Topology-Hiding Computation Beyond Semi-Honest Adversaries

Topology-hiding communication protocols allow a set of parties, connected by an incomplete network with unknown communication graph, where each party only knows its neighbors, to construct a complete communication network such that the network topology remains hidden even from a powerful adversary who can corrupt parties. This communication network can then be used to perform arbitrary tasks, for example secure multi-party computation, in a topology-hiding manner. Previously proposed protocols could only tolerate passive corruption. This paper proposes protocols that can also tolerate fail-corruption (i.e., the adversary can crash any party at any point in time) and so-called semi-malicious corruption (i.e., the adversary can control a corrupted party\u27s randomness), without leaking more than an arbitrarily small fraction of a bit of information about the topology. A small-leakage protocol was recently proposed by Ball et al. [Eurocrypt\u2718], but only under the unrealistic set-up assumption that each party has a trusted hardware module containing secret correlated pre-set keys, and with the further two restrictions that only passively corrupted parties can be crashed by the adversary, and semi-malicious corruption is not tolerated. Since leaking a small amount of information is unavoidable, as is the need to abort the protocol in case of failures, our protocols seem to achieve the best possible goal in a model with fail-corruption. Further contributions of the paper are applications of the protocol to obtain secure MPC protocols, which requires a way to bound the aggregated leakage when multiple small-leakage protocols are executed in parallel or sequentially. Moreover, while previous protocols are based on the DDH assumption, a new so-called PKCR public-key encryption scheme based on the LWE assumption is proposed, allowing to base topology-hiding computation on LWE. Furthermore, a protocol using fully-homomorphic encryption achieving very low round complexity is proposed

Is Information-Theoretic Topology-Hiding Computation Possible?

Topology-hiding computation (THC) is a form of multi-party computation over an incomplete communication graph that maintains the privacy of the underlying graph topology. Existing THC protocols consider an adversary that may corrupt an arbitrary number of parties, and rely on cryptographic assumptions such as DDH. In this paper we address the question of whether information-theoretic THC can be achieved by taking advantage of an honest majority. In contrast to the standard MPC setting, this problem has remained open in the topology-hiding realm, even for simple privacy-free functions like broadcast, and even when considering only semi-honest corruptions. We uncover a rich landscape of both positive and negative answers to the above question, showing that what types of graphs are used and how they are selected is an important factor in determining the feasibility of hiding topology information-theoretically. In particular, our results include the following. We show that topology-hiding broadcast (THB) on a line with four nodes, secure against a single semi-honest corruption, implies key agreement. This result extends to broader classes of graphs, e.g., THB on a cycle with two semi-honest corruptions. On the other hand, we provide the first feasibility result for information-theoretic THC: for the class of cycle graphs, with a single semi-honest corruption. Given the strong impossibilities, we put forth a weaker definition of distributional-THC, where the graph is selected from some distribution (as opposed to worst-case). We present a formal separation between the definitions, by showing a distribution for which information theoretic distributional-THC is possible, but even topology-hiding broadcast is not possible information-theoretically with the standard definition. We demonstrate the power of our new definition via a new connection to adaptively secure low-locality MPC, where distributional-THC enables parties to reuse a secret low-degree communication graph even in the face of adaptive corruptions

Topology-Hiding Computation Beyond Logarithmic Diameter

A distributed computation in which nodes are connected by a partial communication graph is called \emph{topology-hiding} if it does not reveal information about the graph (beyond what is revealed by the output of the function). Previous results [Moran, Orlov, Richelson; TCC\u2715] have shown that topology-hiding computation protocols exist for graphs of logarithmic diameter (in the number of nodes), but the feasibility question for graphs of larger diameter was open even for very simple graphs such as chains, cycles and trees. In this work, we take a step towards topology-hiding computation protocols for arbitrary graphs by constructing protocols that can be used in a large class of {\em large-diameter networks}, including cycles, trees and graphs with logarithmic \emph{circumference}. Our results use very different methods from [MOR15] and can be based on a standard assumption (such as DDH)

Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users. In this paper, we propose the first secure aggregation framework, named Turbo-Aggregate, that in a network with $N$ users achieves a secure aggregation overhead of $O(N\log{N})$, as opposed to $O(N^2)$, while tolerating up to a user dropout rate of $50\%$. Turbo-Aggregate employs a multi-group circular strategy for efficient model aggregation, and leverages additive secret sharing and novel coding techniques for injecting aggregation redundancy in order to handle user dropouts while guaranteeing user privacy. We experimentally demonstrate that Turbo-Aggregate achieves a total running time that grows almost linear in the number of users, and provides up to $40\times$ speedup over the state-of-the-art protocols with up to $N=200$ users. Our experiments also demonstrate the impact of model size and bandwidth on the performance of Turbo-Aggregate

Scalable secure multi-party network vulnerability analysis via symbolic optimization

Threat propagation analysis is a valuable tool in improving the cyber resilience of enterprise networks. As these networks are interconnected and threats can propagate not only within but also across networks, a holistic view of the entire network can reveal threat propagation trajectories unobservable from within a single enterprise. However, companies are reluctant to share internal vulnerability measurement data as it is highly sensitive and (if leaked) possibly damaging. Secure Multi-Party Computation (MPC) addresses this concern. MPC is a cryptographic technique that allows distrusting parties to compute analytics over their joint data while protecting its confidentiality. In this work we apply MPC to threat propagation analysis on large, federated networks. To address the prohibitively high performance cost of general-purpose MPC we develop two novel applications of optimizations that can be leveraged to execute many relevant graph algorithms under MPC more efficiently: (1) dividing the computation into separate stages such that the first stage is executed privately by each party without MPC and the second stage is an MPC computation dealing with a much smaller shared network, and (2) optimizing the second stage by treating the execution of the analysis algorithm as a symbolic expression that can be optimized to reduce the number of costly operations and subsequently executed under MPC.We evaluate the scalability of this technique by analyzing the potential for threat propagation on examples of network graphs and propose several directions along which this work can be expanded

Asynchronous provably-secure hidden services

The client-server architecture is one of the most widely used in the Internet for its simplicity and flexibility. In practice the server is assigned a public address so that its services can be consumed. This makes theserver vulnerable to a number of attacks such as Distributed Denial of Service (DDoS), censorship from authoritarian governments or exploitationof software vulnerabilities. In this work we propose an asynchronous protocol for allowing a client to issue requests to a server without revealing any information about the location of the server. In addition, our solution reveals limited information about the network topology, leaking only the distance from the client to the corrupted participants. We also provide a simulation-based security definition capturing the requirement described above. Our protocol is secure in the semi-honest model against any number of colluding participants, and has linear communication complexity. Finally, we extend our solution to handle active adversaries. We show that malicious participants can only trigger a premature termination of the protocol, in which case they are identified. For this solution the communication complexity becomes quadratic. To the best of our knowledge our solution is the first asynchronous protocol that provides strong security guarantees

OPFE: Outsourcing Computation for Private Function Evaluation

Outsourcing secure multiparty computation(SMC) protocols has allowed resource-constrained devices to take advantage of these developing cryptographic primitives with great efficiency. While the existing constructions for outsourced SMC guarantee input and output privacy, they require that all parties know the function being evaluated. Thus, stronger security guarantees are necessary in applications where the function itself needs to be kept private. We develop the first linear-complexity protocols for outsourcing private function evaluation (PFE), a subset of SMC protocols that provide both input and function privacy. Assuming a semi-honest function holder, we build on the most efficient two-party PFE constructions to develop outsourced protocols that are secure against a semi-honest, covert, or malicious Cloud server and malicious mobile devices providing input to the function. Our protocols require minimal symmetric key operations and only two rounds of communication from the mobile participants. As a secondary contribution, we develop a technique for combining public and private sub-circuits in a single computation called partially-circuit private (PCP) garbling. This novel garbling technique allows us to apply auxiliary circuits to check for malicious behavior using only free-XOR overhead gates rather than the significantly more costly PFE gate construction. These protocols demonstrate the feasibility of outsourced PFE and provide a first step towards developing privacy-preserving applications for use in Cloud computing

