From Lewko, I understand the difference between an adaptive and selective model:
- Adaptive model: the attacker can adaptively query the challenger for private keys.
- 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)?