基於Shamir的(k, n)門檻方法之影像分享

Image Sharing Based on Shamir's (k, n) Threshold Scheme

劉毅成(Yi-Cheng Liu)

指導教授 ： 陳朝欽

國立清華大學/電機資訊學院/資訊系統與應用研究所/碩士(2011年)

https://doi.org/10.6843/NTHU.2011.00685

摘要

A typical technique of image sharing is that the dealer separates the secret image into n shared images and distributes them to n participants such that any k of them can recover the secret image while fewer than k shared images cannot get sufficient information to reveal the secret image. The idea of image sharing comes from the (k, n) threshold scheme independently investigated by Blakley and Shamir in 1979.
　　In this thesis, we implement a method of secret image sharing which is based on the concept of affine cipher and the idea of Thien and Lin’s scheme to get the permutation image and generate the shared images. In the proposed method, we choose two numbers, (a, b), as the key and use them to shuffle the pixel locations and meanwhile preserve the same histogram before the sharing step. The method scrambles the relative locations between the original pixels to avoid the exposure of silhouettes of shared images. Experiments with two different images and permutation keys are provided.

關鍵字

秘密分享 ； 影像分享 ； (k, n)門檻方法

並列摘要

一般典型的秘密影像分享技術，是由一莊家將秘密影像切分成n張分享的子圖，並交由n位參與者保管，使得只要收集到其中任k張就能回復秘密影像，同時若少於k張則無法得知足夠的訊息去還原這張秘密影像。這個影像分享的觀念來自於1979年，由Blakley及Shamir所各別研究提出的(k, n)門檻方法。
　　在本篇論文中，我們提出一個方法來實作秘密影像分享，其中利用affine cipher的概念與林志青教授等所提出的架構，來得到重組後的影像與產生分享的子圖。在所提出的方法中，於分享的步驟前，我們選定(a, b)兩個數來當作鑰匙，並利用它們來對像素位置做洗牌，同時保有原來直方圖的分布。這個方法打亂了原來像素間的相關位置，避免使分享的子圖暴露出秘密影像的輪廓。我們提供了兩張影像與兩組重組鑰匙來做為實驗結果。

並列關鍵字

secret sharing ； image sharing ； (k, n) threshold scheme

參考文獻

[Chan1998] C.C. Chang and R.J. Hwang, “Sharing secret images using shadow codebooks,” Information Sciences, vol. 111, no. 1-4, 335-345, 1998.

[Chan2002] C.C. Chang, C.S. Tsai, and T.S. Chen, “Sharing multiple secrets in digital images,” Journal of Systems and Software, vol. 64, no. 2, 163-170, 2002.

[Chan2008] C.C. Chang, Y.P. Hsieh, and C.H. Lin, “Sharing secrets in stego images with authentication,” Pattern Recognition, vol. 41, no. 10, 3130-3137, 2008.

[Chen2009] C.C. Chen, C.C. Chen, and Y.C. Lin, “Weighted modulated secret image sharing method,” Electronic Imaging, vol. 18, no. 4, 1-6, 2009.

[John1998] N.F. Johnson and S. Jajodia, “Exploring steganography: Seeing the Unseen,” IEEE Computer, vol. 31, no. 2, 26-34, 1998.