Combining Shamir & Additive Secret Sharing to Improve Efficiency of SMC Primitives Against Malicious Adversaries

Secure multi-party computation provides a wide array of protocols for mutually distrustful parties be able to securely evaluate functions of private inputs. Within recent years, many such protocols have been proposed representing a plethora of strategies to securely and efficiently handle such computation. These protocols have become increasingly efficient, but their performance still is impractical in many settings. We propose new approaches to some of these problems which are either more efficient than previous works within the same security models or offer better security guarantees with comparable efficiency. The goals of this research are to improve efficiency and security of secure multi-party protocols and explore the application of such approaches to novel threat scenarios. Some of the novel optimizations employed are dynamically switching domains of shared secrets, asymmetric computations, and advantageous functional transformations, among others. Specifically, this work presents a novel combination of Shamir and Additive secret sharing to be used in parallel which allows for the transformation of efficient protocols secure against passive adversaries to be secure against active adversaries. From this set of primitives we propose the construction of a comparison protocol which can be implemented under that approach with a complexity which is more efficient than other recent works for common domains of interest. Finally, we present a system which addresses a critical security threat for the protection and obfuscation of information which may be of high consequence.Comment: arXiv admin note: text overlap with arXiv:1810.0157

Low-latency mix networks for anonymous communication

Every modern online application relies on the network layer to transfer information, which exposes the metadata associated with digital communication. These distinctive characteristics encapsulate equally meaningful information as the content of the communication itself and allow eavesdroppers to uniquely identify users and their activities. Hence, by exposing the IP addresses and by analyzing patterns of the network traffic, a malicious entity can deanonymize most online communications. While content confidentiality has made significant progress over the years, existing solutions for anonymous communication which protect the network metadata still have severe limitations, including centralization, limited security, poor scalability, and high-latency. As the importance of online privacy increases, the need to build low-latency communication systems with strong security guarantees becomes necessary. Therefore, in this thesis, we address the problem of building multi-purpose anonymous networks that protect communication privacy. To this end, we design a novel mix network Loopix, which guarantees communication unlinkability and supports applications with various latency and bandwidth constraints. Loopix offers better security properties than any existing solution for anonymous communications while at the same time being scalable and low-latency. Furthermore, we also explore the problem of active attacks and malicious infrastructure nodes, and propose a Miranda mechanism which allows to efficiently mitigate them. In the second part of this thesis, we show that mix networks may be used as a building block in the design of a private notification system, which enables fast and low-cost online notifications. Moreover, its privacy properties benefit from an increasing number of users, meaning that the system can scale to millions of clients at a lower cost than any alternative solution

An Efficient 2-Party Private Function Evaluation Protocol Based on Half Gates

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Private function evaluation (PFE) is a special case of secure multi-party computation (MPC), where the function to be computed is known by only one party. PFE is useful in several real-life applications where an algorithm or a function itself needs to remain secret for reasons such as protecting intellectual property or security classification level. In this paper, we focus on improving 2-party PFE based on symmetric cryptographic primitives. In this respect, we look back at the seminal PFE framework presented by Mohassel and Sadeghian at Eurocrypt’13. We show how to adapt and utilize the well-known half gates garbling technique (Zahur et al., Eurocrypt’15) to their constant-round 2-party PFE scheme. Compared to their scheme, our resulting optimization significantly improves the efficiency of both the underlying Oblivious Evaluation of Extended Permutation (OEP) and secure 2-party computation (2PC) protocols, and yields a more than 40% reduction in overall communication cost (the computation time is also slightly decreased and the number of rounds remains unchanged)