A key-recovery attack is an adversary's attempt to recover the cryptographic key of an encryption scheme.
[1]: 52 Historically, cryptanalysis of block ciphers has focused on key-recovery, but security against these sorts of attacks is a very weak guarantee since it may not be necessary to recover the key to obtain partial information about the message or decrypt message entirely.
Consequently, the maximum key-recovery advantage attainable by any algorithm with a fixed amount of computational resources is a measure of how difficult it is to recover a cipher's key.
It is defined as the probability that the adversary algorithm can guess a cipher's randomly selected key, given a fixed amount of computational resources.
[3] An extremely low KR advantage is essential for an encryption scheme's security.