1 置换多项式与密码体系设f(x)是一个整系数多项式,m>1是整数,当x过模m的一个完全剩余系,f(x)也过模m的一个完全剩余系,则称f(x)是模m的一个置换多项式。此时,f(x)正好导出{0,1,…,m-1}的一个置换,f(x)也叫模m剩余类环Z/(m)上的一个置换多项式。当m=p是一个素数时,则称f(x)是有限域F_p上的一个置换多项式。如果q=p~1,类似地可定义有限域F_q上的置换多项式。 1 Permutation Polynomial and Cryptosystem Let f (x) be an integer coefficient polynomial, m> 1 be an integer. When a complete remnant of xmodule m, f (x) is also a complete remnant of m, then we say f (x) is a permutation polynomial of modulo m. In this case, f (x) just derives a permutation of {0,1, ..., m-1}, and f (x) is also called a permutation polynomial on the remaining ring Z / (m) of modulo m. When m = p is a prime number, then f (x) is a permutation polynomial on the finite field F_p. If q = p ~ 1, we can similarly define the permutation polynomial on the finite field F_q.