Verification of Peer-to-peer Algorithms: A Case Study

Abstract

The problem of maintaining structured peer-to-peer (P2P) overlay networks in the presence of concurrent joins and failures of nodes is the subject of intensive research. The various algorithms underlying P2P systems are notoriously difficult to design and analyse. Thus, when verifying P2P algorithms, a real challenge is to find an adequate level of abstraction at which to model the algorithms and perform the verifications. In this paper, we propose an abstract model for structured P2P networks with ring topology. Our model is based on process algebra, which, with its well-developed theory, provides the right level of abstraction for the verification of many basic P2P algorithms. As a case study, we verify the correctness of the stabilization algorithm of Chord, one of the best-known P2P overlay networks. To show the correctness of the algorithm, we provide a specification and an implementation of the Chord system in process algebra and establish bisimulation equivalence between the two.

A Mechanized Model for CAN Protocols

“…no churn) using CCS, a process algebra. In a subsequent work, Bakshi et al [1] used π-calculus to prove the correctness properties of Chord in the pure-join model of the protocol. Zave, in her work [19] proved the Chord protocol in its two models: the pure-join and full, using the Alloy analyzer.…”

“…Building high-assurance distributed applications which are correct remains a very difficult challenge but various methods have emerged over the years to tackle it [1,2,5,11,19]. Theorem proving seems to be among the best method to prove generic properties on distributed systems of arbitrary size; in particular verification techniques based on model-checking are, in general, limited to systems of a predefined size and suffer from combinatorial explosion.…”

Formal Specification of the Kademlia and the Kad Routing Tables in Maude

“…Bakhshi and Gurov give in [1] a formal verification of Chord's stabilization algorithm using the π-calculus. Lately Lu, Merz, and Weidenbach [3] have…”

Verifying Security Property of Peer-to-Peer Systems Using CSP

“…They verify that the routing protocol in DKS, under the static case (when no node joining or leaving), is correct. Bakhshi et al [16] model Chord in π-calculus and verify that the stabilization protocol in Chord is correct.…”