植基於數系統的不對稱密碼法

Abstract

在計算機上,有很多的安全問題;其中一個安全問題是討論有關資料的保護 以防止它被竊取或破壞。隨著網路和資料庫系統的增加,這種安全問題更 為重要。在這篇論文中,我們定義了一種叫(B,M)的數系統;它是一種廣義 的數系統以至於任何的N-ary數系統都可以用 (B,M)數系統來表示。在(B, M)數系統上,我們也設計了一個新的不對稱密碼法;就執行效率而言,加密 和解密的演算法都十分的有效率。在密把碼分析方面,分析結果告訴我們 它的資料擴展度在某些B的狀況下合理;更由於加上隨機因素,它的私匙更 難猜測,因此我們的密碼法可稱為一個有效的不對稱密碼法。 There are many security problems in computer systems. One of them discussed is how to protect private data from taping and destorying. As the use of network and database systems grows, the security problem has become more and more important. In this paper, we define a new concept, (B,M) number system. It is well known that any n-ary number system can be expressed as a (B,M) number system. A new asymmetric cipher based on (B,M) number systems is designed here. To improve performance, efficient algorithms for en- cryption and decryption are also presented in this thesis. In our cryptanalysis, it shows that data expansion is rea- sonable for some B. By considering random factors involved, Our private key sequence is very hard to guess. Therefore, our cipher deserves an efficient asymmetric cryptosystem.