A class of permutation trinomials over finite fields of odd characteristic

作者：Tu, Ziran; Zeng, Xiangyong^*

来源：Cryptography and Communications, 2019, 11(4): 563-583.

DOI：10.1007/s12095-018-0307-4

• Finite field
• Permutation trinomial
• Trace function

This paper studies the permutation behavior of the polynomial f(x)=x+a1xq(q-1)+1+a2x2(q-1)+1 in Fq2[x] for odd q, and finds a set of the coefficient pairs (a1,a2) that leads f(x) to be a permutation of Fq2. We transform the problem of proving that f is a permutation into determining the number of solutions to some low-degree equations in the unit circle of F(q)2.

• 出版日期2019-7
• 单位河南大学; 湖北大学