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I'm reading A Practical Public Key Cryptosystem Provably Secure against Adaptive Chosen Ciphertext Attack and here define Semantic Security ...

Semantic security, dened by Goldwasser and Micali [14], captures the intu- ition that an adversary should not be able to obtain any partial information about a message given its encryption. However, this guarantee of secrecy is only valid when the adversary is completely passive,

but in the abstract of other paper Semantically Secure McEliece Public-Key Cryptosystems –Conversions for McEliece PKC say

we propose slightly modified versions of McEliece PKC that can be proven, in the random oracle model, to be semantically secure against adaptive chosen-ciphertext attacks.

I'm confusing Why if semantic security is for passive attacks exists the term "secure against adaptive chosen-ciphertext attacks", when Adaptative Chosen ciphertext attack is a model to active attacks?

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The initial notion of semantic security from Goldwasser and Micali has been shown to be euqivalent to what we call today indistinguishability under chosen plaintext attacks (IND-CPA). Yes that's only security against a passive adversary and actually the weakest reasonable security notion that we use today.

The authors of the second paper you link seem to use the term semantically secure in a slightly misleading way in the cited part of the paper. What they actually mean is a much stronger notion which is better known as indistinguishability under adaptively chosen ciphertext attacks (IND-CCA2), which covers active adversaries.

However, this "wording" the authors are using seems to be used by various authors in the way that semantically secure against is seen to be equal to providing indistinguishability under. Also, it is common that when only saying semantically secure, then one means IND-CPA, i.e., a passive adversary. But if one says semantically secure against (adaptively) chosen message attacks, then (IND-CCA1) IND-CCA2 is meant, i.e., an active adversary.

If you read in some parts of the remainder of the second paper you cite from, you will find the correct use:

Under the assumption that this inverting problem is hard, we investigated, in the random oracle mode, how to convert this hard problem into the hard problem of breaking the indistinguishability of encryption with CCA2.

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then actually the word "semantically secure" is not only for passive attacks ... –  juaninf Mar 11 at 20:26
    
@juanif actually, it is a "slight abuse of notation". if you only say semantically secure, then IND-CPA is meant, i.e., a passive adversary. But if you say semantically secure against (adaptively) chosen message attacks, then (IND-CCA1) IND-CCA2 is meant, i.e., an active adversary. –  DrLecter Mar 11 at 20:29

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