Fog computing is transforming the network edge into an intelligent platform by bringing storage, computing, control, and networking functions closer to end-users, things, and sensors. How to allocate multiple resource types (e.g., CPU, memory, bandwidth) of capacity-limited heterogeneous fog nodes to competing services with diverse requirements and preferences in a fair and efficient manner is a challenging task. To this end, we propose a novel market-based resource allocation framework in which the services act as buyers and fog resources act as divisible goods in the market. The proposed framework aims to compute a market equilibrium (ME) solution at which every service obtains its favorite resource bundle under the budget constraint while the system achieves high resource utilization. This work extends the General Equilibrium literature by considering a practical case of satiated utility functions. Also, we introduce the notions of non-wastefulness and frugality for equilibrium selection, and rigorously demonstrate that all the non-wasteful and frugal ME are the optimal solutions to a convex program. Furthermore, the proposed equilibrium is shown to possess salient fairness properties including envy-freeness, sharing-incentive, and proportionality. Another major contribution of this work is to develop a privacy-preserving distributed algorithm, which is of independent interest, for computing an ME while allowing market participants to obfuscate their private information. Finally, extensive performance evaluation is conducted to verify our theoretical analyses.
Another approach to enable data privacy is to employ cryptographic techniques such as Garble Circuit (GC) @cite_45 and Fully Homomorphic Encryption (HE) @cite_31 , which are often used in secure multi-party computation @cite_38 . However, HE is computationally expensive due to public key operations and GC has expensive communication costs. Hence, these cryptographic approaches are not suitable for distributed optimization which typically needs many iterations to converge. Indeed, @cite_26 is the only work that we are aware of studying privacy-preserving decentralized optimization. Different from their proposed algorithm that based on ADMM and partially homomorphic cryptography, part is and simpler.
@cite_38 @cite_31 @cite_45 @cite_26
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We propose a privacy-preserving framework for learning visual classifiers by leveraging distributed private image data. This framework is designed to aggregate multiple classifiers updated locally using private data and to ensure that no private information about the data is exposed during and after its learning procedure. We utilize a homomorphic cryptosystem that can aggregate the local classifiers while they are encrypted and thus kept secret. To overcome the high computational cost of homomorphic encryption of high-dimensional classifiers, we (1) impose sparsity constraints on local classifier updates and (2) propose a novel efficient encryption scheme named doubly-permuted homomorphic encryption (DPHE) which is tailored to sparse high-dimensional data. DPHE (i) decomposes sparse data into its constituent non-zero values and their corresponding support indices, (ii) applies homomorphic encryption only to the non-zero values, and (iii) employs double permutations on the support indices to make them secret. Our experimental evaluation on several public datasets shows that the proposed approach achieves comparable performance against state-of-the-art visual recognition methods while preserving privacy and significantly outperforms other privacy-preserving methods. We consider a problem where multiple agents participate in solving a quadratic optimization problem subject to linear inequality constraints in a privacy-preserving manner. Several variables of the objective function as well as the constraints are privacy-sensitive and are known to different agents. We propose a privacy-preserving protocol based on partially homomorphic encryption where each agent encrypts its own information before sending it to an untrusted cloud computing infrastructure. To find the optimal solution the cloud applies a gradient descent algorithm on the encrypted data without the ability to decrypt it. The privacy of the proposed protocol against coalitions of colluding agents is analyzed using the cryptography notion of zero knowledge proofs. Secure two-party computation enables two parties to evaluate a function cooperatively without revealing to either party anything beyond the function’s output. The garbled-circuit technique, a generic approach to secure two-party computation for semi-honest participants, was developed by Yao in the 1980s, but has been viewed as being of limited practical significance due to its inefficiency. We demonstrate several techniques for improving the running time and memory requirements of the garbled-circuit technique, resulting in an implementation of generic secure two-party computation that is significantly faster than any previously reported while also scaling to arbitrarily large circuits. We validate our approach by demonstrating secure computation of circuits with over 10 9 gates at a rate of roughly 10 ms per garbled gate, and showing order-of-magnitude improvements over the best previous privacy-preserving protocols for computing Hamming distance, Levenshtein distance, Smith-Waterman genome alignment, and AES. Many deployments of secure multi-party computation (MPC) in practice have used information-theoretic three-party protocols that tolerate a single, semi-honest corrupt party, since these protocols enjoy very high efficiency. We propose a new approach for secure three-party computation (3PC) that improves security while maintaining practical efficiency that is competitive with traditional information-theoretic protocols. Our protocol is based on garbled circuits and provides security against a single, malicious corrupt party. Unlike information-theoretic 3PC protocols, ours uses a constant number of rounds. Our protocol only uses inexpensive symmetric-key cryptography: hash functions, block ciphers, pseudorandom generators (in particular, no oblivious transfers) and has performance that is comparable to that of Yao's (semi-honest) 2PC protocol. We demonstrate the practicality of our protocol with an implementation based on the JustGarble framework of (S&P 2013). The implementation incorporates various optimizations including the most recent techniques for efficient circuit garbling. We perform experiments on several benchmarking circuits, in different setups. Our experiments confirm that, despite providing a more demanding security guarantee, our protocol has performance comparable to existing information-theoretic 3PC.