Privacy amplification theorem for bounded storage eavesdropper

In this paper, we consider a situation such that legitimate parties, Alice and Bob, share an identical source to generate a secret key, and an eavesdropper, Eve, can access a correlated data that is stored in a storage with bounded size. Then, Alice and Bob want to extract a secret as long as possible. We show a privacy amplification theorem for this problem, i.e., we clarify the rate of key generation for given rate of Eve's storage. The problem can be regarded as a dual randomness generation problem of the Wyner-Ahlswede-Körner type source coding system, and the techniques used in the proof are exchanged, i.e., the so-called Markov lemma is used in the converse part, and the so-called image size characterization is used in the direct part.