Multiple point cloud encryption based on principal component analysis and fractional Fourier transform

doi:10.23919/JSEE.2026.000092

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 393-411.doi: 10.23919/JSEE.2026.000092

• ELECTRONICS TECHNOLOGY • Previous Articles

Multiple point cloud encryption based on principal component analysis and fractional Fourier transform

Xinze LI¹(), Lei YU¹(), Jiafa NIE²^,*(), Yan SUN¹()

¹College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
²Academy of Robotics Engineering, Harbin Far East Institute of Technology, Harbin 150001, China

Received:2024-03-15 Accepted:2025-12-22 Online:2026-04-18 Published:2026-04-30
Contact: Jiafa NIE E-mail:619052927@qq.com;yulei@hrbeu.edu.cn;jacky_niejiafa@sina.com;919986211@qq.com
About author:
LI Xinze was born in 1997. He received his B.S. degree in 2019. He is currently pursuing his M.S. degree in Harbin Engineering University. His research interests are optical image encryption and its applications. E-mail: 619052927@qq.com

YU Lei was born in 1977. She received her Ph.D. degree in signal and information processing from Harbin Engineering University, in 2008. She is a professor in Harbin Engineering University. Her research interests are image processing and image stabilization. E-mail: yulei@hrbeu.edu.cn

NIE Jiafa was born in 1978. He received his B.S. degree in communication engineering from Harbin Engineering University, in 1999, and M.S. degree in communication and information system from Harbin Engineering University, in 2004. He had worked in ERICSSON for 14 years and now is engaged in electronic design for Harbin Far East Institute of Technology, working in the field of signal processing and electronic system design. E-mail: jacky_niejiafa@sina.com

SUN Yan was born in 1997. She received her B.S. degree in 2019. She is currently pursuing her Ph.D. degree in Harbin Engineering University. Her research interests are digital holographic imaging and its applications. E-mail: 919986211@qq.com
Supported by:
The work was supported by National Natural Science Foundation of China (61771155).

Abstract

Abstract:

In view of the large amount of data and dense pixel points in point cloud files, this article proposes a multiple point cloud file encryption algorithm based on principal component analysis (PCA) and fractional Fourier transform (FrFT). In this method, a point cloud data matrix (PCDM) is generated by extracting the coordinates and color information of the point cloud, then using PCA to reduce the dimension of a sequence of PCDMs, which are spliced and scrambled to produce a feature vector matrix and a dimension-reduced matrix (DRM) for encryption and reconstruction. Then using the hyperchaotic Lorenz system to generate the random phase masks and the orders of the FrFT. These two parameters will be used as keys to encrypt the point cloud feature vector matrix. The simulation results verify that the encryption algorithm can quickly encrypt multiple point cloud files, and the quality of the point cloud files obtained by decryption and reconstruction is good. The algorithm also has a large enough key space and highly sensitive keys, which means it has good security and strong robustness to different attacks.

Key words: image encryption, point cloud, hyperchaotic system, principal component analysis, fractional Fourier Transform

Xinze LI, Lei YU, Jiafa NIE, Yan SUN. Multiple point cloud encryption based on principal component analysis and fractional Fourier transform[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 393-411.

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References 30

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Serial number	File name	Number of pixels
1	Apple	3 161
2	Ball	949
3	Calculator	2 330
4	Camera	1 959
5	Lemon	2 207
6	Soda_can	3 805
7	Tomato	1 622
8	Toothbrush	1 021
9	Water_bottle	3 513

File name	CC	File name	CC
Apple	0.000 55	Soda_can	0.004 93
Ball	0.001 11	Tomato	0.001 86
Calculator	0.002 63	Toothbrush	0.0005 37
Camera	0.002 31	Water_bottle	0.0001 14
Lemon	0.003 42

File name	CC	File name	CC
Apple	0.027 2	Soda_can	0.051 6
Ball	0.017 3	Tomato	0.060 3
Calculator	0.003 6	Toothbrush	0.021 9
Camera	0.124 0	Water_bottle	0.023 4
Lemon	0.021 3

File name	CC	File name	CC
Apple	0.999 97	Soda_can	0.999 93
Ball_	1	Tomato	1
Calculator	0.999 96	Toothbrush	1
Camera	0.999 99	Water_bottle	0.999 96
Lemon	1

File	Pixel correlation
File	Horizontal	Vertical	Diagonal
R-channel	0.996 5	0.996 8	0.994 7
G-channel	0.996 8	0.997 6	0.995 4
B-channel	0.996 7	0.997 2	0.994 5
DRI	0.701 2	−0.067 6	−0.073 9
Encrypted image	−0.006 6	−0.000 8	−0.004 4
Lena [12]	0.001 8	0.000 3	−0.001 4
Lena [30] R-channel	−0.000 5	−0.007 2	−0.004 9
Lena [30] G-channel	−0.002 5	−0.005 5	−0.005 5
Lena [30] B-channel	0.003 0	−0.001 9	−0.000 4

Multiple point cloud encryption based on principal component analysis and fractional Fourier transform

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Salt & pepper noise intensity	CC of PCDM(“apple.pcd”)	CC in [12]
0	1	1
0.01	0.7691	0.6981
0.03	0.5856	0.5007
0.06	0.5016	0.2919

Occlusion level/%	CC	CC in [12]
0	1	1
3	0.992 83	0.591 7
5	0.985 81	0.504 5
13	0.955 11	0.332 6
25	0.918 72	0.252 9

Number of point clouds	1	4	9
The size of PCDM	256×238=60 928	256×238×4=243 712	256×238×9=548 352
The size of the eigenvector matrix	256×30=7 680	256×120=30 720	256×270=69 120
Data compression ratio/%	87.4	87.4	87.4
Data volume increase ratio (compared to one point cloud)/%	−	300	800
PCA time/s	0.036	0.08	0.194
Encryption time/s	0.168	0.334	1.278
Decryption time/s	0.13	0.354	1.431
Total time/s	0.334	0.768	2.903
Total time increase ratio data/% (compared to one point cloud)	−	129.9	769.2

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