Privacy amplification of distributed encrypted sources with correlated keys

Abstract

In this paper, we consider a system where multiple sources are encrypted in separated nodes and sent through their respective public communication channels into a joint sink node. We are interested at the problem on protecting the security of an already existing system such above, which is found out to have correlated encryption keys. In particular, we focus on finding a solution without introducing additional secret keys and with minimal modification to minimize the cost and the risk of bringing down an already running system. We propose a solution under a security model where an eavesdropper obtains all ciphertexts, i.e., encrypted sources, by accessing available public communication channels. Our main technique is to use encoders of certain linear codes to encode the ciphertexts before sending them to public communication channels. We show that if the rates of linear codes are within a certain rate region: (1) the success probability of any eavesdropper to extract the original sources from the encoded ciphertexts without the keys is negligible, while (2) one who has legitimate keys is able to retrieve the original source data with negligible error probability.