機率為基礎之像素不擴展的多機密影像視覺密碼最佳化模型

A Probability-based Optimization Model for Sharing Multiple Secret Images without Pixel Expansion

 

侯永昌

國立中央大學資訊管理研究所

320桃園縣中壢市五權里2鄰中大路300

E-mail: ychou@mgt.ncu.edu.tw

 

許慶昇

國立中央大學資訊管理研究所

320桃園縣中壢市五權里2中大路300

E-mail: cshsu60@ms52.hinet.net

摘要

視覺密碼方法的特色在於其解密過程是透過人類視覺系統而不需要利用任何計算機資源與複雜的解密演算法。因此,在一些無法使用電腦解密的情況下,視覺式的秘密分享方法是一個很好的解決方案。大部分的視覺密碼方法都是使用像素擴展的技巧;因此,分享影像的大小會被擴展成機密影像的若干倍。像素擴展的結果不但使得分享影像不易攜帶,也會造成儲存空間的浪費。此外,大部分的視覺密碼方法只允許分享單一機密影像,而無法分享多張機密影像。在本文中,我們提出一個不需要像素擴展,又能分享多張機密影像的視覺密碼方法。我們的方法使用機率的觀念,並且結合安全性與對比兩項指標,建構出多機密影像視覺密碼方法的多目標最佳化模型。此外,我們利用遺傳演算法來求解多目標最佳化的問題。實驗結果顯示,我們的方法不但能達成像素不擴展與分享多張機密影像的目的;同時,遺傳演算法也能找到令人滿意的解答。

關鍵詞:視覺密碼、視覺機密分享、遺傳演算法。

Abstract

Visual cryptography is characterized by its decryption process that is done by human eyes; that is, there is no need for computers and complex decryption algorithms. Consequently, it is a good solution while computers are not available for decryption. Most visual cryptography methods are based on the technique of pixel expansion; therefore, the size of each share is larger than that of the secret image. Pixel expansion not only results in distortion of shares, but also consumes much more storage space. Besides, most visual cryptography schemes are limited to share only one secret image, whereas the ability to share multiple secret images is not available. In this paper, we propose a method to share multiple secret images without pixel expansion. Our method uses the concept of probability and considers both security and contrast to construct a multi-objective optimization model. To solve the optimization problems, we employ genetic algorithms. Experimental results show that our method is effective in sharing multiple secret images without pixel expansion. Additionally, experimental results also indicate that genetic algorithms can find satisfactory solutions.

Keywords: Visual Cryptography, Visual Secret Sharing, Genetic Algorithms