Based On The Integer Solution Of Matrix Equation And Its Inverse Matrix Solution To Design System Of The New Cryptography

This paper focuses on the first part of a class of symmetric solutions of matrix equation.And is the necessary and sufficient condition of the solution and the recursive calculation formula of matrix is symmetric solutions.Recursive formula and get the sufficient and necessary conditions and the unique solution of symmetric matrix solution,and studied the method for finding the inverse matrix.A numerical example illustrates the recursive formula is correct.The second part is to discuss the problem of solving a class of unique integer finite field matrix equation.And based on the unique solution of the problem of such a matrix equation,design communication password.Numerical experiments verify the feasibility of the new system and application code and correctness.The third part discusses the unique solution of the problem based on finite domain matrix equations,the design of new types of password system,combined with numerical experiments to verify the new password system and application feasibility and correctness.