IDEA系統之研究

Abstract

在本論文中，我們探究了在暴力搜尋法下比DES 更安全的IDEA系統。它使用了混合不同的代數群之間的運算來提昇密碼方法的安全性。我們將IDEA 密碼系統的行為數學化，並且找出一個和IDEA同構的系統，把此同構系統中不同代數群間的運算用我們所自行定義的記號來表示，而得到一致性的算數式藉以做進一步的分析。 在未來的有關這方面的研究工作上，我們將會致力於找出此同構密碼系統中僅具有左單元素或右單位元素的代數群，我們將會在所展開的代數式中加入或刪除一些項，以使它在破解上較困難且較容易實作，同時保證編密碼和解密的工作仍然正確無誤。

In this paper, we will investigate IDEA system which is the more secure than DES system by brute-force cryptanalysis. It uses the mixing operations from different algebraic groups to enhance its security. We model the IDEA system mathematically and look for an isomorphic system of IDEA. The operations of different groups is represented by our notations and the results is an arithmetic expression consistently to help us analyze the isomorphic system. In the future of this research, we will devote to the study of this isomorphic system's groups which are only left identity or right identity. We would add or delete some terms from expansion expansion expressions to make it harder to break and easier to implement so that the encryption and the decryption still work.