In this paper, a public key knapsack cryptosystem algorithm is based on the security to a difficulty of polynomial factorization in computer communication networks is proposed. For the proposed public key knapsack cryptosystem, a polynomial vector Q(x,y,z) is formed by transform of superincreasing vector P, a polynomial g(x,y,z) is selected. Next then, the two polynomials Q(x,y,z) and g(x,y,z) is decided on the public key. The enciphering first selects plaintext vector. Then the ciphertext R(x,y,z) is computed using the public key polynomials and a random integer $alpha$. For the deciphering of ciphertext R(x,y,z), the plaintext is determined using the roots x, y, z of a polynomial g(x,y,z)=0 and the increasing property of secrety key vector. Therefore a public key knapsack cryptosystem is based on the security to a difficulty of factorization of a polynomial g(x,y,z)=0 with three variables. The propriety of the proposed public key cryptosystem algorithm is verified with the computer simulation.