基于小波变换的分数阶傅里叶变换多图加密技术研究

孔德照; 沈学举; 林超; 高宇辰

doi:doi:10.3788/lop50.091002

激光与光电子学进展, 2013, 50 (9): 091002, 网络出版: 2013-08-21

基于小波变换的分数阶傅里叶变换多图加密技术研究

Multi-Image Encryption Based on Wavelet Transform and Fractional Fourier Transform

论文大纲

孔德照 ^1,*沈学举 ¹林超 ¹高宇辰 ²

作者单位

¹ 军械工程学院光学与电子工程系, 河北石家庄 050003

² 酒泉卫星发射中心, 甘肃酒泉 732750

摘要

以小波变换和分数傅里叶变换为基本理论依据，介绍了一种基于小波变换的分数阶傅里叶变换多图加密技术，丰富了多图加密的方法。该方法充分利用了小波变换的多分辨率分解的特性，结合分数傅里叶变换，不仅有效完成了多图加密，而且实现了各图像独立的处理，加密后，每个图像都会有自己独立的密钥。分析了小波变换类型和变换级次对加、解密效果的影响，并对算法的应用做了分析和说明。数值模拟验证了该方法的可行性，表明该算法较好地解决了多图加密系统容量不足的问题，不仅增大了密钥空间，提高了安全性，还提高了算法应用的多样性和灵活性。最后，提出了一种可行实现装置来实现该方案。

Abstract

A multi-image encryption scheme based on optical wavelet transform (OWT) and fractional Fourier transform (FrFT) is proposed, which enriches the multi-image encryption method. The scheme combines OWT and FrFT to make full use of multi-resolution decomposition of wavelet transform (WT). WT can focus most energy of the original images on the low-frequency parts, so the sizes of images can be reduced as far as possible without loss of image quality. The mentioned properties can not only realize the multi-image encryption, but also make sure each image is processed alone. When encryption is finished, each image will get its own independent keys. Analysis of encrypted effects is completed. Furthermore, the influence of WT type and order are analyzed, and application and analysis of independent keys are accomplished as well. Numerical simulation verifies the feasibility of the scheme and shows that the problem of insufficient capacity is solved better. The security of the method is analyzed. It can be concluded that the method expands the space of keys, which improves the security. Moreover, the application of independent keys makes the variability and flexibility of scheme increase, which means that multi-user decryption, cascade, and multi-user authentication can be achieved. A simple photoelectric mixed device to realize the scheme is proposed.

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孔德照, 沈学举, 林超, 高宇辰. 基于小波变换的分数阶傅里叶变换多图加密技术研究[J]. 激光与光电子学进展, 2013, 50(9): 091002. Kong Dezhao, Shen Xueju, Lin Chao, Gao Yuchen. Multi-Image Encryption Based on Wavelet Transform and Fractional Fourier Transform[J]. Laser & Optoelectronics Progress, 2013, 50(9): 091002.

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