Digital orthophoto map encryption based on QR code and GS phase retrieval

doi:10.11947/j.AGCS.2025.20230053

Abstract

Abstract:

To address the protection and secure transmission of digital orthophoto map (DOM) information in network environments, this study proposes a novel DOM encryption method that combines QR code and GS phase retrieval in two stages: ① The image data (RGB channels) of the DOM is encoded using the GS algorithm to generate three phase-only holograms. These holograms are scrambled and diffused using pseudorandom sequences generated by the Lorenz hyperchaotic system, enhancing the sensitivity of the optical keys and the ciphertext's sensitivity to plaintext changes through chaotic system properties and diffusion mechanisms. ② The geographic information of the DOM, along with partial keys and user authorization information, are encoded into a QR code and embedded into the three phase-only holograms. The three holograms with embedded QR codes are then synthesized into a meaningless white noise color image, serving as the final ciphertext. Experimental results for DOM in different scenes demonstrate that this method achieves unified encryption of both the DOM image data and geographic information. The decrypted images are highly consistent with the original plaintext images, achieving a peak signal-to-noise ratio of over 39 dB. Evaluation metrics including the correlation coefficient, structural similarity index measure, change rate of pixel number, and normalized change intensity, are close to their ideal values, outperforming existing methods. In addition to traditional chaos parameters, the GS parameters, such as diffraction distance and reference light wavelength, serve as the key, ensuring the method has a large key space (approximately 10¹⁴¹). Minor changes to the plaintext completely alter the ciphertext, and pixel values are statistically independent. The method exhibits strong robustness against ciphertext-only attacks, known-plaintext attacks, chosen-plaintext attacks, chosen-ciphertext attacks, and noise attacks, making it highly valuable for the protection and secure transmission of raster geographic data, including DOM.

Key words: digital orthophoto map, QR code, GS phase retrieval, optical encryption, chaos encryption

CLC Number:

P237

Jun WU, Yiren SHEN, Gang XU, Xuemei ZHAO. Digital orthophoto map encryption based on QR code and GS phase retrieval[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(3): 493-509.

