Finite Field Theory In The Design Of New Key Exchange Technology

Nowadays, the computer network technology and the information technology have been getting more and more important. How to assure the information security is one of the most important fields. At present, much information security depends on the cryptography. As a branch of it, key exchange is a very important subject in the information security. People want to communicate securely with each other through non-security channel, the establishment of session key is very critical. Therefore, research on key exchange protocol is important both in theory signification and application. In this paper, we study the key exchange protocol based on finite field.The main contributions of the paper are listed as follows:(1) Investigate the numerical algorithm of the multi-modulus system of linear equations, analyzed and summarized the Diffie-Hellman key exchange technology and the key exchange techniques based on generalized inverse matrix.(2) Study the commutator of the group theory, design a new key exchange protocol based on the commutator, in order to share a session key between two or more parties, the security of the protocol depends on whether can solve the conjugate problem.(3) Further, we study the p-commutator theory of the group theory, put forward the concept of p-conjugate, design a key exchange protocol based on p-commutator theory, the numerical examples are given to verify the agreement is correct and feasible.(4) Define the concept of multi-modular matrix equation and obtained a numerical solution of the equation. Based on the idea of D-H key exchange, design a key exchange scheme based on the multi-modular matrix equation. At last, a numerical example is given to test and verify the numerical solution and the key exchange scheme.