Relations between semantic security and indistinguishability against cpa, non-adaptive cca and adaptive cca in comparison based framework

In this paper we try to unify the frameworks of definitions of semantic security, indistinguishability and non-malleability by defining semantic security in comparison based framework. This facilitates the study of relations among these goals against different attack models and makes the proof of the equivalence of semantic security and indistinguishability easier and more understandable. Besides, our proof of the equivalence of semantic security and indistinguishability does not need any intermediate goals such as non devidability to change the definition framework.