區塊加密法以及NNR加密法之研究

Abstract

本論文中, 我們研究現有的區塊加密法, 探討他們的設計觀念和安全性質.並且分析知名的攻擊法, 進而提出方法加強現有的區塊加密法以抵御可能的攻擊.另外, 我們並且研究和設計 NNR 加密法. 我們將亂數加入明文中建立 homophonic 加密法, 並且測試其對差分攻擊法的影響.另外, 我們提出動態取代盒加密法, 並分析其對線性攻擊法的防禦能力. 我們修改原 SAFER 加密法, 使他可以使用同一個演算法進行加密和解密, 另一個修改的版本則是可以一次加密不定長度的明文. 我們建立參入亂數的加密模式, 並且分析他對暴力,差分和線性攻擊法的防禦能力.另外, 我們利用亂數,賀序函數和區塊加密法來建立 MAC 機制, 稱為不確定訊息驗證碼. 我們定義不確定數值表示法和確定數值表示法, 並且利用這兩種表示法來建立一個新的加密方法, 稱為 NDC.

In this thesis, we study the modern famous block ciphers. Their design concepts and security properties are explored. Many attacks threatening to the block ciphers are examined and new methods are proposed to strengthen the block ciphers to defeat some of these attacks. Furthermore, some applications of the block ciphers are explored. In the next portion of the thesis, we also progress to construct and examine the NNR ciphers. We survey and classify the structures, adopted operations and subkey schedukings of the modern block ciphers. A table is used to list these features of the currently existent block ciphers. There are many types of cryptanalytic attacks. Each of them is introduced briefly. Their threats to the famous block ciphers are also presented. We reconstruct an existent block cipher to be a homophonic cipher by inserting random bits into specific positions of the input of the original block cipher. We examine the resisting ability of the new block cipher to dufferential attacks. Illustrating by DES, the effect is as desired. We propose a method to strengthen the block ciphers against linear attacks by rearranging order of S-boxes dynamically. The effect to DES is discussed as an illustration. With some rectification a block cipher may be reconstructed to be self-recoverable for getting compact program modules and accepting variable length plaintext for better diffusion of an encrypted message. Here, we modify the original design of the SAFER cipher to make it corresponding to these concepts. We investigate the mode of block cipher encryption in which a random number is added into the process of an encryption. Many manners of adding the random number are examined for the capabilities to defeat brute-force,differential and linear attacks. Block ciphers can be applied to construct an MAC mechanism. Here, we suggest an MAC scheme which combines a hash function and a block cipher in order. We strengthen this scheme to prevent the problem of leaking the intermediate hash value between the hash function and the block cipher by additional random bits. We construct a nondeterministic number representation (NNR) system which maps an integer to a set of vector and a deterministic number representation (DNR) system which maps an integer to a single vector. Applying an NNR and a DNR system, a cryptosystem named as an NNR-DNR Cipher (NDC) is constructed.The main property of NDC is that a plaintext may be probabilistically mapped to different ciphertexts for a given key. This feature may increase the difficulty of cryptanalysis.