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2017-02-14
F. Quader, V. Janeja, J. Stauffer.  2015.  "Persistent threat pattern discovery". 2015 IEEE International Conference on Intelligence and Security Informatics (ISI). :179-181.

Advanced Persistent Threat (APT) is a complex (Advanced) cyber-attack (Threat) against specific targets over long periods of time (Persistent) carried out by nation states or terrorist groups with highly sophisticated levels of expertise to establish entries into organizations, which are critical to a country's socio-economic status. The key identifier in such persistent threats is that patterns are long term, could be high priority, and occur consistently over a period of time. This paper focuses on identifying persistent threat patterns in network data, particularly data collected from Intrusion Detection Systems. We utilize Association Rule Mining (ARM) to detect persistent threat patterns on network data. We identify potential persistent threat patterns, which are frequent but at the same time unusual as compared with the other frequent patterns.

2017-02-09
Alejandro Domininguez-Garcia, University of Illinois at Urbana-Champaign, Bahman Gharesifard, University of Illinois at Urbana-Champaign, Tamer Başar, University of Illinois at Urbana-Champaign.  2013.  A Price-Based Approach to Control of Networked Distributed Energy Resources.

We introduce a framework for controlling the energy provided or absorbed by distributed energy resources (DERs) in power distribution networks. In this framework, there is a set of agents referred to as aggregators that interact with the wholesale electricity market, and through some market-clearing mechanism, are requested (and will be compensated for) to provide (or absorb) certain amount of active (or reactive) power over some period of time. In order to fulfill the request, each aggregator interacts with a set of DERs and offers them some price per unit of active (or reactive) power they provide (or absorb); the objective is for the aggregator to design a pricing strategy for incentivizing DERs to change its active (or reactive) power consumption (or production) so as they collectively provide the amount that the aggregator has been asked for. In order to make a decision, each DER uses the price information provided by the aggregator and some estimate of the average active (or reactive) power that neighboring DERs can provide computed through some exchange of information among them; this exchange is described by a connected undirected graph. The focus is on the DER strategic decision-making process, which we cast as a game. In this context, we provide sufficient conditions on the aggregator's pricing strategy under which this game has a unique Nash equilibrium. Then, we propose a distributed iterative algorithm that adheres to the graph that describes the exchange of information between DERs that allows them to seek for this Nash equilibrium. We illustrate our results through several numerical simulations.

Presented as part of the DIMACS Workshop on Energy Infrastructure: Designing for Stability and Resilience, Rutgers University, Piscataway, NJ, February 20-22, 2013

2017-02-03
Bahman Gharesifard, University of Illinois at Urbana-Champaign, Tamer Başar, University of Illinois at Urbana-Champaign, Alejandro D. Domínguez-García, University of Illinois at Urbana-Champaign.  2013.  Price-based Distributed Control for Networked Plug-in Electric Eehicles. 2013 American Control Conference.

We introduce a framework for controlling the charging and discharging processes of plug-in electric vehicles (PEVs) via pricing strategies. Our framework consists of a hierarchical decision-making setting with two layers, which we refer to as aggregator layer and retail market layer. In the aggregator layer, there is a set of aggregators that are requested (and will be compensated for) to provide certain amount of energy over a period of time. In the retail market layer, the aggregator offers some price for the energy that PEVs may provide; the objective is to choose a pricing strategy to incentivize the PEVs so as they collectively provide the amount of energy that the aggregator has been asked for. The focus of this paper is on the decision-making process that takes places in the retail market layer, where we assume that each individual PEV is a price-anticipating decision-maker. We cast this decision-making process as a game, and provide conditions on the pricing strategy of the aggregator under which this game has a unique Nash equilibrium. We propose a distributed consensus-based iterative algorithm through which the PEVs can seek for this Nash equilibrium. Numerical simulations are included to illustrate our results.

2016-12-09
2016-12-01
Pierre McCauley, University of Illinois at Urbana-Champaign, Brandon Nsiah-Ababio, University of Illinois at Urbana-Champaign, Joshua Reed, University of Illinois at Urbana-Champaign, Faramola Isiaka, University of Illinois at Urbana-Champaign, Tao Xie, University of Illinois at Urbana-Champaign.  2016.  Preliminary Analysis of Code Hunt Data Set from a Contest. 2nd International Code Hunt Workshop on Educational Software Engineering (CHESE 2016).

