Linear Diophantine equation as public key of cryptography use ternary number system

In this paper , we will define multiple orthogonal vector of Diophantine equation on specific conditions. We will solve the Diophantine equation with this vector in ternary number system and develop special relationships for it , {0,1,2} , then we will present a new public key cryptosystem based on multiple orthogonal vector with an example to illustrate the system.