Elsevier

Performance Evaluation

Volume 69, Issue 12, December 2012, Pages 643-661
Performance Evaluation

Performance modelling of anonymity protocols

https://doi.org/10.1016/j.peva.2012.08.001Get rights and content

Abstract

Anonymous network communication protocols provide privacy for Internet-based communication. In this paper, we focus on the performance and scalability of anonymity protocols. In particular, we develop performance models for two anonymity protocols from the prior literature (Buses and Taxis), as well as our own newly proposed protocol (Motorcycles). Using a combination of experimental implementation, simulation, and analysis, we show that: (1) the message latency of the Buses protocol is O(N2), scaling quadratically with the number of participants; (2) the message latency of the Taxis protocol is O(N), scaling linearly with the number of participants; (3) the message latency of the Motorcycles protocol is O(log2N), scaling logarithmically with the number of participants. Motorcycles can provide scalable anonymous network communication, without compromising the strength of anonymity provided by Buses or Taxis.

Introduction

Certain Internet applications require anonymity, wherein the identities of communicating participants are concealed. These applications can be used both for benevolent social purposes (e.g., crime stoppers, freedom of speech, on-line counselling for victims of abuse, protecting human rights, and whistle blowing), as well as for nefarious purposes1(e.g., criminal activities, illegal file-sharing, malware distribution, and terrorism). In general, anonymous communication provides privacy, and eliminates the risks associated with compromised identities.

Anonymous communication on the Internet is supported using anonymity protocols [1]. These protocols protect the identities of communicating parties from others, thus ensuring privacy for network-based communication. Such protocols can provide both data anonymity and connection anonymity. Data anonymity [2] removes identifying data in messages, such as the sender address in an e-mail. Connection anonymity [2] obscures the traffic communication patterns, preventing traffic analysis that traces a message through the network from the initiator (the original sender of a message) to the responder (the final receiver of a message). Connection anonymity can be further subdivided into sender anonymity, receiver anonymity, mutual anonymity, and unlinkability [3]. The type of connection anonymity required is application-dependent.

Two important characteristics of anonymity protocols are the strength of anonymity that they provide, and the scalability of the protocol itself. The strength of an anonymity protocol is usually measured in an information-theoretic sense, by determining the probability that an attacker or observer can identify communicating parties. These issues are well addressed in the security and privacy literature. Scalability refers to the communication overhead associated with a protocol (e.g., end-to-end latency), and how this grows with the size of the network. These issues are less well-studied in the literature, particularly since few anonymity protocols are implemented and used in practice. For example, Boukerche et al. [4] study an anonymous routing protocol for wireless ad hoc networks, but only using simulation.

There is typically a tradeoff between strength of anonymity and the scalability of an anonymity protocol. For example, strong anonymity can be provided by aggregating many messages into batches (mixes) before forwarding them, but the batching process itself increases the end-to-end message delay. Similarly, anonymity can be fortified with dummy cover traffic (i.e., fake messages) in the network, but this increases the bandwidth consumption on the network as well as the processing overhead for participating nodes.

In this paper, we focus on the performance and scalability of three anonymous network communication protocols: Buses, Taxis, and Motorcycles. We focus on the end-to-end message latency in these protocols, and how this latency scales with the network size (i.e., number of participants). To the best of our knowledge, our paper is the first to provide a detailed performance analysis of multiple anonymity protocols to assess their practical scalability.

The primary contributions in this paper are the following:

  • We use analysis, experiments, and simulation to show that the end-to-end message latency of the Buses protocol is O(N2), scaling quadratically with the size of the network.

  • We use analysis, experiments, and simulation to show that the message latency of the Taxis protocol is O(N), scaling linearly with the network size.

  • We propose a new anonymity protocol, Motorcycles, that improves upon Buses and Taxis.

  • We use analysis, experiments, and simulation to show that the message latency of the Motorcycles protocol is O(log2N), scaling logarithmically with the network size.

The rest of this paper is organized as follows. Section 2 provides background information on anonymous communication. Section 3 describes the three anonymity protocols analysed in our paper. Sections 4 High-level performance model, 5 Detailed models present our analysis of these protocols. Section 6 presents simulation and experimental results to validate our analytical models. Finally, Section 7 concludes the paper.

