Understanding Statistical Disclosure: A Least Squares Approach

Abstract

Abstract. It is widely accepted that Disclosure Attacks are effective against high-latency anonymous communication systems. A number of Disclosure Attack variants can be found in the literature that effectively de-anonymize traffic sent through a threshold mix. Nevertheless, these attacks' performance has been mostly evaluated through simulation and how their effectiveness varies with the parameters of the system is not well-understood. We present the LSDA, a novel disclosure attack based on the Maximum Likelihood (ML) approach, in which user profiles are estimated solving a Least Squares problem. Further, contrary to previous heuristic-based attacks, our approach allows to analytically derive formulae that characterize the profiling error of the LSDA with respect to the system's parameters. We verify through simulation that our predictors for the error closely model reality, and that the LSDA recovers users' profiles with greater accuracy than its predecessors.

A Least Squares approach to user profiling in pool mix-based anonymous communication systems

“…We have studied the applicability of the Least Squares Disclosure Attack [11], [12] to pool mixes. Our empirical evaluation confirms that our formulas describing the error of the attack against a threshold binomial pool mix closely model reality.…”

“…In [11] we show that a Maximum Likelihood formulation leads, after some simplifications, to the following estimate for vector p T .…”

“…We will use the following result, which is proven in [11]. Let M be an arbitrary matrix of size ρ × ρ, and U T .…”

“…In this paper we study the applicability of the Least Squares Disclosure Attack (LSDA) [11] to pool mixes. This attack models profiling as a Least Squares problem, and yields profiles that minimize the error between the actual number of output messages and a prediction based on the input messages.…”

Towards an Analysis of Passive Attacks on Anonymous Communication Systems

“…Fernando Pérez-González from University of Vigo and Troncoso from K.U.Leuven propose a method of Least Squares Disclosure Attack based on Maximum Likelihood in 2012 [13]. In the attack, the evaluation of the user's profile information to solve the least square problem.…”