Is semantic security equivalent to IND-CPA?
If a PKE scheme like ElGamal is semantically secure, can we say it is IND-CPA?
What's the relationship between semantic security and IND-CPA?
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$\begingroup$ TL;DR: In my understanding a scheme is semantically secure under a specific attack scenario. Commonly when semantic security is mentioned without indicating the scenario then it probably comes down to IND-CPA, but I'd check the context. You might say that semantic security covers the IND part of IND-XXX :P Not posting this as an answer, as I hope that a more canonical answer is possible. $\endgroup$– Maarten Bodewes ♦Commented Apr 25 at 13:16
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$\begingroup$ Interestingly, I couldn't find a dupe of this basic question, that closes is this Why is "semantically secure" important for cryptosystems?. It is so basic that almost all modern books cover this. $\endgroup$– kelalakaCommented Apr 25 at 18:03
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1$\begingroup$ Semantic security is equivalent to IND-CPA security for public key encryption (PKE), as mentioned in @Mahesh S R's answer. But in more advanced forms of PKE, like functional encryption, these concepts of security are NOT equal. Semantic security for FE is stronger than IND-CPA security IACR 2010/556 and IACR 2010/543. $\endgroup$– user1035648Commented Apr 29 at 8:45
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Goldwasser and Micali showed that semantic security-CPA and IND-CPA and equivalent. In-fact Watanabe et al. (see figure 1) showed that semantic security and indistinguishability are equivalent under any form of attack.
