Formalization of information-theoretic security for key agreement, revisited

In this paper, we investigate relationships between the following formalizations of information-theoretic security for key agreement protocols which may have agreement-errors: formalizations extended (or relaxed) from Shannon´s perfect secrecy by using mutual information and statistical distance; and the ones of composable security by Maurer et al. and Canetti. Then, we explicitly show that those are essentially equivalent. We also derive lower bounds on the adversary´s (or distinguisher´s) advantage and the size of a correlated randomness resource required under all of the above formalizations at once through our relationships. In addition, we observe impossibility results which easily follow from the lower bounds.