Code Hunt (https://www.codehunt.com/) from Microsoft Research is a web-based serious gaming platform being popularly used for various programming contests. In this paper, we demonstrate preliminary statistical analysis of a Code Hunt data set that contains the programs written by students (only) worldwide during a contest over 48 hours. There are 259 users, 24 puzzles (organized into 4 sectors), and about 13,000 programs submitted by these users. Our analysis results can help improve the creation of puzzles in a future contest.

2016-11-17
Phuong Cao, University of Illinois at Urbana-Champaign, Ravishankar Iyer, University of Illinois at Urbana-Champaign, Zbigniew Kalbarczyk, University of Illinois at Urbana-Champaign, Eric Badger, University of Illinois at Urbana-Champaign, Surya Bakshi, University of Illinois at Urbana-Champaign, Simon Kim, University of Illinois at Urbana-Champaign, Adam Slagell, University of Illinois at Urbana-Champaign, Alex Withers, University of Illinois at Urbana-Champaign.  2016.  Preemptive Intrusion Detection – Practical Experience and Detection Framework.

Using stolen or weak credentials to bypass authentication is one of the top 10 network threats, as shown in recent studies. Disguising as legitimate users, attackers use stealthy techniques such as rootkits and covert channels to gain persistent access to a target system. However, such attacks are often detected after the system misuse stage, i.e., the attackers have already executed attack payloads such as: i) stealing secrets, ii) tampering with system services, and ii) disrupting the availability of production services.

In this talk, we analyze a real-world credential stealing attack observed at the National Center for Supercomputing Applications. We show the disadvantages of traditional detection techniques such as signature-based and anomaly-based detection for such attacks. Our approach is a complement to existing detection techniques. We investigate the use of Probabilistic Graphical Model, specifically Factor Graphs, to integrate security logs from multiple sources for a more accurate detection. Finally, we propose a security testbed architecture to: i) simulate variants of known attacks that may happen in the future, ii) replay such attack variants in an isolated environment, and iii) collect and share security logs of such replays for the security research community.

Pesented at the Illinois Information Trust Institute Joint Trust and Security and Science of Security Seminar, May 3, 2016.

2016-11-16
Ravishankar K. Iyer, University of Illinois at Urbana-Champaign, Phuong Cao, University of Illinois at Urbana-Champaign.  2015.  Preemptive Intrusion Detection: Theoretical Framework and Real-world Measurements.

Presented at the NSA SoS Quarterly Lablet Meeting, January 2015 by Ravi Iyer.

Presented at the Illinois SoS Bi-Weekly Meeting, February 2015 by Phuong Cao.

2016-10-07
Pradeep Murukannaiah, Jessica Staddon, Heather Lipford, Bart Knijnenburg.  2016.  PrIncipedia: A Privacy Incidents Encyclopedia. Privacy Law Scholars Conference.

A thorough understanding of society’s privacy incidents is of paramount importance for technical solutions, training/education, social research, and legal scholarship in privacy. The goal of the PrIncipedia project is to provide this understanding by developing the first comprehensive database of privacy incidents, enabling the exploration of a variety of privacy-related research questions. We provide a working definition of “privacy incident” and evidence that it meets end-user perceptions of privacy. We also provide semi-automated support for building the database through a learned classifier that detects news articles about privacy incidents.

[Anonymous].  2016.  PrIncipedia: A Privacy Incidents Encyclopedia. Privacy Law Scholars Conference.

A thorough understanding of society's privacy incidents  is of paramount importance for technical solutions, training/education, social research, and legal scholarship in privacy. The goal of the PrIncipedia project is to provide this understanding by developing the first comprehensive database of privacy incidents, enabling the exploration of a variety of privacy-related research questions. We provide a working definition of ``privacy incident'' and evidence that it meets end-user perceptions of privacy. We also provide semi-automated support for building the database through a learned classifier that detects news articles about privacy incidents.

2016-07-01
Zielinska, Olga, Welk, Allaire, Mayhorn, Christopher B., Murphy-Hill, Emerson.  2016.  The Persuasive Phish: Examining the Social Psychological Principles Hidden in Phishing Emails. Proceedings of the Symposium and Bootcamp on the Science of Security. :126–126.

Phishing is a social engineering tactic used to trick people into revealing personal information [Zielinska, Tembe, Hong, Ge, Murphy-Hill, & Mayhorn 2014]. As phishing emails continue to infiltrate users' mailboxes, what social engineering techniques are the phishers using to successfully persuade victims into releasing sensitive information?

