A "secret sharing system" permits a secret to be shared among n trustees in such a way that any k of them can recover the secret, but any k-1 have complete uncertainty about it. A linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by Shamir and can also be viewed as a deterministic version of Blakley's probabilistic method. Bounds on the maximum value of n for a given k and secret size are derived for any system, linear or nonlinear. The proposed scheme achieves the lower bound which, for practical purposes, differs insignificantly from the upper bound. The scheme may be extended to protect several secrets. Methods to protect against deliberate tampering by any of the trustees are also presented.

/pdf/on-secret-sharing-systems-59gndgfqve.pdf

On secret sharing systems

A unified approach to the formal description and validation of several distributed protocols is presented. After introducing two basic protocols, a series of known and new protocols for connectivity test, shortest path, and path updating are described and validated. All protocols are extended to networks with changing topology.

Distributed network protocols

An algorithm that provides minimum delay routing in a data communication network using virtual line-switching is presented. The algorithm uses distributed computation in the sense that the nodes of the network update their information in an orderly fashion based on messages received from their neighbors. Receipt of these messages also triggers the various steps of the update and rerouting, so that these operations are performed in appropriate sequencing. For stationary input requirements and fixed topology the algorithm reduces network delay at each step and provides loop-free routing in the network. The method also provides an algorithm for quasi-static routing, when the input flows are slowly changing.

/pdf/optimal-distributed-routing-for-virtual-line-switched-data-3c8zbdcy1p.pdf

Optimal Distributed Routing for Virtual Line-Switched Data Networks

Two new versions of a distributed protocol for establishing and maintaining loop-free routing tables for communication networks with changing topology are presented. The protocols here possess significant advantages over previous versions in terms of complexity of the node algorithm and of the validation procedure, as well as the communication and storage needs. In addition, we present a procedure for establishing new and disrupted calls in a virtual or physical circuit-switched network, and for canceling existing calls, such that each call is loop-free and is established according to the routing tables provided by the protocol.

Advances in Verifiable Fail-Safe Routing Procedures

This article presents three protocols for obtaining maximum flow in a network by using distributed computation. Each node in the network has memory and processing capabilities and coordinates the algorithm with its neighbors by means of control messages. In the order presented, each protocol employs less communication than the previous one, but requires more time and node computation.

Decentralized maximum‐flow protocols

An algorithm fQr adaptive routing in data-conmunication networks is presented. The algorithm uses distributed computation, provides loop-fre_ routing for each destination in the network, adapts to changes in network flows and is completely failsafe. The latter means that after arbitrary failures and additions of nodes and links, the network recovers in finite time in the sense of providing routing paths between all physically connected nodes. Proofs of all these properties are provided in a separate paper.

R. G. Gallager

Papers

A recoverable protocol for loop-free distributed routing