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References 39

[1]	张祖勋, 郭大海, 柯涛, 等. 抗震救灾中航空摄影测量的应急响应[J]. 遥感学报, 2008, 12(6): 852-857.
	ZHANG Zuxun, GUO Dahai, KE Tao, et al. The use of aerial photogrammetry in the fast response for China earthquake rescue[J]. Journal of Remote Sensing, 2008, 12(6): 852-857.
[2]	李德仁, 眭海刚, 单杰. 论地理国情监测的技术支撑[J]. 武汉大学学报(信息科学版), 2012, 37(5): 505-512,502.
	LI Deren, SUI Haigang, SHAN Jie. Discussion on key technologies of geographic national conditions monitoring[J]. Geomatics and Information Science of Wuhan University, 2012, 37(5): 505-512,502.
[3]	CHUNG Y H. A spread random interleaver based efficient DES algorithm for personal cloud computing environments[J]. The Journal of the Korean Institute of Information and Communication Engineering, 2013, 17(1): 41-48.
[4]	WADI S M, ZAINAL N. High definition image encryption algorithm based on AES modification[J]. Wireless Personal Communications, 2014, 79(2): 811-829.
[5]	SONG Xidan, WANG Yulin. Homomorphic cloud computing scheme based on hybrid homomorphic encryption[C]//Proceedings of the 3rd IEEE International Conference on Computer and Communications. Chengdu: IEEE, 2017: 2450-2453.
[6]	KOBLITZ N, MENEZES A, VANSTONE S. The state of elliptic curve cryptography[J]. Designs, Codes and Cryptography, 2000, 19: 173-193.
[7]	朱长青, 任娜, 徐鼎捷. 地理信息安全技术研究进展与展望[J]. 测绘学报, 2022, 51(6): 1017-1028.DOI:. doi: 10.11947/j.AGCS.2022.20220172
	ZHU Changqing, REN Na, XU Dingjie. Geo-information security technology: progress and prospects[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(6): 1017-1028.DOI:. doi: 10.11947/j.AGCS.2022.20220172
[8]	张翰林, 王青山, 邹永初. 复合混沌系统的矢量数据加密研究[J]. 测绘科学, 2012, 37(5): 87-89.
	ZHANG Hanlin, WANG Qingshan, ZOU Yongchu. Encryption of vector data based on composite chaotic system[J]. Science of Surveying and Mapping, 2012, 37(5): 87-89.
[9]	时向勇, 李先华, 郑成建. 基于椭圆曲线密码体制的遥感图像加密算法[J]. 武汉大学学报(信息科学版), 2010, 35(11): 1309-1313.
	SHI Xiangyong, LI Xianhua, ZHENG Chengjian. New encryption approach based on ECC for remote sensing images[J]. Geomatics and Information Science of Wuhan University, 2010, 35(11): 1309-1313.
[10]	彭翔, 汤红乔, 田劲东. 双随机相位编码光学加密系统的唯密文攻击[J]. 物理学报, 2007, 56(5): 2629-2636.
	PENG Xiang, TANG Hongqiao, TIAN Jindong. Ciphertext-only attack on double random phase encoding optical encryption system[J]. Acta Physica Sinica, 2007, 56(5): 2629-2636.
[11]	吴军, 王刚, 徐刚. 结合计算全息与混沌的彩色图像加密方法[J]. 光学学报, 2021, 41(19): 1909001.
	WU Jun, WANG Gang, XU Gang. Color image encryption method based on computer generated hologram and chaos[J]. Acta Optica Sinica, 2021, 41(19): 1909001.
[12]	刘禹佳, 徐熙平, 徐嘉鸿, 等. 基于矢量运算和副像相位掩模的遥感图像加密技术[J]. 光子学报, 2019, 48(2): 210002.
	LIU Yujia, XU Xiping, XU Jiahong, et al. Remote sensing image encryption using vector operations and secondary image phase masks[J]. Acta Photonica Sinica, 2019, 48(2): 210002.
[13]	CHO J, KIM S, PARK S, et al. DC-free on-axis holographic display using a phase-only spatial light modulator[J]. Optics Letters, 2018, 43(14): 3397-3400.
[14]	WANG Xiaohui, CHANG Keming, CHEN Chun, et al. Low-noise and fast three-dimensional information encryption based on the double-phase method[J]. Optical Review, 2021, 28(2): 190-198.
[15]	王雪光, 李明, 于娜娜, 等. 基于空间角度复用和双随机相位的多图像光学加密方法[J]. 物理学报, 2019, 68(24): 77-86.
	WANG Xueguang, LI Ming, YU Nana, et al. Multiple-image encryption method based on spatial angle multiplexing and double random phase encoding[J]. Acta Physica Sinica, 2019, 68(24): 77-86.
[16]	许祥馨, 常军, 武楚晗, 等. 基于双随机相位编码的局部混合光学加密系统[J]. 物理学报, 2020, 69(20): 235-245.
	XU Xiangxin, CHANG Jun, WU Chuhan, et al. Local hybrid optical encryption system based on double random phase encoding[J]. Acta Physica Sinica, 2020, 69(20): 235-245.
[17]	PENG Fei, JIANG Wenyan, QI Ying, et al. Separable robust reversible watermarking in encrypted 2D vector graphics[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2020, 30(8): 2391-2405.
[18]	REFREGIER P, JAVIDI B. Optical image encryption based on input plane and Fourier plane random encoding[J]. Optics Letters, 1995, 20(7): 767-769.
[19]	周辉, 谢红薇, 张昊, 等. 混沌系统和DNA编码的并行遥感图像加密算法[J]. 中国图象图形学报, 2021, 26(5): 1081-1094.
	ZHOU Hui, XIE Hongwei, ZHANG Hao, et al. Parallel remote sensing image encryption algorithm based on chaotic map and DNA encoding[J]. Journal of Image and Graphics, 2021, 26(5): 1081-1094.
[20]	MA He, LIU Juan, YANG Minqiang, et al. Influence of limited random-phase of objects on the image quality of 3D holographic display[J]. Optics Communications, 2017, 385: 153-159.
[21]	MENG Xiangfeng, CAI Luzhong, YANG Xiulun, et al. Information security system by iterative multiple-phase retrieval and pixel random permutation[J]. Applied Optics, 2006, 45(14): 3289-3297.
[22]	LI Jinyang, CHEN Li, CAI Wenyang, et al. Holographic encryption algorithm based on bit-plane decomposition and hyperchaotic Lorenz system[J]. Optics & Laser Technology, 2022, 152: 108127.
[23]	郭媛, 敬世伟. 基于L-L级联混沌与矢量分解的无损压缩光学图像加密[J]. 光子学报, 2020, 49(7): 710002.
	GUO Yuan, JING Shiwei. Lossless compression optical image encryption based on L-L cascade chaos and vector decomposition[J]. Acta Photonica Sinica, 2020, 49(7): 710002.
[24]	SITU G, PEDRINI G, OSTEN W. Strategy for cryptanalysis of optical encryption in the Fresnel domain[J]. Applied Optics, 2010, 49(3): 457-462.
[25]	XU Shujiang, WANG Jizhi, YANG Suxiang. An improved image encryption algorithm based on chaotic maps[J]. Chinese Physics B, 2008, 17(11): 4027-4032.
[26]	郭媛, 许鑫, 敬世伟, 等. 一种混合混沌虚拟光学图像加密方法[J]. 光子学报, 2019, 48(7): 710002.
	GUO Yuan, XU Xin, JING Shiwei, et al. Virtual optical image encryption method based on hybrid chaotic system[J]. Acta Photonica Sinica, 2019, 48(7): 710002.
[27]	ZHANG Ying, HE Yi, ZHANG Jing, et al. Multiple digital image encryption algorithm based on chaos algorithm[J]. Mobile Networks and Applications, 2022, 27(4): 1349-1358.
[28]	SUI Liansheng, XU Minjie, TIAN Ailing. Optical noise-free image encryption based on quick response code and high dimension chaotic system in gyrator transform domain[J]. Optics and Lasers in Engineering, 2017, 91: 106-114.
[29]	BARRERA J F, MIRA-AGUDELO A, TORROBA R. Experimental QR code optical encryption: noise-free data recovering[J]. Optics Letters, 2014, 39(10): 3074-3077.
[30]	SITU Guohai, ZHANG Jingjuan. A lensless optical security system based on computer-generated phase only masks[J]. Optics Communications, 2004, 232(1-6): 115-122.
[31]	WANG Xingyuan, WANG Mingjun. A hyperchaos generated from Lorenz system[J]. Physica A: Statistical Mechanics and Its Applications, 2008, 387(14): 3751-3758.
[32]	PAVLIDIS T, SWARTZ J, WANG Y P. Information encoding with two-dimensional bar codes[J]. Computer, 1992, 25(6): 18-28.
[33]	LIN Peiyu. Distributed secret sharing approach with cheater prevention based on QR code[J]. IEEE Transactions on Industrial Informatics, 2016, 12(1): 384-392.
[34]	TAO Shaohua, YUAN Xiaocong. Practical implementation of the phase-quantization technique in an iterative Fourier-transform algorithm[J]. Applied Optics, 2004, 43(10): 2089-2092.
[35]	NOROUZI B, SEYEDZADEH S M, MIRZAKUCHAKI S, et al. A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos[J]. Multimedia Tools and Applications, 2015, 74(3): 781-811.
[36]	WANG Xingyuan, TENG Lin, QIN Xue. A novel colour image encryption algorithm based on chaos[J]. Signal Processing, 2012, 92(4): 1101-1108.
[37]	ZHU Wei, YANG Geng, CHEN Lei, et al. An improved image encryption algorithm based on double random phase encoding and chaos[J]. Acta Optica Sinica, 2014, 34(6): 0607001.
[38]	BEN FARAH M A, GUESMI R, KACHOURI A, et al. A novel chaos based optical image encryption using fractional Fourier transform and DNA sequence operation[J]. Optics & Laser Technology, 2020, 121: 105777.
[39]	盖琦, 王明伟, 李智磊, 等. 基于离散四元数傅里叶变换的双随机相位加密技术[J]. 物理学报, 2008, 57(11): 6955-6961.
	GAI Qi, WANG Mingwei, LI Zhilei, et al. Doubled random-phase encryption based on discrete quaternion Fourier-transforms[J]. Acta Physica Sinica, 2008, 57(11): 6955-6961.