Cialdini's [2007] six principles of persuasion (authority, social proof, liking/similarity, commitment/consistency, scarcity, and reciprocation) have been linked to elements of phishing emails [Akbar 2014; Ferreira, & Lenzini 2015]; however, the findings have been conflicting. Authority and scarcity were found as the most common persuasion principles in 207 emails obtained from a Netherlands database [Akbar 2014], while liking/similarity was the most common principle in 52 personal emails available in Luxemborg and England [Ferreira et al. 2015]. The purpose of this study was to examine the persuasion principles present in emails available in the United States over a period of five years.

Two reviewers assessed eight hundred eighty-seven phishing emails from Arizona State University, Brown University, and Cornell University for Cialdini's six principles of persuasion. Each email was evaluated using a questionnaire adapted from the Ferreira et al. [2015] study. There was an average agreement of 87% per item between the two raters.

Spearman's Rho correlations were used to compare email characteristics over time. During the five year period under consideration (2010--2015), the persuasion principles of commitment/consistency and scarcity have increased over time, while the principles of reciprocation and social proof have decreased over time. Authority and liking/similarity revealed mixed results with certain characteristics increasing and others decreasing.

The commitment/consistency principle could be seen in the increase of emails referring to elements outside the email to look more reliable, such as Google Docs or Adobe Reader (rs(850) = .12, p =.001), while the scarcity principle could be seen in urgent elements that could encourage users to act quickly and may have had success in eliciting a response from users (rs(850) = .09, p =.01). Reciprocation elements, such as a requested reply, decreased over time (rs(850) = -.12, p =.001). Additionally, the social proof principle present in emails by referring to actions performed by other users also decreased (rs(850) = -.10, p =.01).

Two persuasion principles exhibited both an increase and decrease in their presence in emails over time: authority and liking/similarity. These principles could increase phishing rate success if used appropriately, but could also raise suspicions in users and decrease compliance if used incorrectly. Specifically, the source of the email, which corresponds to the authority principle, displayed an increase over time in educational institutes (rs(850) = .21, p <.001), but a decrease in financial institutions (rs(850) = -.18, p <.001). Similarly, the liking/similarity principle revealed an increase over time of logos present in emails (rs(850) = .18, p <.001) and decrease in service details, such as payment information (rs(850) = -.16, p <.001).

The results from this study offer a different perspective regarding phishing. Previous research has focused on the user aspect; however, few studies have examined the phisher perspective and the social psychological techniques they are implementing. Additionally, they have yet to look at the success of the social psychology techniques. Results from this study can be used to help to predict future trends and inform training programs, as well as machine learning programs used to identify phishing messages.

2016-06-23
Adwait Nadkarni, Benjamin Andow, William Enck, Somesh Jha.  2016.  Practical DIFC Enforcement on Android. USENIX Security Symposium.

Smartphone users often use private and enterprise data with untrusted third party applications.  The fundamental lack of secrecy guarantees in smartphone OSes, such as Android, exposes this data to the risk of unauthorized exfiltration.  A natural solution is the integration of secrecy guarantees into the OS.  In this paper, we describe the challenges for decentralized information flow control (DIFC) enforcement on Android.  We propose context-sensitive DIFC enforcement via lazy polyinstantiation and practical and secure network export through domain declassification.  Our DIFC system, Weir, is backwards compatible by design, and incurs less than 4 ms overhead for component startup.  With Weir,  we demonstrate practical and secure DIFC enforcement on Android.

2016-04-12
Dong Jin, Illinois Institute of Technology, David Nicol, University of Illinois at Urbana-Champaign.  2015.  Parallel Simulation and Virtual-machine-based Emulation of Software-defined Network. ACM Transactions on Modeling and Computer Simulation. 26(1)

The emerging software-defined networking (SDN) technology decouples the control plane from the data plane in a computer network with open and standardized interfaces, and hence opens up the network designers’ options and ability to innovate. The wide adoption of SDN in industry has motivated the development of large-scale, high-fidelity testbeds for evaluation of systems that incorporate SDN. In this article, we develop a framework to support OpenFlow-based SDN simulation and distributed emulation, by leveraging our prior work on a hybrid network testbed with a parallel network simulator and a virtual-machine-based emulation system. We show how to exploit typical SDN controller behaviors to handle performance issues caused by the centralized controller in parallel discrete-event simulation. In particular, we develop an asynchronous synchronization algorithm for passive SDN controllers and design a two-level architecture for active SDN controllers. We evaluate the system performance, showing good scalability. Finally, we present a case study, using the testbed, to evaluate network verification applications in an SDN-based data center network. CCS Concepts: Networks→Network simulations; Computing methodologies→Simulation

