2012/06/30 by Nihar B. Shah, Shah, Nihar B., K. V. Rashmi +3
Computer Science · Mathematics · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.CR #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1207.0120
Extended version of a paper presented at the International Symposium on Information Theory (ISIT) 2013
arxiv created 2014/10/22 · arxiv updated 2014/10/23
Shamir's (n, k) threshold secret sharing is an important component of several cryptographic protocols, such as those for secure multiparty-computation and key management. These protocols typically assume the presence of direct communication links from the dealer to all participants, in which case the dealer can directly pass the shares of the secret to each participant. In this paper, we consider the problem of secret sharing when the dealer does not have direct communication links to all the participants, and instead, the dealer and the participants form a general network. Existing methods are based on secure message transmissions from the dealer to each participant requiring considerable coordination in the network. In this paper, we present a distributed algorithm for disseminating shares over a network, which we call the SNEAK algorithm, requiring each node to know only the identities of its one-hop neighbours. While SNEAK imposes a stronger condition on the network by requiring the dealer to be what we call k-propagating rather than k-connected as required by the existing solutions, we show that in addition to being distributed, SNEAK achieves significant reduction in the communication cost and the amount of randomness required.