Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

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

A New Cryptosystem Based On Hidden Order Groups

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in multiparty protocols. We demonstrate this by presenting a key agreement protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols, since they are redundan

Efficient noninteractive certification of RSA moduli and beyond

In many applications, it is important to verify that an RSA public key (N; e) speci es a permutation over the entire space ZN, in order to prevent attacks due to adversarially-generated public keys. We design and implement a simple and e cient noninteractive zero-knowledge protocol (in the random oracle model) for this task. Applications concerned about adversarial key generation can just append our proof to the RSA public key without any other modi cations to existing code or cryptographic libraries. Users need only perform a one-time veri cation of the proof to ensure that raising to the power e is a permutation of the integers modulo N. For typical parameter settings, the proof consists of nine integers modulo N; generating the proof and verifying it both require about nine modular exponentiations. We extend our results beyond RSA keys and also provide e cient noninteractive zero- knowledge proofs for other properties of N, which can be used to certify that N is suitable for the Paillier cryptosystem, is a product of two primes, or is a Blum integer. As compared to the recent work of Auerbach and Poettering (PKC 2018), who provide two-message protocols for similar languages, our protocols are more e cient and do not require interaction, which enables a broader class of applications.https://eprint.iacr.org/2018/057First author draf

Privacy-Preserving and Outsourced Multi-User k-Means Clustering

Many techniques for privacy-preserving data mining (PPDM) have been investigated over the past decade. Often, the entities involved in the data mining process are end-users or organizations with limited computing and storage resources. As a result, such entities may want to refrain from participating in the PPDM process. To overcome this issue and to take many other benefits of cloud computing, outsourcing PPDM tasks to the cloud environment has recently gained special attention. We consider the scenario where n entities outsource their databases (in encrypted format) to the cloud and ask the cloud to perform the clustering task on their combined data in a privacy-preserving manner. We term such a process as privacy-preserving and outsourced distributed clustering (PPODC). In this paper, we propose a novel and efficient solution to the PPODC problem based on k-means clustering algorithm. The main novelty of our solution lies in avoiding the secure division operations required in computing cluster centers altogether through an efficient transformation technique. Our solution builds the clusters securely in an iterative fashion and returns the final cluster centers to all entities when a pre-determined termination condition holds. The proposed solution protects data confidentiality of all the participating entities under the standard semi-honest model. To the best of our knowledge, ours is the first work to discuss and propose a comprehensive solution to the PPODC problem that incurs negligible cost on the participating entities. We theoretically estimate both the computation and communication costs of the proposed protocol and also demonstrate its practical value through experiments on a real dataset.Comment: 16 pages, 2 figures, 5 table

Confidential Boosting with Random Linear Classifiers for Outsourced User-generated Data

User-generated data is crucial to predictive modeling in many applications. With a web/mobile/wearable interface, a data owner can continuously record data generated by distributed users and build various predictive models from the data to improve their operations, services, and revenue. Due to the large size and evolving nature of users data, data owners may rely on public cloud service providers (Cloud) for storage and computation scalability. Exposing sensitive user-generated data and advanced analytic models to Cloud raises privacy concerns. We present a confidential learning framework, SecureBoost, for data owners that want to learn predictive models from aggregated user-generated data but offload the storage and computational burden to Cloud without having to worry about protecting the sensitive data. SecureBoost allows users to submit encrypted or randomly masked data to designated Cloud directly. Our framework utilizes random linear classifiers (RLCs) as the base classifiers in the boosting framework to dramatically simplify the design of the proposed confidential boosting protocols, yet still preserve the model quality. A Cryptographic Service Provider (CSP) is used to assist the Cloud's processing, reducing the complexity of the protocol constructions. We present two constructions of SecureBoost: HE+GC and SecSh+GC, using combinations of homomorphic encryption, garbled circuits, and random masking to achieve both security and efficiency. For a boosted model, Cloud learns only the RLCs and the CSP learns only the weights of the RLCs. Finally, the data owner collects the two parts to get the complete model. We conduct extensive experiments to understand the quality of the RLC-based boosting and the cost distribution of the constructions. Our results show that SecureBoost can efficiently learn high-quality boosting models from protected user-generated data