Nymbler: Privacy-enhanced Protection from Abuses of Anonymity

Anonymous communications networks help to solve the real and important problem of enabling users to communicate privately over the Internet. However, by doing so, they also introduce an entirely new problem: How can service providers on the Internet---such as websites, IRC networks and mail servers---allow anonymous access while protecting themselves against abuse by misbehaving anonymous users? Recent research efforts have focused on using anonymous blacklisting systems (also known as anonymous revocation systems) to solve this problem. As opposed to revocable anonymity systems, which enable some trusted third party to deanonymize users, anonymous blacklisting systems provide a way for users to authenticate anonymously with a service provider, while enabling the service provider to revoke access from individual misbehaving anonymous users without revealing their identities. The literature contains several anonymous blacklisting systems, many of which are impractical for real-world deployment. In 2006, however, Tsang et al. proposed Nymble, which solves the anonymous blacklisting problem very efficiently using trusted third parties. Nymble has inspired a number of subsequent anonymous blacklisting systems. Some of these use fundamentally different approaches to accomplish what Nymble does without using third parties at all; so far, these proposals have all suffered from serious performance and scalability problems. Other systems build on the Nymble framework to reduce Nymble's trust assumptions while maintaining its highly efficient design. The primary contribution of this thesis is a new anonymous blacklisting system built on the Nymble framework---a nimbler version of Nymble---called Nymbler. We propose several enhancements to the Nymble framework that facilitate the construction of a scheme that minimizes trust in third parties. We then propose a new set of security and privacy properties that anonymous blacklisting systems should possess to protect: 1) users' privacy against malicious service providers and third parties (including other malicious users), and 2) service providers against abuse by malicious users. We also propose a set of performance requirements that anonymous blacklisting systems should meet to maximize their potential for real-world adoption, and formally define some optional features in the anonymous blacklisting systems literature. We then present Nymbler, which improves on existing Nymble-like systems by reducing the level of trust placed in third parties, while simultaneously providing stronger privacy guarantees and some new functionality. It avoids dependence on trusted hardware and unreasonable assumptions about non-collusion between trusted third parties. We have implemented all key components of Nymbler, and our measurements indicate that the system is highly practical. Our system solves several open problems in the anonymous blacklisting systems literature, and makes use of some new cryptographic constructions that are likely to be of independent theoretical interest

On the difficult tradeoff between security and privacy: Challenges for the management of digital identities

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-19713-5_39The deployment of security measures can lead in many occasions to an infringement of users’ privacy. Indeed, nowadays we have many examples about surveillance programs or personal data breaches in online service providers. In order to avoid the latter problem, we need to establish security measures that do not involve a violation of privacy rights. In this communication we discuss the main challenges when conciliating information security and users’ privacy.This work was supported by Comunidad de Madrid (Spain) under the project S2013/ICE-3095-CM (CIBERDINE)

Zero-Knowledge Argument for Polynomial Evaluation with Application to Blacklists

Verification of a polynomial’s evaluation in a secret committed value plays a role in cryptographic applications such as non-membership or membership proofs. We construct a novel special honest verifier zero-knowledge argument for correct polynomial evaluation. The argument has logarithmic communication cost in the degree of the polynomial, which is a significant improvement over the state of the art with cubic root complexity at best. The argument is relatively efficient to generate and very fast to verify compared to previous work. The argument has a simple public-coin 3-move structure and only relies on the discrete logarithm assumption. The polynomial evaluation argument can be used as a building block to construct zero-knowledge membership and non-membership arguments with communication that is logarithmic in the size of the blacklist. Non-membership proofs can be used to design anonymous blacklisting schemes allowing online services to block misbehaving users without learning the identity of the user. They also allow the blocking of single users of anonymization networks without blocking the whole network

ECC2K-130 on NVIDIA GPUs

Abstract. Computations of small discrete logarithms are feasible even in "secure" groups, and are used as subroutines in several cryptographic protocols in the literature. For example, the Boneh-Goh-Nissim degree-2-homomorphic public-key encryption system uses generic square-root discrete-logarithm methods for decryption. This paper shows how to use a small group-specific table to accelerate these subroutines. The cost of setting up the table grows with the table size, but the acceleration also grows with the table size. This paper shows experimentally that computing a discrete logarithm in an interval of order takes only 1.93

Computing Elliptic Curve Discrete Logarithms with Improved Baby-step Giant-step Algorithm

The negation map can be used to speed up the computation of elliptic curve discrete logarithms using either the baby-step giant-step algorithm (BSGS) or Pollard rho. Montgomery\u27s simultaneous modular inversion can also be used to speed up Pollard rho when running many walks in parallel. We generalize these ideas and exploit the fact that for any two elliptic curve points $X$ and $Y$, we can efficiently get $X-Y$ when we compute $X+Y$. We apply these ideas to speed up the baby-step giant-step algorithm. Compared to the previous methods, the new methods can achieve a significant speedup for computing elliptic curve discrete logarithms in small groups or small intervals. Another contribution of our paper is to give an analysis of the average-case running time of Bernstein and Lange\u27s ``grumpy giants and a baby\u27\u27 algorithm, and also to consider this algorithm in the case of groups with efficient inversion. Our conclusion is that, in the fully-optimised context, both the interleaved BSGS and grumpy-giants algorithms have superior average-case running time compared with Pollard rho. Furthermore, for the discrete logarithm problem in an interval, the interleaved BSGS algorithm is considerably faster than the Pollard kangaroo or Gaudry-Schost methods

