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From Lewko, I understand the difference between an adaptive and selective model:

  1. Adaptive model: the attacker can adaptively query the challenger for private keys.
  2. Selective model: the attacker has to declare the challenge message BEFORE he can see the public parameters setup.

Now comes to Rouselakis with static model:

All queries done by the attacker are sent to the challenger immediately after seeing the public parameters.

This is what I understand: After seeing the public parameters, the attacker sends a batch of requests to the challenger, and the challenger replies a batch of responses.

Q1: The word "immediately" confuses me. Why immediately after seeing the public parameters?

Q2: How "weaker" is static model than the adaptive model? Can anyone give an example that the attacker can break this scheme by sending "adaptive" requests to the challenger (but not all requests in one patch)?

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Towards Q1 -- immediately should just mean that the adversary has no more information as the public parameters (so it doesn't have to be "few seconds" but. "without any intermediate messages")

Towards Q2 -- assume you have some system with a weakness like the following: If you get to send an valid encryption to the challenger, the challenger responds with the master key. You won't be able to exploit that in the static model (with overwhelming probability) but in the adaptive case it's easy

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  • $\begingroup$ Many thanks @ChristophEgger now I understand question 1. But can you explain more about "If you get to send an valid encryption to the challenger, the challenger responds with the master key." for the case of Rouselakis? I do not quite understand why the challenger responds with the master key. Normally, the challenger only responds with secret keys... I am a beginner but am willing to understand it. $\endgroup$ – Tri Vo Hoang Nov 4 '18 at 20:52

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