2015-12-29
Yasir Khan, Ehab Al-Shaer.  2015.  Property-Based Verification of Evolving ddd Petri Nets. International Conference of Software Engineering Advances.
2015-11-23
YoungMin Kwon, University of Illinois at Urbana-Champaign, Gul Agha, University of Illinois at Urbana-Champaign.  2014.  Performance Evaluation of Sensor Networks by Statistical Modeling and Euclidean Model Checking. ACM Transactions on Sensor Networks. 9(4)

Modeling and evaluating the performance of large-scale wireless sensor networks (WSNs) is a challenging problem. The traditional method for representing the global state of a system as a cross product of the states of individual nodes in the system results in a state space whose size is exponential in the number of nodes. We propose an alternative way of representing the global state of a system: namely, as a probability mass function (pmf) which represents the fraction of nodes in different states. A pmf corresponds to a point in a Euclidean space of possible pmf values, and the evolution of the state of a system is represented by trajectories in this Euclidean space. We propose a novel performance evaluation method that examines all pmf trajectories in a dense Euclidean space by exploring only finite relevant portions of the space. We call our method Euclidean model checking. Euclidean model checking is useful both in the design phase—where it can help determine system parameters based on a specification—and in the evaluation phase—where it can help verify performance properties of a system. We illustrate the utility of Euclidean model checking by using it to design a time difference of arrival (TDoA) distance measurement protocol and to evaluate the protocol’s implementation on a 90-node WSN. To facilitate such performance evaluations, we provide a Markov model estimation method based on applying a standard statistical estimation technique to samples resulting from the execution of a system.

Minas Charalambides, University of Illinois at Urbana-Champaign, Peter Dinges, University of Illinois at Urbana-Champaign, Gul Agha, University of Illinois at Urbana-Champaign.  2012.  Parameterized Concurrent Multi-Party Session Types. 11th International Workshop on Foundations of Coordination Languages and Self-Adaptive Systems (FOCLASA 2012). 91:16-30.

Session types have been proposed as a means of statically verifying implementations of communication protocols. Although prior work has been successful in verifying some classes of protocols, it does not cope well with parameterized, multi-actor scenarios with inherent asynchrony. For example, the sliding window protocol is inexpressible in previously proposed session type systems. This paper describes System-A, a new typing language which overcomes many of the expressiveness limitations of prior work. System-A explicitly supports asynchrony and parallelism, as well as multiple forms of parameterization. We define System-A and show how it can be used for the static verification of a large class of asynchronous communication protocols.

2015-11-18
Phuong Cao, University of Illinois at Urbana-Champaign, Eric Badger, University of Illinois at Urbana-Champaign, Adam Slagell, University of Illinois at Urbana-Champaign, Zbigniew Kalbarczyk, University of Illinois at Urbana-Champaign, Ravishankar Iyer, University of Illinois at Urbana-Champaign.  2015.  Preemptive Intrusion Detection: Theoretical Framework and Real-World Measurements. Symposium and Bootcamp on the Science of Security, (HotSoS 2015).

This paper presents a Factor Graph based framework called AttackTagger for highly accurate and preemptive detection of attacks, i.e., before the system misuse. We use secu- rity logs on real incidents that occurred over a six-year pe- riod at the National Center for Supercomputing Applica- tions (NCSA) to evaluate AttackTagger. Our data consist of security incidents that led to compromise of the target system, i.e., the attacks in the incidents were only identified after the fact by security analysts. AttackTagger detected 74 percent of attacks, and the majority them were detected before the system misuse. Finally, AttackTagger uncovered six hidden attacks that were not detected by intrusion de- tection systems during the incidents or by security analysts in post-incident forensic analysis.

2015-11-17
Ray Essick, University of Illinois at Urbana-Champaign, Ji-Woong Lee, Pennsylvania State University, Geir Dullerud, University of Illinois at Urbana-Champaign.  2014.  Path-By-Path Output Regulation of Switched Systems With a Receding Horizon of Modal Knowledge. American Control Conference (ACC).