Practical zero-knowledge Protocols based on the discrete logarithm Assumption

Zero-knowledge proofs were introduced by Goldwasser, Micali, and Rackoff. A zero-knowledge proof allows a prover to demonstrate knowledge of some information, for example that they know an element which is a member of a list or which is not a member of a list, without disclosing any further information about that element. Existing constructions of zero-knowledge proofs which can be applied to all languages in NP are impractical due to their communication and computational complexity. However, it has been known since Guillou and Quisquater's identification protocol from 1988 and Schnorr's identification protocol from 1991 that practical zero-knowledge protocols for specific problems exist. Because of this, a lot of work was undertaken over the recent decades to find practical zero-knowledge proofs for various other specific problems, and in recent years many protocols were published which have improved communication and computational complexity. Nevertheless, to find more problems which have an efficient and practical zero-knowledge proof system and which can be used as building blocks for other protocols is an ongoing challenge of modern cryptography. This work addresses the challenge, and constructs zero-knowledge arguments with sublinear communication complexity, and achievable computational demands. The security of our protocols is only based on the discrete logarithm assumption. Polynomial evaluation arguments are proposed for univariate polynomials, for multivariate polynomials, and for a batch of univariate polynomials. Furthermore, the polynomial evaluation argument is applied to construct practical membership and non-membership arguments. Finally, an efficient method for proving the correctness of a shuffle is proposed. The proposed protocols have been tested against current state of the art versions in order to verify their practicality in terms of run-time and communication cost. We observe that the performance of our protocols is fast enough to be practical for medium range parameters. Furthermore, all our verifiers have a better asymptotic behavior than earlier verifiers independent of the parameter range, and in real life settings our provers perform better than provers of existing protocols. The analysis of the results shows that the communication cost of our protocols is very small; therefore, our new protocols compare very favorably to the current state of the art

Efficient Zero-Knowledge Proofs and Applications

Zero-knowledge proofs provide a means for a prover to convince a verifier that some claim is true and nothing more. The ability to prove statements while conveying zero information beyond their veracity has profound implications for cryptography and, especially, for its applicability to privacy-enhancing technologies. Unfortunately, the most common zero-knowledge techniques in the literature suffer from poor scalability, which limits their usefulness in many otherwise promising applications. This dissertation addresses the problem of designing communication- and computation-efficient protocols for zero-knowledge proofs and arguments of propositions that comprise many "simple" predicates. In particular, we propose a new formal model in which to analyze batch zero-knowledge protocols and perform the first systematic study of systems for batch zero-knowledge proofs and arguments of knowledge. In the course of this study, we suggest a general construction for batch zero-knowledge proof systems and use it to realize several new protocols suitable for proving knowledge of and relationships among large batches of discrete logarithm (DL) representations in prime-order groups. Our new protocols improve on existing protocols in several ways; for example, among the new protocols is one with lower asymptotic computation cost than any other such system in the literature. We also tackle the problem of constructing batch proofs of partial knowledge, proposing new protocols to prove knowledge of a DL that is equal to at least k-out-of-n other DLs, at most k-out-of-n other DLs, or exactly k-out-of-n other DLs. These constructions are particularly interesting as they prove some propositions that appear difficult to prove using existing techniques, even when efficiency is not a primary consideration. We illustrate the applicability of our new techniques by using them to construct efficient protocols for anonymous blacklisting and reputation systems

Improving Security and Performance in Low Latency Anonymous Networks

Conventional wisdom dictates that the level of anonymity offered by low latency anonymity networks increases as the user base grows. However, the most significant obstacle to increased adoption of such systems is that their security and performance properties are perceived to be weak. In an effort to help foster adoption, this dissertation aims to better understand and improve security, anonymity, and performance in low latency anonymous communication systems. To better understand the security and performance properties of a popular low latency anonymity network, we characterize Tor, focusing on its application protocol distribution, geopolitical client and router distributions, and performance. For instance, we observe that peer-to-peer file sharing protocols use an unfair portion of the network’s scarce bandwidth. To reduce the congestion produced by bulk downloaders in networks such as Tor, we design, implement, and analyze an anonymizing network tailored specifically for the BitTorrent peer-to-peer file sharing protocol. We next analyze Tor’s security and anonymity properties and empirically show that Tor is vulnerable to practical end-to-end traffic correlation attacks launched by relatively weak adversaries that inflate their bandwidth claims to attract traffic and thereby compromise key positions on clients’ paths. We also explore the security and performance trade-offs that revolve around path length design decisions and we show that shorter paths offer performance benefits and provide increased resilience to certain attacks. Finally, we discover a source of performance degradation in Tor that results from poor congestion and flow control. To improve Tor’s performance and grow its user base, we offer a fresh approach to congestion and flow control inspired by techniques from IP and ATM networks