QKD secrecy for privacy amplification matrices with selective individual attacks

A customary solution for privacy amplification in practical QKD systems is to use randomly generated binary (Toeplitz) matrices. In the literature, the security of such a solution is usually justified by invoking an information theoretic bound for which: 1) the eavesdropper is assumed to have learned exactly (or at most) t bits of information from the reconciled key; and 2) the measure of information leakage is taken as average over all possible realizations of the privacy amplification matrix. We derive the information leakage for statistical knowledge of the eavesdropper attack and for fixed realizations of the hashing matrix used for privacy amplification