1976年,Diffie和Hellman提出了陷门单向函数,可以用来构造一种新的密码体制——公开钥密码,受到了人们普遍的重视。目前,巳经给出了几类陷门单向函数,如重要的RSA公开钥密体制(参看R. Rivest, A. Shamir, L. Adleman, Communications of the ACM 20(1978),120—126)。 本文用有限域F_p上多项式的性质,给出一类新的陷门单向函数。我们有以下的定理 In 1976, Diffie and Hellman proposed a trapdoor one-way function, which can be used to construct a new cryptosystem - the public key cryptosystem and received the universal attention. At present, several types of trapdoor one-way functions have been presented, such as the important RSA public key system (see R. Rivest, A. Shamir, L. Adleman, Communications of the ACM 20 (1978), 120-126) . In this paper, we use the properties of polynomials on the finite field F_p to give a new trapdoor one-way function. We have the following theorem