We address a discrete-time LQG control problem over a fixed performance window and apply a receding-horizon type control strategy, resulting in an exact solution to the problem in terms of semidefinite programming. The systems considered take parameters from a finite set, and switch between them according to an automaton. The controller has a finite preview of future parameters, beyond which only the set of parameters is known. We provide necessary and sufficient convex con- ditions for the existence of a controller which guarantees both exponential stability and finite-horizon performance levels for the system; the performance levels may differ according to the particular parameter sequence within the performance window. A simple, physics-based example is provided to illustrate the main results.

Zhenqi Huang, University of Illinois at Urbana-Champaign, Sayan Mitra, University of Illinois at Urbana-Champaign.  2014.  Proofs from Simulations and Modular Annotations. 17th International Conference on Hybrid Systems: Computation and Control (HSCC 2014).

We present a modular technique for simulation-based bounded verification for nonlinear dynamical systems. We introduce the notion of input-to-state discrepancy of each subsystem Ai in a larger nonlinear dynamical system A which bounds the distance between two (possibly diverging) trajectories of Ai in terms of their initial states and inputs. Using the IS discrepancy functions, we construct a low dimensional deter- ministic dynamical system M (δ). For any two trajectories of A starting δ distance apart, we show that one of them bloated by a factor determined by the trajectory of M con- tains the other. Further, by choosing appropriately small δ’s the overapproximations computed by the above method can be made arbitrarily precise. Using the above results we de- velop a sound and relatively complete algorithm for bounded safety verification of nonlinear ODEs. Our preliminary ex- periments with a prototype implementation of the algorithm show that the approach can be effective for verification of nonlinear models.

2015-11-12
Xia, Weiyi, Kantarcioglu, Murat, Wan, Zhiyu, Heatherly, Raymond, Vorobeychik, Yevgeniy, Malin, Bradley.  2015.  Process-Driven Data Privacy. Proceedings of the 24th ACM International on Conference on Information and Knowledge Management. :1021–1030.

The quantity of personal data gathered by service providers via our daily activities continues to grow at a rapid pace. The sharing, and the subsequent analysis of, such data can support a wide range of activities, but concerns around privacy often prompt an organization to transform the data to meet certain protection models (e.g., k-anonymity or E-differential privacy). These models, however, are based on simplistic adversarial frameworks, which can lead to both under- and over-protection. For instance, such models often assume that an adversary attacks a protected record exactly once. We introduce a principled approach to explicitly model the attack process as a series of steps. Specically, we engineer a factored Markov decision process (FMDP) to optimally plan an attack from the adversary's perspective and assess the privacy risk accordingly. The FMDP captures the uncertainty in the adversary's belief (e.g., the number of identied individuals that match the de-identified data) and enables the analysis of various real world deterrence mechanisms beyond a traditional protection model, such as a penalty for committing an attack. We present an algorithm to solve the FMDP and illustrate its efficiency by simulating an attack on publicly accessible U.S. census records against a real identied resource of over 500,000 individuals in a voter registry. Our results demonstrate that while traditional privacy models commonly expect an adversary to attack exactly once per record, an optimal attack in our model may involve exploiting none, one, or more indiviuals in the pool of candidates, depending on context.

2015-05-06
Stephens, B., Cox, A.L., Singla, A., Carter, J., Dixon, C., Felter, W..  2014.  Practical DCB for improved data center networks. INFOCOM, 2014 Proceedings IEEE. :1824-1832.

Storage area networking is driving commodity data center switches to support lossless Ethernet (DCB). Unfortunately, to enable DCB for all traffic on arbitrary network topologies, we must address several problems that can arise in lossless networks, e.g., large buffering delays, unfairness, head of line blocking, and deadlock. We propose TCP-Bolt, a TCP variant that not only addresses the first three problems but reduces flow completion times by as much as 70%. We also introduce a simple, practical deadlock-free routing scheme that eliminates deadlock while achieving aggregate network throughput within 15% of ECMP routing. This small compromise in potential routing capacity is well worth the gains in flow completion time. We note that our results on deadlock-free routing are also of independent interest to the storage area networking community. Further, as our hardware testbed illustrates, these gains are achievable today, without hardware changes to switches or NICs.

Meng Zhang, Bingham, J.D., Erickson, J., Sorin, D.J..  2014.  PVCoherence: Designing flat coherence protocols for scalable verification. High Performance Computer Architecture (HPCA), 2014 IEEE 20th International Symposium on. :392-403.

