一個解決Ｍ問題的方法

Abstract

由於希爾加密法(Hill cipher)無法抵抗已知明文(Known-plaintext)與 選擇明文(Chosen-plaintext)之攻擊,本論文將針對此弱點加以分析並提 出一安全有效之加密法。為使已知明文及選擇明文攻擊法無法生效,本系 統將每一明文區塊(block)連結(Concate-nate)一隨機字元(Random String),使得相同之明文於每次加密皆能獲得不同之密文,然後除了傳統 希爾加密法金匙(Key Matrix)之矩陣相乘外,再利用不同基底數的轉換( Number Base Conversion)加強隨機字元擴散(Diffuse)的效果。由於性能 的要求,本論文將所有的明文,隨機字元及金匙矩陣皆由二進位(Binary)表 示,如此使得所有運算皆能簡化為邏輯運算(Logical Operation),不但利 於硬體製作,更使金匙產生之速度大為提昇。最後將如何將隨機字元由明 文區塊中去除定義為Ｍ問題並提出多種方法加以探討。 Several researchers had considered the disadvantages of Hill cipher and triedt o overcome the weakness because of revealing under the known-plaintext attacka nd chosen-plaintext attack.In this thesis, we concatenated the plaintext block with a random string. Sothe ciphertext would be different by using the differ ent random string. That canprevent from the known-plaintext attack and chosen- plaintext attack. Based on amore secure number system with different bases and an enforced transformation ofthe enciphering matrix, this cryptosystem appear s to be more robust, faster andeasier to implement on computer by using base 2 .Finally, we describe the M-problem and propose some solutions to recover our plaintext and truncate the needless random string.