由於科技日新月異的發展，高機密資料的傳輸已經成為一個備受重視的議題。如何在分享過程中避免遭受到惡意的攻擊，是在資訊安全上一個重大的挑戰。影像分享是一個典型的保密技術，分配者將秘密影像分成n張子影像並且把子影像分配給n個參與者，我們可以透過從中蒐集至少k張子影像，還原出秘密影像，但是在少於k張子影像的情況，是無法獲得足夠的資訊來進行還原的。
在此篇論文中，我們提出一套新的方法來實作Thien和Lin根據Shamir的(k,n)門檻值所提出的應用。此方法最主要的優點在於使用了Vandermonde matrix來取代Lagrange interpolation，減少了要解出多項式中係數值的計算複雜度。此外，在使用傳統的Shamir門檻值架構時，我們解決了實際可能造成的精確度失準，並且由我們的步驟也可以消除由Lagrange interpolation所引起的謬誤。在(4,6)的門檻值設定之下，實驗結果顯示提出的方法能完整的還原出秘密影像。

Due to the rapid development of technology, a transmission of highly sensitive data has become an attentional issue. How to avoid malicious attacks during sharing phase is a substantial challenge in information security. Image sharing is a typical technique to protect secret image that the dealer divides the secret image into n shadow images and distributes them to n participants such that by collecting k of them can recover the secret image. Fewer than k shadow images would not be sufficient to reveal the secret image.
We propose a new method to implement the Thein and Lin’s application based on Shamir’s (k,n) threshold scheme in this thesis. The advantage of our method is that we reduce the computational complexity by replacing Lagrange interpolation with Vandermonde matrix to figure out the coefficients located in the polynomial in the sharing phase. In addition to this benefit, we come out the fact that we encounter the possible loss of precision by making use of traditional Shamir’s (k,n) threshold scheme, and our process could eliminate the fallacy generated by Lagrange interpolation. Experimental results of (4,6) threshold show that the proposed method can completely recover the secret image.

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