The goal of this work is to design cache coherence protocols with many cores that can be verified with state-of-the-art automated verification methodologies. In particular, we focus on flat (non-hierarchical) coherence protocols, and we use a mostly-automated methodology based on parametric verification (PV). We propose several design guidelines that architects should follow if they want to design protocols that can be parametrically verified. We experimentally evaluate performance, storage overhead, and scalability of a protocol verified with PV compared to a highly optimized protocol that cannot be verified with PV.

Sayed, B., Traore, I..  2014.  Protection against Web 2.0 Client-Side Web Attacks Using Information Flow Control. Advanced Information Networking and Applications Workshops (WAINA), 2014 28th International Conference on. :261-268.

The dynamic nature of the Web 2.0 and the heavy obfuscation of web-based attacks complicate the job of the traditional protection systems such as Firewalls, Anti-virus solutions, and IDS systems. It has been witnessed that using ready-made toolkits, cyber-criminals can launch sophisticated attacks such as cross-site scripting (XSS), cross-site request forgery (CSRF) and botnets to name a few. In recent years, cyber-criminals have targeted legitimate websites and social networks to inject malicious scripts that compromise the security of the visitors of such websites. This involves performing actions using the victim browser without his/her permission. This poses the need to develop effective mechanisms for protecting against Web 2.0 attacks that mainly target the end-user. In this paper, we address the above challenges from information flow control perspective by developing a framework that restricts the flow of information on the client-side to legitimate channels. The proposed model tracks sensitive information flow and prevents information leakage from happening. The proposed model when applied to the context of client-side web-based attacks is expected to provide a more secure browsing environment for the end-user.

Sumit, S., Mitra, D., Gupta, D..  2014.  Proposed Intrusion Detection on ZRP based MANET by effective k-means clustering method of data mining. Optimization, Reliabilty, and Information Technology (ICROIT), 2014 International Conference on. :156-160.

Mobile Ad-Hoc Networks (MANET) consist of peer-to-peer infrastructure less communicating nodes that are highly dynamic. As a result, routing data becomes more challenging. Ultimately routing protocols for such networks face the challenges of random topology change, nature of the link (symmetric or asymmetric) and power requirement during data transmission. Under such circumstances both, proactive as well as reactive routing are usually inefficient. We consider, zone routing protocol (ZRP) that adds the qualities of the proactive (IARP) and reactive (IERP) protocols. In ZRP, an updated topological map of zone centered on each node, is maintained. Immediate routes are available inside each zone. In order to communicate outside a zone, a route discovery mechanism is employed. The local routing information of the zones helps in this route discovery procedure. In MANET security is always an issue. It is possible that a node can turn malicious and hamper the normal flow of packets in the MANET. In order to overcome such issue we have used a clustering technique to separate the nodes having intrusive behavior from normal behavior. We call this technique as effective k-means clustering which has been motivated from k-means. We propose to implement Intrusion Detection System on each node of the MANET which is using ZRP for packet flow. Then we will use effective k-means to separate the malicious nodes from the network. Thus, our Ad-Hoc network will be free from any malicious activity and normal flow of packets will be possible.

Shaohua Tang, Lingling Xu, Niu Liu, Xinyi Huang, Jintai Ding, Zhiming Yang.  2014.  Provably Secure Group Key Management Approach Based upon Hyper-Sphere. Parallel and Distributed Systems, IEEE Transactions on. 25:3253-3263.

Secure group communication systems have become increasingly important for many emerging network applications. An efficient and robust group key management approach is indispensable to a secure group communication system. Motivated by the theory of hyper-sphere, this paper presents a new group key management approach with a group controller (GC). In our new design, a hyper-sphere is constructed for a group and each member in the group corresponds to a point on the hyper-sphere, which is called the member's private point. The GC computes the central point of the hyper-sphere, intuitively, whose “distance” from each member's private point is identical. The central point is published such that each member can compute a common group key, using a function by taking each member's private point and the central point of the hyper-sphere as the input. This approach is provably secure under the pseudo-random function (PRF) assumption. Compared with other similar schemes, by both theoretical analysis and experiments, our scheme (1) has significantly reduced memory and computation load for each group member; (2) can efficiently deal with massive membership change with only two re-keying messages, i.e., the central point of the hyper-sphere and a random number; and (3) is efficient and very scalable for large-size groups.

Slomovic, A..  2014.  Privacy Issues in Identity Verification. Security Privacy, IEEE. 12:71-73.

Identity verification plays an important role in creating trust in the economic system. It can, and should, be done in a way that doesn't decrease individual privacy.