Section snippets

Anonymity techniques

Anonymous communication is a vibrant research area with many anonymity schemes proposed [1], [5], [6]. Delay-tolerant applications, such as e-mail, can use strong anonymous communication schemes [7]. However, interactive applications, such as Web browsing and SSH, require lower overhead to minimize the end-to-end message latency.

Designing a strong anonymous communication scheme with low latency is a challenge [8]. As an interim solution, anonymous communication schemes such as Crowds [9] and

Buses

There are several versions of the Buses protocol described in [17]; we now focus on a specific version that we have implemented and demonstrated experimentally [18].

There are three key innovations in our version of the Buses protocol. First, we use owned seats. This feature restricts participating nodes to only insert messages into specific (owned) seats on the bus. This feature drastically reduces the number of bus seats required, while avoiding the random seat collisions that can occur in the

High-level performance model

In this section, we first develop a high-level mathematical model to characterize end-to-end message delay in our anonymity protocols. This unified model applies for all three protocols of interest. We then refine the analysis to produce closed-form solutions for each protocol.

Detailed models

This section presents detailed performance models for several special cases. First, we consider the case when there are no queueing delays (i.e., QC0). Here, results are obtained for the asymptotic scalability of the three protocols. Second, we use a Poisson assumption to obtain explicit expressions for the queueing delay when K=1. Third, we show how the model can be extended to handle heterogeneous message generation rates and message acknowledgements, respectively. Section 6 validates our

Numerical results

In this section, we validate our analytical model for the anonymity protocols, and present numerical results illustrating the performance and scalability of these protocols. We start with cross-validation of our analytical models and simulation models using small-scale experimental results. We then consider larger network scenarios using simulation and analysis. Finally, we consider the effects of protocol configuration parameters and offered load.

Conclusions

In this paper, we focus on the performance and scalability of anonymous network communication protocols. In particular, we develop end-to-end message latency models for three anonymity protocols: Buses, Taxis, and Motorcycles. The latter is a new anonymity protocol proposed in this paper.

Using a combination of analytical, experimental, and simulation results, we show that the message latency of the Buses protocol scales quadratically with the number of participants, while that of the Taxis

Acknowledgements

The authors thank the reviewers for their constructive feedback and suggestions, which helped to improve the clarity of the final paper. We are also grateful to Ibrahim Ismail, who implemented the first-ever prototype of the Motorcycles protocol for his M.Sc. thesis [35]. Financial support for this work was provided by Canada’s Natural Sciences and Engineering Research Council (NSERC), and by the Informatics Circle of Research Excellence (iCORE) in the Province of Alberta.

Niklas Carlsson is an Assistant Professor at Linkoping University, Sweden. He received his M.Sc. degree in Engineering Physics from Umea University in Sweden, and his Ph.D. in Computer Science from the University of Saskatchewan, Canada. His research interests are in the areas of design, modelling, and performance evaluation of distributed systems and networks.

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  • Cited by (0)

    Niklas Carlsson is an Assistant Professor at Linkoping University, Sweden. He received his M.Sc. degree in Engineering Physics from Umea University in Sweden, and his Ph.D. in Computer Science from the University of Saskatchewan, Canada. His research interests are in the areas of design, modelling, and performance evaluation of distributed systems and networks.

    Carey Williamson is a Professor in the Department of Computer Science at the University of Calgary. He holds a B.Sc. (Honours) in Computer Science from the University of Saskatchewan, and a Ph.D. in Computer Science from Stanford University. His research interests include Internet protocols, wireless networks, network traffic measurement, network simulation, and Web performance.

    Andreas Hirt is a regional team leader for strategic reporting at Northern Health Authority in Prince George, BC, Canada, as well as an Adjunct Professor in the Department of Computer Science at the University of Northern British Columbia (UNBC). He received a B.Sc. (Distinction) in Computer Science from UNBC in 2002, as well as M.Sc. and Ph.D. degrees from the University of Calgary in 2004 and 2010, respectively. His research interests include networking, security, cryptography, and business intelligence.

    Michael Jacobson Jr. is an Associate Professor at the University of Calgary in the Department of Computer Science, and a member of the Centre for Information Security and Cryptography. He received a B.Sc. (Hon.) and M.Sc. from the University of Manitoba and Dr. rer. nat. from the Technical University of Darmstadt in 1999. His research interests are cryptography and related applications of computational number theory, especially as applied to algebraic number fields and function fields. Professor Jacobson is a member of the IEEE and ACM.

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