有限域F_(2n)上一类二项式的密码学性质

Cryptographic properties of a class of binomials over finite field F_(2n)

研究了有限域F_(2n)上一类二次函数F(x)=x^(22t+1)+x^(2t+1)的密码学性质,其中gcd(n,t)=1.基于有限域上线性化多项式和二次型的理论,确定了F(x)的差分谱,并计算其非线性度.特别地,当n为奇数时,计算出了它的Walsh谱.作为应用,利用F(x)构造了两类线性码,并确定了它们的重量分布.

The cryptographic properties of a class of binomials F(x)=x^(22t+1)+x^(2t+1)over finite field F_(2n) are investigated where gcd(n,t)=1.Based on the theory of linearized polynomials and quadratic forms,the differential spectrum of F(x)is determined,and its nonlinearity is also calculated.In particular,the Walsh spectrum of F(x)is obtainted for odd n.Finally,as applications,two binary linear codes are constructed from F(x)and their weight distributions are derived.