Since their proof is not composable, we revisit it using a universally composable framework. It turns out that the above argument is insufficient: information about the hash function is in fact leaked in every round to the adversary, and after a bounded finite amount of rounds it is completely known. We show however that this leak is very small, and Wegman and Carter's protocol is still $\epsilon$-secure, if $\epsilon$-almost strongly universal hash functions are used. This implies that the secret key corresponding to the choice of hash function can be recycled for any task without any additional error than this $\epsilon$.
We illustrate this by applying it to quantum key distribution (QKD): if the same hash function is recycled to authenticate the classical communication in every round of a QKD protocol, and used $\ell$ times per round, the total error after $r$ rounds is upper bounded by $r(\ell\epsilon+\epsilon')$, where $\epsilon'$ is the error of one round of QKD given an authentic channel.Category / Keywords: secret-key cryptography / authentication, composability Date: received 7 Feb 2012, last revised 31 May 2012 Contact author: chportma at gmail com Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Note: Corrected typos, updated introduction and references. Version: 20120531:105554 (All versions of this report) Discussion forum: Show discussion | Start new discussion