What does it mean when we say something like „we need more than polynomial time many cipher texts“? I understand it as „an adversarial can run for polynomial time and try as many messages as possible in an exhaustive search on our encoded message in this time. We need more messages than the maximum the adversarial can reach in this time frame“.
- is this a correct understanding?
- can we specify the size of the set of messages more concretely, maybe in a formula that depends on the polynomial? Or does this not make sense here?
- And what does it mean if we need „more than polynomial, for example exponential time many messages“? How many messages would that be?
For context: I am watching the lecture of Shafi Goldwasser on basics of cryptography. She uses this phrase in this lecture around the notion of computational indistinguishability (see link below).
Edit: see around minute 39:
https://youtu.be/7YfYYIvyYb8?si=hrH73yDpkCuGb9W9
PS this is my first post, please let me know if I do something wrong.
