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.

Encryption using a matrix of symmetry and matrix inverse symmetry

This paper presents a new type of encryption, using a matrix asymmetric and symmetric matrix inverse matrix clear text, which is an internal encryption. As well as asymmetric encryption, where the ciphertext is inversely symmetric matrix. Decryption matrix related to any asymmetric encryption keys depends on public and private, and is applied to the coded messages used in the current system ASCII our computers.