Privacy preserving distributed optimization using homomorphic encryption

This paper studies how a system operator and a set of agents securely execute a distributed projected gradient-based algorithm. In particular, each participant holds a set of problem coefficients and/or states whose values are private to the data owner. The concerned problem raises two questions: how to securely compute given functions; and which functions should be computed in the first place. For the first question, by using the techniques of homomorphic encryption, we propose novel algorithms which can achieve secure multiparty computation with perfect correctness. For the second question, we identify a class of functions which can be securely computed. The correctness and computational efficiency of the proposed algorithms are verified by two case studies of power systems, one on a demand response problem and the other on an optimal power flow problem.Comment: 24 pages, 5 figures, journa

Insecurity of Transformation-Based Privacy-Preserving Linear Programming

Rakendusmatemaatikat kasutatakse paljudes reaalse maailma probleemides. Nende probleemide lahendamine võib olla seotud tundlike andmetega. Sellisel juhul läheb tarvis krüptograafilisi meetodeid. Kuigi on tõestatud, et iga funktsiooni saab arvutada turvaliselt, on küsimus selles, kuidas teha seda efektiivselt. Üldiselt võib olla keeruline lahendada optimeerimisülesandeid nii turvaliselt kui ka efektiivselt, kuid häid lahendeid saab leida kitsamatele ülesannete klassidele, näiteks lineaarse planeerimise ülesannetele. Käesolev töö annab ülevaate teisenduspõhisest privaatsust säilitavast lineaarsest planeerimisest, tutvustades mõningaid probleeme eelmistes töödes ja näidates teisenduspõhise meetodi ebaturvalisust. Töö esitab konkreetseid ründeid olemasolevate teisendusmeetodite vastu. Töös pakutakse välja võimalikud viisid nende rünnete eest kaitsmiseks ja seejärel näidatakse, et mõned teisenduspõhise meetodi puudused ei ole üldse ületatavad, vähemalt eelmistes töödes kasutatud teatud teisenduste klassi raamesse jäädes.Applied mathematics is used in many real-world problems. Solving some of these problems may involve sensitive data. In this case, cryptographic techniques become necessary. Although it has been proven that any function can be computed securely, it is still a question how to do it efficiently. While it may be difficult to solve optimization tasks securely and efficiently in general, there may still be solutions for some particular classes of tasks, such as linear programming. This thesis gives an overview of the transformation-based privacy-preserving linear programming. The thesis introduces some problems of this approach that have been present in the previous works and demonstrates its insecurity. It presents concrete attacks against published methods following this approach. Possible methods of protection against these attacks are proposed. It has been proven that there are issues that cannot be resolved at all using the particular known class of efficient transformations that has been used before

Privacy-Preserving Outsourcing of Large-Scale Nonlinear Programming to the Cloud

The increasing massive data generated by various sources has given birth to big data analytics. Solving large-scale nonlinear programming problems (NLPs) is one important big data analytics task that has applications in many domains such as transport and logistics. However, NLPs are usually too computationally expensive for resource-constrained users. Fortunately, cloud computing provides an alternative and economical service for resource-constrained users to outsource their computation tasks to the cloud. However, one major concern with outsourcing NLPs is the leakage of user's private information contained in NLP formulations and results. Although much work has been done on privacy-preserving outsourcing of computation tasks, little attention has been paid to NLPs. In this paper, we for the first time investigate secure outsourcing of general large-scale NLPs with nonlinear constraints. A secure and efficient transformation scheme at the user side is proposed to protect user's private information; at the cloud side, generalized reduced gradient method is applied to effectively solve the transformed large-scale NLPs. The proposed protocol is implemented on a cloud computing testbed. Experimental evaluations demonstrate that significant time can be saved for users and the proposed mechanism has the potential for practical use.Comment: Ang Li and Wei Du equally contributed to this work. This work was done when Wei Du was at the University of Arkansas. 2018 EAI International Conference on Security and Privacy in Communication Networks (SecureComm

Practical Privacy-Preserving Multiparty Linear Programming Based on Problem Transformation

International audienceCryptographic solutions to privacy-preserving multi-party linear programming are slow. This makes them unsuitable for many economically important applications, such as supply chain optimization, whose size exceeds their practically feasible input range. In this paper we present a privacy-preserving transformation that allows secure outsourcing of the linear program computation in an efficient manner. We evaluate security by quantifying the leakage about the input after the transformation and present implementation results. Using this transformation, we can mostly replace the costly cryptographic operations and securely solve problems several orders of magnitude larger