Abstract: Our definition of semantic security was introduced,and we tried to integrate the frameworks of definitions of semantic security, non-distinguishability and non-expandability by analysing semantic security in comparison based framework. This facilitates the study of relations among these goals against different attack models, and we made a slightly modified definition of classifying based on comparison and then we studied our proof of equation of semantic security and classifying in the new framework. This way makes the proof of the equation of semantic security and non-dis-tinguishability easier and more understandable.

Key words: Information security, Semantic frame, Information space, Encryption, Equation