A new approach on cryptanalysis is proposed where the goal is to explore the fundamental limits of a specific class of attacks against a particular cryptosystem. As a first step, the approach is applied on ABSG, which is an LFSR-based stream cipher where irregular decimation techniques are utilized. Consequently, under some mild assumptions, which are common in cryptanalysis, the tight lower bounds on the algorithmic complexity of successful Query-Based Key-Recovery attacks are derived for two different setups of practical interest. The proofs rely on the concept of ``typicality'' of information theory.