Distributed Sequential Consensus in Networks: Analysis of Partially Connected Blockchains with Uncertainty

This work presents a theoretical and numerical analysis of the conditions under which distributed sequential consensus is possible when the state of a portion of nodes in a network is perturbed. Specifically, it examines the consensus level of partially connected blockchains under failure/attack events. To this end, we developed stochastic models for both verification probability once an error is detected and network breakdown when consensus is not possible. Through a mean field approximation for network degree we derive analytical solutions for the average network consensus in the large graph size thermodynamic limit. The resulting expressions allow us to derive connectivity thresholds above which networks can tolerate an attack.

[1]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[2]  M. Draief,et al.  Distributed Binary Consensus in Dynamic Networks , 2013, ISCIS.

[3]  Doug Terry,et al.  Epidemic algorithms for replicated database maintenance , 1988, OPSR.

[4]  Alessandro Vespignani.  Modelling dynamical processes in complex socio-technical systems , 2011, Nature Physics.

[5]  Christian Decker,et al.  Information propagation in the Bitcoin network , 2013, IEEE P2P 2013 Proceedings.

[6]  Stefan Seebacher,et al.  Blockchain Technology as an Enabler of Service Systems: A Structured Literature Review , 2017, IESS.

[7]  Hamed Mohsenian-Rad,et al.  Dynamic Load Altering Attacks Against Power System Stability: Attack Models and Protection Schemes , 2017, IEEE Transactions on Smart Grid.

[8]  R. Monasson.  Diffusion, localization and dispersion relations on “small-world” lattices , 1999 .

[9]  Praveen Gauravaram,et al.  Blockchain for IoT security and privacy: The case study of a smart home , 2017, 2017 IEEE International Conference on Pervasive Computing and Communications Workshops (PerCom Workshops).

[10]  Holger Paul Keeler,et al.  Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay , 2015, Perform. Evaluation.

[11]  Emin Gün Sirer,et al.  Majority Is Not Enough: Bitcoin Mining Is Vulnerable , 2013, Financial Cryptography.

[12]  Jürgen Scheffran.  The complexity of security , 2008 .

[13]  Priyanka More,et al.  Privacy Preserving Data Analytics for Smart Homes , 2015 .

[14]  S. Redner,et al.  Voter models on heterogeneous networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Hubert Ritzdorf,et al.  On the Security and Performance of Proof of Work Blockchains , 2016, IACR Cryptol. ePrint Arch..

[16]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[17]  Francisco Prieto Castrillo,et al.  A Stochastic Process Approach to Model Distributed Computing on Complex Networks , 2014, Journal of Grid Computing.

[18]  Roger Wattenhofer,et al.  The Science of the Blockchain , 2016 .

[19]  Rachid Guerraoui,et al.  Consensus in Asynchronous Distributed Systems: A Concise Guided Tour , 1999, Advances in Distributed Systems.

[20]  Javier Bajo,et al.  Self-Organizing Architecture for Information Fusion in Distributed Sensor Networks , 2015, Int. J. Distributed Sens. Networks.

[21]  Keith Marzullo,et al.  Synchronous Consensus for dependent process failures , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[22]  Gil Baram,et al.  Critical Infrastructures and their Interdependence in a Cyber Attack – The Case of the U . , 2015 .

[23]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[24]  Yaneer Bar-Yam.  New England Complex Systems Institute series on complexity , 2000 .

[25]  Richard M. Karp,et al.  Randomized rumor spreading , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[26]  Rodrigo Roman,et al.  On the features and challenges of security and privacy in distributed internet of things , 2013, Comput. Networks.

[27]  Luigi Alfredo Grieco,et al.  Security, privacy and trust in Internet of Things: The road ahead , 2015, Comput. Networks.

[28]  Rodgers,et al.  Diffusion in a sparsely connected space: A model for glassy relaxation. , 1988, Physical review. B, Condensed matter.