational accuracy of computers can lead to periodicity in long chaotic sequences, making them unsuitable for encrypting objects with large amounts of data. By combining the Chaos-LSTM model and CSP algorithm, a geographic information encryption system is proposed. First, the Chaos-LSTM model is used to output chaotic sequences with high spectral entropy (SE) complexity. Then, a shorter chaotic sequence is selected and proliferated using the CSP algorithm to generate chaotic proliferation sequences that match the encrypted object; a randomness analysis is conducted and testing is performed on it. Finally, using geographic images as encryption objects, the chaotic proliferation sequence, along with the scrambling and diffusion algorithms, are combined to form the encryption system, which is implemented on the ZYNQ platform. The system’s excellent confidentiality performance and scalability are proved by software testing and hardware experiments, making it suitable for the confidentiality peers of various encryption objects with outstanding application value.

基于Chaos-LSTM与混沌序列增殖的地理信息数据加密系统

[1]Alexan W, Elkandoz M, Mashaly M, et al., 2023. Color image encryption through chaos and KAA map. IEEE Access, 11:11541-11554.

[2]Cao Y, Zhao YL, Wang Q, et al., 2022. The evolution of quantum key distribution networks: on the road to the Qinternet. IEEE Commun Surv Tutor, 24(2):839-894.

[3]Chen X, Qian S, Yu F, et al., 2020. Pseudorandom number generator based on three kinds of four-wing memristive hyperchaotic system and its application in image encryption. Complexity, 2020:8274685.

[4]De la Fraga LG, Mancillas-López C, Tlelo-Cuautle E, 2021. Designing an authenticated Hash function with a 2D chaotic map. Nonl Dyn, 104(4):4569-4580.

[5]De la Fraga LG, Ovilla-Martínez B, Tlelo-Cuautle E, 2023. Echo state network implementation for chaotic time series prediction. Microprocess Microsyst, 103:104950.

[6]Gabr M, Korayem Y, Chen YL, et al., 2023. R³—rescale, rotate, and randomize: a novel image cryptosystem utilizing chaotic and hyper-chaotic systems. IEEE Access, 11:119284-119312.

[7]Gonzalez-Zapata AM, De la Fraga LG, Ovilla-Martinez B, et al., 2023. Enhanced FPGA implementation of echo state networks for chaotic time series prediction. Integration, 92:48-57.

[8]Hosseinzadeh R, Zarebnia M, Parvaz R, 2019. Hybrid image encryption algorithm based on 3D chaotic system and choquet fuzzy integral. Opt Laser Technol, 120:105698.

[9]Irfan M, Ali A, Khan MA, et al., 2020. Pseudorandom number generator (PRNG) design using hyper-chaotic modified robust logistic map (HC-MRLM). Electronics, 9(1):104.

[10]Jia YQ, Shelhamer E, Donahue J, et al., 2014. Caffe: convolutional architecture for fast feature embedding. Proc 22^nd ACM Int Conf on Multimedia, p.675-678.

[11]Lin HR, Wang CH, Cui L, et al., 2022. Hyperchaotic memristive ring neural network and application in medical image encryption. Nonl Dyn, 110(1):841-855.

[12]Liu XC, Mou J, Zhang YS, et al., 2024. A new hyperchaotic map based on discrete memristor and meminductor: dynamics analysis, encryption application, and DSP implementation. IEEE Trans Ind Electron, 71(5):5094-5104.

[13]Lorenz EN, 1963. Deterministic nonperiodic flow. J Atmos Sci, 20(2):130-141.

[14]Man ZL, Li JQ, Di XQ, et al., 2021. Double image encryption algorithm based on neural network and chaos. Chaos Sol Fract, 152:111318.

[15]Martins P, Sousa L, Mariano A, 2017. A survey on fully homomorphic encryption: an engineering perspective. ACM Comput Surv, 50(6):83.

[16]Murillo-Escobar MA, Meranza-Castillón MO, López-Gutiérrez RM, et al., 2019. Suggested integral analysis for chaos-based image cryptosystems. Entropy, 21(8):815.

[17]Murillo-Escobar MA, Cruz-Hernández C, Cardoza-Avendaño L, et al., 2022. Multibiosignal chaotic encryption scheme based on spread spectrum and global diffusion process for e-health. Biomed Signal Process Contr, 78:104001.

[18]Pareschi F, Rovatti R, Setti G, 2012. On statistical tests for randomness included in the NIST SP800-22 test suite and based on the binomial distribution. IEEE Trans Inform Forens Secur, 7(2):491-505.

[19]Rehman AU, Liao XF, Ashraf R, et al., 2018. A color image encryption technique using exclusive-OR with DNA complementary rules based on chaos theory and SHA-2. Optik, 159:348-367.

[20]Sahu HK, Jadhav V, Sonavane S, et al., 2016. Cryptanalytic attacks on international data encryption algorithm block cipher. Defence Sci J, 66(6):582-589.

[21]Teh JS, Alawida M, Sii YC, 2020. Implementation and practical problems of chaos-based cryptography revisited. J Inform Secur Appl, 50:102421.

[22]Tezcan C, 2022. Key lengths revisited: GPU-based brute force cryptanalysis of DES, 3DES, and PRESENT. J Syst Archit, 124:102402.

[23]Tlelo-Cuautle E, Díaz-Muñoz JD, González-Zapata AM, et al., 2020. Chaotic image encryption using Hopfield and Hindmarsh–Rose neurons implemented on FPGA. Sensors, 20(5):1326.

[24]Ullah S, Zheng JB, Din N, et al., 2023. Elliptic curve cryptography; applications, challenges, recent advances, and future trends: a comprehensive survey. Comput Sci Rev, 47:100530.

[25]Wan YJ, Gu SQ, Du BX, 2020. A new image encryption algorithm based on composite chaos and hyperchaos combined with DNA coding. Entropy, 22(2):171.

[26]Wu XJ, Kan HB, Kurths J, 2015. A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl Soft Comput, 37:24-39.

[27]Wu XJ, Wang DW, Kurths J, et al., 2016. A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system. Inform Sci, 349-350:137-153.

[28]Xiong PY, Jahanshahi H, Alcaraz R, et al., 2021. Spectral entropy analysis and synchronization of a multi-stable fractional-order chaotic system using a novel neural network-based chattering-free sliding mode technique. Chaos Sol Fract, 144:110576.

[29]Xu SC, Wang XY, Ye XL, 2022. A new fractional-order chaos system of Hopfield neural network and its application in image encryption. Chaos Sol Fract, 157:111889.

[30]Yan S, Gu Z, Park JH, et al., 2023. Synchronization of delayed fuzzy neural networks with probabilistic communication delay and its application to image encryption. IEEE Trans Fuzzy Syst, 31(3):930-940.

[31]Yu F, Zhang ZN, Shen H, et al., 2022. FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient. Chin Phys B, 31(2):020505.

[32]Yu Y, Si XS, Hu CH, et al., 2019. A review of recurrent neural networks: LSTM cells and network architectures. Neur Comput, 31(7):1235-1270.