两类环Z/(m)上Dickson置换多项式的公共不动点

On Common Fixed Point of Two Sets of Dickson Permutation Polinomials over Z/(m)

Dickson置换多项式通常用来构造公开密钥密码体系,其不动点的多少常常表征所构造密码体系的加密混乱程度。文献[1]给出了构成RSA公钥密码体制的一类特殊的Dickson置换多项式(参数α=0)的不动点计数公式,并猜想这类置换多项式的公共不动点计数为3~3,s为m的不同素因子数。文献[2]证明了这一猜想。文献[3]提出了另一类Dickson置换多项式(α=1)的公共不动点计数为5~3的猜想。本文证明了这一猜想,给出了α=-1类Dickson置换多项式公共不动点计数公式。

Dickson permutation polinomials are usually used to compose the public key cryptosys-tem, in which the numbers of fixed points show encrypting confusion degree which can form the cry-ptosystem. Hence, the research of fixed points counting formula is very important. Fixed points counting formula of the kind of special Dickson permutation polynomials (parameter a = 0) which compose RSA system is given in reference [1]. The reference guesses common fixed points counting formula of this kind of Dickson permutation polynomials is 3', where s is distinct factor numbers of m. Mr Sun Qi, in reference [2], proves that conjecture, and proposes that the common fixed points counting formula of another kind of Dickson permutation polynomials (parameter a = 1) is the conjecture for 5'. This paper killfully proves Mr. Sun Qi's conjesture, and also supplies the common fixed points counting formula of Dickson permutation of which parameter a =-1.