Distributed Secret Dissemination Across a Network

TL;DR

This paper introduces SNEAK, a distributed algorithm for secret sharing over networks that reduces communication costs and randomness by requiring only local neighbor knowledge, suitable for networks where the dealer lacks direct links to all participants.

Contribution

The paper presents SNEAK, a novel distributed secret dissemination algorithm that operates efficiently over general networks with minimal network knowledge, improving upon existing methods.

Findings

SNEAK reduces communication cost compared to traditional methods.

SNEAK requires only local neighbor information, simplifying network coordination.

The algorithm achieves secure secret sharing in networks with a stronger network condition.

Abstract

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.