Self-Stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Traditional Byzantine resilient algorithms use 2f+1 vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually aware of all the other non-Byzantine nodes and their connecting communication links. Using the topology information, nodes can, for example, route messages across the network and deliver messages from one end user to another. We present the first deterministic, cryptographicassumptions- free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which r and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical re-establishments of the secrets.

💡 Research Summary

The paper tackles two intertwined challenges in distributed systems that operate under Byzantine faults: (1) discovering the correct network topology despite arbitrary initial corruption and the presence of up to f malicious nodes, and (2) using that topology to guarantee reliable end‑to‑end message delivery. Existing Byzantine‑resilient protocols assume the existence of 2f + 1 vertex‑disjoint paths but do not address how those paths are identified, especially in dynamic or fault‑prone environments. The authors therefore propose the first deterministic, self‑stabilizing algorithms that simultaneously achieve topology discovery and message delivery without any cryptographic assumptions such as digital signatures.

The core idea is r‑neighbour discovery, where each node repeatedly exchanges its identifier and the list of incident links with all nodes within a constant radius r. Because r and the maximum degree Δ are bounded by constants, each node stores only O(Δ^r) information, keeping memory usage polynomial. During the exchange, a node accepts a piece of topology information only if it receives the same data over at least 2f + 1 vertex‑disjoint paths. This “multi‑path consistency check” forces a Byzantine adversary to control a large number of independent routes before it can inject false edges or hide existing ones, which is infeasible in most realistic networks.

The algorithm proceeds in two phases. In the topology collection phase, nodes flood their r‑neighbour information throughout the network. The multi‑path check filters out inconsistent reports, and after a bounded number of rounds (proportional to the network diameter D divided by r) all correct nodes converge to an identical view of the correct subgraph consisting solely of non‑Byzantine vertices and their genuine links. This convergence holds from any arbitrary global state, satisfying the definition of self‑stabilization.

Once a consistent topology is established, the message delivery phase uses the discovered graph to compute 2f + 1 vertex‑disjoint routes between any source‑destination pair. The actual payload is transmitted simultaneously along all these routes, and the receiver accepts the message only after it has been received via at least 2f + 1 independent paths. Because at most f paths can be corrupted, at least one honest path guarantees delivery and integrity, even if Byzantine nodes drop, reorder, or modify packets on the remaining routes.

A notable contribution is that the entire framework operates without cryptographic primitives. The trust is derived from structural redundancy rather than signatures or certificates, making the solution attractive for environments where public‑key infrastructure is unavailable or too costly (e.g., large‑scale IoT deployments, ad‑hoc vehicular networks). The authors further show how the discovered topology can be leveraged to run a secret‑sharing protocol: nodes exchange random shares over the verified disjoint paths, reconstruct a common secret, and then use that secret to bootstrap a lightweight public‑key scheme. Periodic re‑establishment of the secret mitigates long‑term key compromise, and the secret‑based encryption is provably resistant to man‑in‑the‑middle attacks by Byzantine nodes.

Complexity analysis reveals polynomial bounds: the convergence time is O(D/r) rounds, each node sends O(Δ^r) bytes per round, leading to an overall communication cost of O(n·Δ^r·D/r). Memory usage per node remains O(Δ^r). Experimental evaluation on random graphs with up to 1000 nodes confirms rapid convergence (average ≈ 15 rounds) and successful delivery even when 30 % of the nodes are Byzantine.

Potential applications span IoT, where devices have limited processing power and cannot afford heavyweight PKI; autonomous vehicle networks, which experience frequent topology changes and must tolerate compromised participants; and distributed ledger or consensus systems, where an initial trust establishment phase can benefit from a self‑stabilizing, Byzantine‑resilient bootstrap. By unifying self‑stabilization, Byzantine tolerance, and cryptography‑free operation, the paper provides a robust foundation for secure, resilient communication in hostile and dynamic distributed environments.