Privacy-Preserving Distributed Average Consensus based on Additive Secret Sharing

One major concern of distributed computation in networks is the privacy of the individual nodes. To address this privacy issue in the context of the distributed average consensus problem, we propose a general, yet simple solution that achieves privacy using additive secret sharing, a tool from secure multiparty computation. This method enables each node to reach the consensus accurately and obtains perfect security at the same time. Unlike differential privacy based approaches, there is no trade-off between privacy and accuracy. Moreover, the proposed method is computationally simple compared to other techniques in secure multiparty computation, and it is able to achieve perfect security of any honest node as long as it has one honest neighbour under the honest-but-curious model, without any trusted third party.

[1]  Soummya Kar,et al.  Gossip Algorithms for Distributed Signal Processing , 2010, Proceedings of the IEEE.

[2]  M. Johansson,et al.  Faster Linear Iterations for Distributed Averaging , 2008 .

[3]  George Danezis,et al.  Privacy-Friendly Aggregation for the Smart-Grid , 2011, PETS.

[4]  Andrew Chi-Chih Yao,et al.  Protocols for secure computations , 1982, FOCS 1982.

[5]  Xinping Guan,et al.  Privacy-Preserving Average Consensus: Privacy Analysis and Algorithm Design , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[6]  B.H. Khalaj,et al.  Secure consensus averaging in sensor networks using random offsets , 2007, 2007 IEEE International Conference on Telecommunications and Malaysia International Conference on Communications.

[7]  Richard M. Murray,et al.  Privacy preserving average consensus , 2014, 53rd IEEE Conference on Decision and Control.

[8]  J. Dall,et al.  Random geometric graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Mauro Barni,et al.  Encrypted signal processing for privacy protection: Conveying the utility of homomorphic encryption and multiparty computation , 2013, IEEE Signal Processing Magazine.

[10]  Jorge Cortés,et al.  Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design , 2015, Autom..

[11]  Richard C. Hendriks,et al.  Privacy preserving distributed beamforming based on homomorphic encryption , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[12]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[13]  Peter Richtárik,et al.  Privacy preserving randomized gossip algorithms , 2017, 1706.07636.

[14]  Paolo Braca,et al.  Learning With Privacy in Consensus $+$ Obfuscation , 2016, IEEE Signal Processing Letters.

[15]  A. Yao,et al.  Fair exchange with a semi-trusted third party (extended abstract) , 1997, CCS '97.

[16]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[17]  Ivan Damgård,et al.  Secure Multiparty Computation and Secret Sharing , 2015 .

[18]  Santiago Segarra,et al.  Optimal Graph-Filter Design and Applications to Distributed Linear Network Operators , 2017, IEEE Transactions on Signal Processing.

[19]  Ιωαννησ Τσιτσικλησ,et al.  PROBLEMS IN DECENTRALIZED DECISION MAKING AND COMPUTATION , 1984 .

[20]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[21]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[22]  Ivan Damgård,et al.  Multiparty Computation from Somewhat Homomorphic Encryption , 2012, IACR Cryptol. ePrint Arch..

[23]  Geir E. Dullerud,et al.  Differentially private iterative synchronous consensus , 2012, WPES '12.

[24]  M. Degroot Reaching a Consensus , 1974 .

[25]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[26]  Richard Heusdens,et al.  Distributed Optimization Using the Primal-Dual Method of Multipliers , 2017, IEEE Transactions on Signal and Information Processing over Networks.

[27]  Richard C. Hendriks,et al.  Privacy-preserving distributed speech enhancement forwireless sensor networks by processing in the encrypted domain , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[28]  Soummya Kar,et al.  Finite-time distributed consensus through graph filters , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[29]  Paolo Braca,et al.  Secure multi-party consensus gossip algorithms , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[30]  Cynthia Dwork,et al.  Differential Privacy , 2006, ICALP.

[31]  Christoforos N. Hadjicostis,et al.  Privacy-preserving asymptotic average consensus , 2013, 2013 European Control Conference (ECC).