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This paper defines perfect security against side channel attacks for a cryptosystem implementation, and discusses the implication of secure notions for a cryptosystem in provable security. Then we give some security notions for symmetric encryption against side channel attacks, UB-SCA (unbreakability in side channel attacks) and IND-CPA-SCA (indistinguishability of chosen plaintext attacks and side channel attacks). On the basis of these definitions, we propose and prove that IND-CPA + UB-SCA ⇒ IND-CPA-SCA by reduction, and IND-CPA-SCA is stronger than IND-CPA or UB-SCA.