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I notice that in many research papers (viz. "Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption" by Cramer and Shoup) the authors showed that their cryptosystem is IND-CCA secure under standard model. What does it mean? What does an adversary have access to in a challenger-adversary game?

Actually, my aim is to get a clear idea on IND-CCA secure under standard model. I am confused on the statemant like "The given public key cryptosystem is IND-CCA secure under Diffie-Hellman assumption ". Is this statemant means that this particuler cryptosystem is IND-CCA secure under standard model?

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    $\begingroup$ If your question changed please consider asking a new one rather than editing your current, especially if it invalidates answers. $\endgroup$
    – SEJPM
    Apr 18, 2016 at 18:19

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Your questions can be split in two:

  1. What is the meaning of IND-CCA secure? What have an adversary access in a challenger-adversary game?

This basically means that the scheme achieves the indistinguishability notion, even if an attacker has access to a decryption oracle. See Easy explanation of "IND-" security notions? for more detail on this.

  1. What is the standard model?

This simply means that no additional assumptions are made for proving the security of the scheme. You see, a lot of crypto proofs require additional assumptions. For example, one of the most used is the Random Oracle Model, which assumes the existence of an ideal hash function that guarantees uniformly-random outputs. Proofs in the standard model are therefore considered more desirable.

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    $\begingroup$ It may also be worth reading about the controversies around random oracles. The random sponge model is supposed to be closer to reality, and thus proofs in the random sponge model are more likely to hold. But it seems there is no prior question on this site about the exact differences between the random sponge and random oracle model. $\endgroup$
    – kasperd
    Apr 14, 2016 at 9:15

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