用牟比乌斯变换逼近有限域上的置换(英文)

Approximating a permutation over finite fields by Mbius transformations

对称密码技术中使用的许多非线性函数是基于牟比乌斯变换构造的,因此很可能保有某些几何不变量.基于牟比乌斯变换,Courtois构造了能够抵抗线性密码分析和差分密码分析的不安全的密码体制.于是通过量化有限域上的映射被牟比乌斯变换逼近的程度,给出了牟比乌斯变换逼近有限域上线性函数的度量的下界,并将我们提出的量与有限域上置换的Carlitz秩进行了比较.

Many nonlinear transformations and hence functions used in symmetric ciphers are may preserve some geometric lnvanants. based on MObius Based on MObius transformations Courtois devised insecure block ciphers which are nonetheless invulnerable against both linear cryptanalysis and differential cryptanalysis. The authors quantified how a mapping on a finite field is approximated by MObius transformations, gave a lower bound to measure how linear functions of a finite field were approximated by MObius transformations, and also compared the proposed quantity with the Carlitz rank of a permutation on a finite field.