串流密碼中組合函數安全性之研究

Abstract

近年來，串流密碼的理論發展得非常快速。一個串流密碼中的密鑰流產生器設計的主要關鍵在於組合函數。基於安全性的理由，一個組合函數需滿足：平衡性、非線性度大、相關免疫性階數高、傳播特徵階數高以及代數級數大等。 本論文將針對組合函數作討論，並提出一些新的技術與改良方法：一、透過基因演算法，尋找一個具有高非線性度之相關免疫函數；二、建構一個具有高傳播特徵階數之相關免疫函數；三、討論基於 上組合函數的性質，並將基於 上的組合函數擴展至 上（p是一個質數），且分析其非線性度與相關免疫性階數。

The theory of the stream cipher has developed quickly these years. The most important of the KeyStream Gernerator of the stream cipher is the combining function. For security reasons, the combining functions should satisfy a few properties such as balanced, large nonlinearity, high order of correlation immune, high order of propergation criterian and large algebratic degree. In this thesis, we discuss the combining functions, and then propose some new techniques and improvements: using genetic algorithm to find correlation immune functions with high nonlinearity, constructing new correlation immune function with high order propergation criterion and discussing properties of combining function over GF(p) and expanding some correlation immune function over GF(2) to GF(p)( p is a prime number), then analysize their nonliearity and order of correlation immune.