S-Box的研究

Abstract

S-Box是私密金匙區塊加密法中最重要的組成部份，在密碼學應用上密碼性強固的S-Box須滿足一些嚴格的密碼性質。這些性質分別為：0-1均衡、均稱、嚴厲雪崩基準、高度非線性、低差異分布與雙向性。而要建構出符合上述性質的S-Box是很困難的。 在這篇碩士論文中，我們提出一個藉由"隨機產生再加以改善"的概念的一個新方法來建造出具有低差異分布性質的S-Box。我們的方法能在改善一個S-Box的差異分布時盡量不影響到這個S-Box的非線性程度。我們的實驗顯示出我們的方法能在大部份的情況下建造出較好的S-Box。

Substitution boxes (S-Boxes) are a crucial component of secret-key block ciphers. Cryptographically strong S-Boxes should satisfy a number of critical cryptographic properties. The properties are: 0-1 balance, regular, strict avalanche criterion , high nonlinearity, low differential distribution and bi-direction. It is difficul to construct such S-Boxes. In this master thesis, we present a novel method to construct low differential distribution S-Boxes by using "randomly-generate-then-improve" concept. Our method improves differential distribution of an S-Box while it does not effect its nonlinearity. Our experients show that our method can construct better S-Boxes in most cases.