The password agreement method based on matrix operation over Min-Plus algebra for safety of secret information sending

Abstract

Key agreement protocol is a method in cryptography. Key agreement protocol is used to overcome the problem of sending secret information over communication lines. A secret key, called password, is needed to secure t he information. Both parties who exchange confidential information must agree on the same key. In this method, both parties exchange mutual general parameters that everyone can see, however from the general parameters the same passwords can be formed and not publicly known. One method that has been used is applying a series of matrix multiplication operation defined over a finite field. In this study, we constructed an algorithm in the form of a key agreement protocol that can be used in the password agreement method which the level of security based on algebraic problem of matrix operation over Z- min plus algebra. Min Plus algebra over Z, that is Z È { + ¥ } with Z is the set of all integers equipped with the minimum and addition operation,  is called idempotent semiring. The results showed that the application of matrix operation over min plus algebra can be used as key agreement protocol in securing secret information.

Key words: secret information, password, Min-Plus algebra