699 research outputs found
Why Botnets Work: Distributed Brute-Force Attacks Need No Synchronization
In September 2017, McAffee Labs quarterly report estimated that brute force
attacks represent 20\% of total network attacks, making them the most prevalent
type of attack ex-aequo with browser based vulnerabilities. These attacks have
sometimes catastrophic consequences, and understanding their fundamental limits
may play an important role in the risk assessment of password-secured systems,
and in the design of better security protocols. While some solutions exist to
prevent online brute-force attacks that arise from one single IP address,
attacks performed by botnets are more challenging. In this paper, we analyze
these distributed attacks by using a simplified model. Our aim is to understand
the impact of distribution and asynchronization on the overall computational
effort necessary to breach a system. Our result is based on Guesswork, a
measure of the number of queries (guesses) required of an adversary before a
correct sequence, such as a password, is found in an optimal attack. Guesswork
is a direct surrogate for time and computational effort of guessing a sequence
from a set of sequences with associated likelihoods. We model the lack of
synchronization by a worst-case optimization in which the queries made by
multiple adversarial agents are received in the worst possible order for the
adversary, resulting in a min-max formulation. We show that, even without
synchronization, and for sequences of growing length, the asymptotic optimal
performance is achievable by using randomized guesses drawn from an appropriate
distribution. Therefore, randomization is key for distributed asynchronous
attacks. In other words, asynchronous guessers can asymptotically perform
brute-force attacks as efficiently as synchronized guessers.Comment: Accepted to IEEE Transactions on Information Forensics and Securit
Centralized vs Decentralized Multi-Agent Guesswork
We study a notion of guesswork, where multiple agents intend to launch a
coordinated brute-force attack to find a single binary secret string, and each
agent has access to side information generated through either a BEC or a BSC.
The average number of trials required to find the secret string grows
exponentially with the length of the string, and the rate of the growth is
called the guesswork exponent. We compute the guesswork exponent for several
multi-agent attacks. We show that a multi-agent attack reduces the guesswork
exponent compared to a single agent, even when the agents do not exchange
information to coordinate their attack, and try to individually guess the
secret string using a predetermined scheme in a decentralized fashion. Further,
we show that the guesswork exponent of two agents who do coordinate their
attack is strictly smaller than that of any finite number of agents
individually performing decentralized guesswork.Comment: Accepted at IEEE International Symposium on Information Theory (ISIT)
201
Soft Guessing Under Log-Loss Distortion Allowing Errors
This paper deals with the problem of soft guessing under log-loss distortion
(logarithmic loss) that was recently investigated by [Wu and Joudeh, IEEE ISIT,
pp. 466--471, 2023]. We extend this problem to soft guessing allowing errors,
i.e., at each step, a guesser decides whether to stop the guess or not with
some probability and if the guesser stops guessing, then the guesser declares
an error. We show that the minimal expected value of the cost of guessing under
the constraint of the error probability is characterized by smooth R\'enyi
entropy. Furthermore, we carry out an asymptotic analysis for a stationary and
memoryless source
Computational Security Subject to Source Constraints, Guesswork and Inscrutability
Guesswork forms the mathematical framework for
quantifying computational security subject to brute-force determination
by query. In this paper, we consider guesswork
subject to a per-symbol Shannon entropy budget. We introduce
inscrutability rate to quantify the asymptotic difficulty of guessing
U out of V secret strings drawn from the string-source and
prove that the inscrutability rate of any string-source supported
on a finite alphabet X, if it exists, lies between the per-symbol
Shannon entropy constraint and log |X|. We show that for a
stationary string-source, the inscrutability rate of guessing any
fraction (1 - ϵ) of the V strings for any fixed ϵ > 0, as V
grows, approaches the per-symbol Shannon entropy constraint
(which is equal to the Shannon entropy rate for the stationary
string-source). This corresponds to the minimum inscrutability
rate among all string-sources with the same per-symbol Shannon
entropy. We further prove that the inscrutability rate of any
finite-order Markov string-source with hidden statistics remains
the same as the unhidden case, i.e., the asymptotic value of hiding
the statistics per each symbol is vanishing. On the other hand, we
show that there exists a string-source that achieves the upper limit
on the inscrutability rate, i.e., log |X|, under the same Shannon
entropy budget
Bounds on inference
Lower bounds for the average probability of error of estimating a hidden
variable X given an observation of a correlated random variable Y, and Fano's
inequality in particular, play a central role in information theory. In this
paper, we present a lower bound for the average estimation error based on the
marginal distribution of X and the principal inertias of the joint distribution
matrix of X and Y. Furthermore, we discuss an information measure based on the
sum of the largest principal inertias, called k-correlation, which generalizes
maximal correlation. We show that k-correlation satisfies the Data Processing
Inequality and is convex in the conditional distribution of Y given X. Finally,
we investigate how to answer a fundamental question in inference and privacy:
given an observation Y, can we estimate a function f(X) of the hidden random
variable X with an average error below a certain threshold? We provide a
general method for answering this question using an approach based on
rate-distortion theory.Comment: Allerton 2013 with extended proof, 10 page
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