# Where is defined the fact of having a “learning” and “challenge” phase in cryptography proofs?

I've read Bellare and Rogaway 2004 and Shoup 2004 about game-based cryptography proofs, but I lack precisions about how should be built the "learning" and "challenge" phases, since my games will probably have this structure.

And what are they suppose to provide anyway ? Security against Adaptive adversaries ? The games I have read are like:

• learning phase: do whatever you're allowed to do
• challenge phase: submit two challenge sets, read what the oracle send you back and guess which set has been chosen

Yet adaptive adversary should mean (citing wikipedia) ciphertexts may be chosen adaptively before and after a challenge ciphertext is given to the attacker

As an example, assume you have a security definition where you want the attacker to get access to $n$ ciphertexts corresponding to some plaintexts $p_1,\ldots,p_n$. If you want a non-adaptive adversary, you define your game to contain an oracle that will take as input $n$ plaintexts and which will return $n$ corresponding ciphertexts and allow only one query. If you want an adaptive adversary, then you would provide a single oracle that takes a plaintext and returns a ciphertext, but which allows itself to be queried $n$ times.