離散分數傅立葉轉換及隨機相位編碼在數位影像安全之應用

Digital Image Security Applications Based on Discrete Fractional Fourier Transforms and Random Phase Encoding

邱偉庭(Wei-Ting Chiu)

指導教授 ： 許文良

中原大學/電機資訊學院/通訊工程碩士學位學程/碩士(2015年)

https://doi.org/10.6840/cycu201500860

摘要

本論文中，我們根據Guo等人所提出的方法[1]，提出了基於離散分數傅立葉的延伸轉換及隨機相位編碼之數位浮水印。我們也根據Tao等人所提出的方法[2]，提出了基於離散分數傅立葉的延伸轉換及隨機相位編碼之雙影像加密法。我們使用多參數離散分數傅立葉轉換(multiple-parameter discrete Fourier fractional transform, MPDFRFT)、隨機離散分數傅立葉轉換(random discrete fractional Fourier transform, RDFRFT)以及實數離散分數傅立葉轉換(real discrete fractional Fourier transform, Real-DFRFT)取代離散分數傅立葉轉換(discrete fractional Fourier transform, DFRFT)搭配隨機相位編碼嵌入數位浮水印和雙影像加密。我們並對嵌入浮水印的影像和加密後的影像進行攻擊，分析與探討前述兩種應用的強健性。
在隨機相位編碼之數位浮水印中，DFRFT具有較好的強健性，在隨機相位編碼雙影像加密方法中RDFRFT具有較好的強健性，在影像的保密性來說，RDFRFT與Real-DFRFT擁有更高的安全性，因為這兩種轉換的次方參數自由度較高。

關鍵字

離散傅立葉轉換；數位浮水印；數位影像安全

並列摘要

In this study, we propose an image watermarking algorithm based on discrete fractional Fourier transform (DFRFT) and its extended transforms with random phase encoding (RPE) base on Guo’s method [1]. We also use discrete fractional Fourier transform and its extended transforms with random phase encoding to encrypt double images using Tao’s technology [2].We use multiple-parameter discrete Fourier fractional (MPDFRFT), random discrete fractional Fourier transform (RDFRFT), and real discrete fractional Fourier transform (Real-DFRFT) to replace discrete fractional Fourier transform for embedding digital watermark and encrypting double images. Then we attack the watermarked image and encrypted images to discuss the robustness of these two methods.
The DFRFT has the best robustness in the random phase encoding of digital watermarking. The RDFRFT has the best robustness in the random phase encoding for encrypting double images. The RDFRFT and the Real-DFRFT can be applied to increases image security, because of their large number of free parameters.

並列關鍵字

Discrete fractional Fourier transform；Digital Image Security；Digital watermarking

參考文獻

[14] 張惟晴（2013）。實數離散分數傅立葉轉換之研究。中原大學通訊工程碩士學位學程碩士論文，桃園。

[1] Qing Guo, Zhengjun Liu and Shutian Liucora "Image watermarking algorithm based on fractional Fourier transform and random phase encoding," Opt. Commun, pp.3918-3923, 2011.

[2] R. Tao, Y. Xin and Y. Wang "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Exp., vol. 15, pp.16067 -16079, 2007.

[3] T. Bianchi , A. Piva and M. Barni "On the implementation of the discrete Fourier transform in the encrypted domain", IEEE Trans. Inform. Forensics Security, vol. 4, no. 1, pp.86 -97, 2009.

[4] C.-C. Shih, "Fractionalization of Fourier transform," Opt. Commun., no. 118, Issues 5-6, pp.495-498, Aug. 1995.