Secure and efficient multiparty private set intersection cardinality

17 USC 105 interim-entered record; under review.The article of record as published may be found at http://dx.doi.org/10.3934/amc.2020071In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most of the cases, PSI allows two parties to securely determine the intersection of their private input sets, and no other information. In this paper, employing a Bloom filter, we propose a Multiparty Private Set Intersection Cardinality (MPSI-CA), where the number of participants in PSI is not limited to two. The security of our scheme is achieved in the standard model under the Decisional Diffie-Hellman (DDH) assumption against semi-honest adversaries. Our scheme is flexible in the sense that set size of one participant is independent from that of the others. We consider the number of modular exponentiations in order to determine computational complexity. In our construction, communication and computation overheads of each participant is O(vmaxk) except that the complexity of the designated party is O(v1), where vmax is the maximum set size, v1 denotes the set size of the designated party and k is a security parameter. Particularly, our MSPI-CA is the first that incurs linear complexity in terms of set size, namely O(nvmaxk), where n is the number of participants. Further, we extend our MPSI-CA to MPSI retaining all the security attributes and other properties. As far as we are aware of, there is no other MPSI so far where individual computational cost of each participant is independent of the number of participants. Unlike MPSI-CA, our MPSI does not require any kind of broadcast channel as it uses star network topology in the sense that a designated party communicates with everyone else

Nonlinear and Complex Dynamics in Economics

This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and �finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specifi�c applications in microeconomics, macroeconomics, and �finance, and discuss the policy relevancy of chaos

Secure and Efficient Multiparty Private Set Intersection Cardinality

The article of record as published may be found at http://dx.doi.org/10.3934/amc.2020071In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most of the cases, PSI allows two parties to securely determine the intersection of their private input sets, and no other information. In this paper, employing a Bloom filter, we propose a Multiparty Private Set Intersection Cardinality (MPSI-CA), where the number of participants in PSI is not limited to two. The security of our scheme is achieved in the standard model under the Decisional Diffie-Hellman (DDH) assumption against semi-honest adversaries. Our scheme is flexible in the sense that set size of one participant is independent from that of the others. We consider the number of modular exponentiations in order to determine computational complexity. In our construction, communication and computation overheads of each participant is O(v max k) except that the complexity of the designated party is O(v1), where v max is the maximum set size, v1 denotes the set size of the designated party and k is a security parameter. Particularly, our MSPI-CA is the first that incurs linear complexity in terms of set size, namely O(nv max k), where n is the number of participants. Further, we extend our MPSI-CA to MPSI retaining all the security attributes and other properties. As far as we are aware of, there is no other MPSI so far where individual computational cost of each participant is independent of the number of participants. Unlike MPSI-CA, our MPSI does not require any kind of broadcast channel as it uses star network topology in the sense that a designated party communicates with everyone else

Understanding interdependency through complex information sharing

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work, we propose to analyze these interactions as different modes of information sharing. Towards this end, we introduce a novel axiomatic framework for decomposing the joint entropy, which characterizes the various ways in which random variables can share information. The key contribution of our framework is to distinguish between interdependencies where the information is shared redundantly, and synergistic interdependencies where the sharing structure exists in the whole but not between the parts. We show that our axioms determine unique formulas for all the terms of the proposed decomposition for a number of cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits.Comment: 39 pages, 4 figure

Study of Fundamental Tradeoff Between Deliverable and Private Information in Statistical Inference

My primary objective in this dissertation is to establish a framework under which I launch a systematic study of the fundamental tradeoff between deliverable and private information in statistical inference. My research was partly motivated by arising and prevailing privacy concerns of users in many machine learning problems. In this dissertation, I begin by introducing examples where I am concerned of privacy leakage versus decision utility in statistical inference problems. I then go into further details about what I have achieved in formulating and solving such problems using information theory related metrics in a variety of settings. Both related works and my own results are later summarized in the first chapter. In the second chapter, I introduce a problem of detecting any subgraph using binary codeword queries. Furthermore, I seek and find limits imposed by the privacy of each graph which help me develop an understanding of privacy versus utility problems. In the third chapter, I shift my focus from the original graphical framework to a more general bin allocation problem motivated by addressing concerns on privacy leakage in regard to users’ web surfing patterns with usage of proxy or VPN services. After problem formulation, I deem it necessary to introduce submodular functions as a means of simplifying such problems and finding their solutions. In chapter four, I expand upon the concept introduced in chapter three by allowing uncertainty between hypotheses and find the relationship between distinguishability, privacy leakage and utility in a deterministic bin allocation framework. In chapters five and six, motivated by my previous works, I shift my focus to the problem of tradeoff between utility and leaked information when a randomization, rather than a deterministic mapping, is introduced as a privacy protecviii tion mechanism. In particular, I first seek solutions using a typical and widely accepted Information Bottleneck (IB) approach. I then detail how the original information bottleneck method does not necessarily provide an optimal solution to the proposed problem. I then offer my own novel approach based upon Augmented Lagrange Multipliers (ALM) and Alternating Direction Method of Multipliers (ADMM) with both theoretical justification and empirical evidence , as well as the inherent structures of both the objective function and privacy constraints. My approach has been shown to attain notable improvements than that under the IB framework, with well justified enhancement on efficiency of local convergence. Finally in chapter seven, I present plans to cope with issues of lacking true statistics, by exploiting a set of information theoretical measures which have been shown to be equipped with more benign properties in robustness against limited amount of training data than the regular mutual information measure