Secure Numerical and Logical Multi Party Operations

We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for trigonometric functions, we use basic mathematical laws in combination with properties of the additive encryption scheme in a novel way. For division and logarithm we use a new approach to compute a Taylor series at a fixed point for all numbers. All our logical operations such as comparisons and large fan-in AND gates are perfectly secure. Our empirical evaluation yields speed-ups of more than a factor of 100 for the evaluated operations compared to the state-of-the-art

Privacy-Preserving Shortest Path Computation

Navigation is one of the most popular cloud computing services. But in virtually all cloud-based navigation systems, the client must reveal her location and destination to the cloud service provider in order to learn the fastest route. In this work, we present a cryptographic protocol for navigation on city streets that provides privacy for both the client's location and the service provider's routing data. Our key ingredient is a novel method for compressing the next-hop routing matrices in networks such as city street maps. Applying our compression method to the map of Los Angeles, for example, we achieve over tenfold reduction in the representation size. In conjunction with other cryptographic techniques, this compressed representation results in an efficient protocol suitable for fully-private real-time navigation on city streets. We demonstrate the practicality of our protocol by benchmarking it on real street map data for major cities such as San Francisco and Washington, D.C.Comment: Extended version of NDSS 2016 pape

On the Efficiency of Classical and Quantum Secure Function Evaluation

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of protocols that use different variants of OT as a black-box. When applied to implementations of OT, these bounds generalize most known results to the statistical case. Our results hold in particular for transformations between a finite number of primitives and for any error. In the second part we study the efficiency of quantum protocols implementing OT. While most classical lower bounds for perfectly secure reductions of OT to distributed randomness still hold in the quantum setting, we present a statistically secure protocol that violates these bounds by an arbitrarily large factor. We then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend OT. Finally, we present two lower bounds for reductions of OT to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds

Cloud-based Quadratic Optimization with Partially Homomorphic Encryption

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party's inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs

Scather: programming with multi-party computation and MapReduce

We present a prototype of a distributed computational infrastructure, an associated high level programming language, and an underlying formal framework that allow multiple parties to leverage their own cloud-based computational resources (capable of supporting MapReduce [27] operations) in concert with multi-party computation (MPC) to execute statistical analysis algorithms that have privacy-preserving properties. Our architecture allows a data analyst unfamiliar with MPC to: (1) author an analysis algorithm that is agnostic with regard to data privacy policies, (2) to use an automated process to derive algorithm implementation variants that have different privacy and performance properties, and (3) to compile those implementation variants so that they can be deployed on an infrastructures that allows computations to take place locally within each participant’s MapReduce cluster as well as across all the participants’ clusters using an MPC protocol. We describe implementation details of the architecture, discuss and demonstrate how the formal framework enables the exploration of tradeoffs between the efficiency and privacy properties of an analysis algorithm, and present two example applications that illustrate how such an infrastructure can be utilized in practice.This work was supported in part by NSF Grants: #1430145, #1414119, #1347522, and #1012798

ODIN: Obfuscation-based privacy-preserving consensus algorithm for Decentralized Information fusion in smart device Networks

The large spread of sensors and smart devices in urban infrastructures are motivating research in the area of the Internet of Things (IoT) to develop new services and improve citizens’ quality of life. Sensors and smart devices generate large amounts of measurement data from sensing the environment, which is used to enable services such as control of power consumption or traffic density. To deal with such a large amount of information and provide accurate measurements, service providers can adopt information fusion, which given the decentralized nature of urban deployments can be performed by means of consensus algorithms. These algorithms allow distributed agents to (iteratively) compute linear functions on the exchanged data, and take decisions based on the outcome, without the need for the support of a central entity. However, the use of consensus algorithms raises several security concerns, especially when private or security critical information is involved in the computation. In this article we propose ODIN, a novel algorithm allowing information fusion over encrypted data. ODIN is a privacy-preserving extension of the popular consensus gossip algorithm, which prevents distributed agents from having direct access to the data while they iteratively reach consensus; agents cannot access even the final consensus value but can only retrieve partial information (e.g., a binary decision). ODIN uses efficient additive obfuscation and proxy re-encryption during the update steps and garbled circuits to make final decisions on the obfuscated consensus. We discuss the security of our proposal and show its practicability and efficiency on real-world resource-constrained devices, developing a prototype implementation for Raspberry Pi devices