(t, n)影像秘密分享技術將一張機密影像分享至n位參與者手中，每位參與者持有一把金鑰及一份分享影像，而集合t位參與者的金鑰及分享影像即能回復原秘密影像。傳統的影像秘密分享多以Shamir-Lagrange方法計算，然而比較演算法間的執行效率，中國餘式定理具有更低的演算法執行複雜度。因此本計畫採用中國餘式定理作為分享與還原計算核心技術，以提高系統使用的可行性。 本計畫擬開發一個能處理影像及聲音的秘密分享系統。在功能上，除了沿用吾人去年執行的國科會計畫成果-相異權重外，另外增加零資訊的金鑰選擇技術與漸進分享功能，建構一個多重功能的影像秘密分享系統。其中，零資訊特性一直是Shamir方法的優點，它代表未達門檻值的分享資訊集合不能得到任何與機密資訊有關的資料。而前人證明只要金鑰的選擇滿足連續質數的條件，以中國餘式定理為基礎設計的秘密分享技術亦能滿足零資訊的特性。而漸進分享功能讓使用者可以在愈多的分享資料下獲得更接近原始資料的還原資料，此功能有提供我們要架構的應用系統，更多的應用可能性。最後，本計畫除了開發影像秘密分享的應用系統外，也期望能擴展至聲音開發上，以增加更多的實用性。 A (t, n) secret image sharing scheme shares a secret image to n participants, in which each one possesses one secret key and one shared image. In recovery, collecting t secret keys and their corresponding shared images are needed. Conventional secret image sharing schemes always adopt Shamir-Lagrange schemes to share and recover the secret image. However, comparing with Chinese Remainder Theorem, Chinese Remainder Theorem based secret sharing scheme has lower time complexity than Shamir-based scheme. Therefore, this project adopts the Chinese Remainder Theorem to deal our sharing processing. This project develops a secret sharing system for dealing image and audio data. The developed system adopts our previous NSC project research result: weighted sharing, and adds zero-knowledge key selection and progressive sharing. The Shamir scheme is well-known a zero-knowledge sharing scheme. However, previous researchers proved that selecting consecutive prime numbers also has the zero-knowledge property in a Chinese Remainder Theorem based scheme. The progressive sharing property meets our system property on more shared data acquires data closer to the original data. At last, this project hopes to develop a secret image sharing system and a secret audio sharing system.