规格序号	国标规格			相位图替换区域尺寸
规格序号	QR码尺寸	L级	H级	相位图替换区域尺寸
1	21×21	152	72	24×24
2	29×29	440	208	32×32
3	45×45	1248	528	48×48
4	61×61	2592	1120	64×64
5	93×93	6360	2728	96×96
6	125×125	11 744	5024	128×128
7	177×177	23 648	10 208	256×256

影像	λ	Z_R	Z_G	Z_B	x₀	y₀	z₀	w₀
Dom1	655	1000	1400	1800	3	1	4	2
Dom2	532	1100	1600	2100	-5	6	4	-1
Dom3	473	1200	1700	2200	2	8	4	6

影像	CC	PSNR/d B	SSIM
Dom1	0.991 5	32.165 4	0.992 2
Dom2	0.996 8	30.446 8	0.997 2
Dom3	0.996 6	34.751 9	0.998 5

影像	NPCR			UACI
影像	R	G	B	R	G	B
Dom1	99.588 3	99.586 4	99.585 2	33.437 3	33.423 4	33.412 6
Dom2	99.604 7	99.599 5	99.605 9	33.432 0	33.429 1	33.435 6
Dom3	99.601 8	99.604 9	99.608 8	33.416 1	33.429 2	33.422 0
文献[37]	99.568 7	99.554 4	99.578 9	33.410 0	33.454 9	33.440 9

密文图像	水平方向	垂直文献	对角方向
Dom1	-0.005 7	-0.002 9	0.003 9
Dom2	-0.002 9	-0.002 4	-0.000 1
Dom3	0.003 6	-0.001 0	-0.000 5
文献[12]	0.033 4	0.024 8	0.028 8
文献[37]	0.000 5	0.004 3	0.006 3
文献[38]	0.069 3	0.061 0	-0.024 2