布林函數在密碼標準上的頻譜分析

Abstract

對稱式加/解密演算法有對於訊息的加/解密效率高，製作成本低，及容易加解密的優點，而其核心元件通常是布林函數， 所以布林函數在密碼學上的特性一直為研究的範疇，在此之前已經有許多學者提出相關的標準，用來檢測布林函數的密碼特性，其中我們將針對下面的標準來討論： (1)調和性、(2)代數冪級數、(3)非線性、 (4)遺傳特性、(5)相關免疫性. 在本篇論文中，我們首先簡介這些密碼檢測標準，利用布林函數經華勒式-哈達瑪轉換在頻譜上的結果來分析，並研究及回顧目前對於這些密碼檢測標準間的關係的研究， 透過了解其相對關係， 我們將提出兩個在同時考慮遺傳特性及相關免疫性標準下的布林函數建構方式。

Symmetric-key cryptography system has many advantages of high performance, low cost of implementation, and easily encrypting or decrypting messages. A core component of these systems is the cryptographic boolean functions. Therefore, it is research topic for boolean functions on the cryptographic properties. Many researchers have provided many cryptographic criteria to verify the cryptographic properties of boolean functions. We focus the following criteria of the cryptographic boolean functions: (1)balancedness,(2)algebraic degree, (3)nonlinearity,(4))propagation criterion,(5)correlation immunity. In this thesis, we first introduce these cryptographic criteria. Using the Walsh-Hadamard transform of boolean function, we analyze the boolean function on cryptographic properties. Moreover, we study and review the relationship among these criteria. From this, We present two new constructions of a strong boolean function under of consideration of propagation criterion and correlation immunity simultaneously.