最大线性正形置换及其性质

Properties of maximal linear orthomorphisms permutations

根据最大线性正形置换可以用于密码体制中非线性置换的构造,利用有限域上的多项式理论以及矩阵理论,研究了最大线性正形置换T的性质.给出了T的幂仍就是最大线性正形置换的充分条件,证明了T的特征多项式为F2上的本原多项式,进一步证明了Fn2为T的不可约空间.

Maximal linear orthomorphism permutations can be used in the constructions of non-linear permutations in the cipher system. Using polynomial theory and matrices theory over the finite fields, the properties of maximal linear orthomorphisms T are studied. The conditions that the power of T is still maximal linear orthomorphisms are given; It is proved that the characteristic polynomial of T is primitive polynomial, and that F^n_2 is the irreducible sub-space of T.