10 research outputs found
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
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
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
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 password queries (guesses) before the correct one is
found in an optimal attack, which is a direct surrogate for the time and the
computational effort. We model the lack of synchronization by a worst-case
optimization in which the queries are received in the worst possible order,
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: 13 pages, 4 figure
Guessing with a Bit of Help
What is the value of a single bit to a guesser? We study this problem in a
setup where Alice wishes to guess an i.i.d. random vector, and can procure one
bit of information from Bob, who observes this vector through a memoryless
channel. We are interested in the guessing efficiency, which we define as the
best possible multiplicative reduction in Alice's guessing-moments obtainable
by observing Bob's bit. For the case of a uniform binary vector observed
through a binary symmetric channel, we provide two lower bounds on the guessing
efficiency by analyzing the performance of the Dictator and Majority functions,
and two upper bounds via maximum entropy and Fourier-analytic /
hypercontractivity arguments. We then extend our maximum entropy argument to
give a lower bound on the guessing efficiency for a general channel with a
binary uniform input, via the strong data-processing inequality constant of the
reverse channel. We compute this bound for the binary erasure channel, and
conjecture that Greedy Dictator functions achieve the guessing efficiency
Multi-User Guesswork and Brute Force Security
The guesswork problem was originally motivated by a desire to quantify computational security for single user systems. Leveraging recent results from its analysis, we extend the remit and utility of the framework to the quantification of the computational security of multi-user systems. In particular, assume that V users independently select strings stochastically from a finite, but potentially large, list. An inquisitor who does not know which strings have been selected wishes to identify U of them. The inquisitor knows the selection probabilities of each user and is equipped with a method that enables the testing of each (user, string) pair, one at a time, for whether that string had been selected by that user. Here, we establish that, unless U=V, there is no general strategy that minimizes the distribution of the number of guesses, but in the asymptote as the strings become long we prove the following: by construction, there is an asymptotically optimal class of strategies; the number of guesses required in an asymptotically optimal strategy satisfies a large deviation principle with a rate function, which is not necessarily convex, that can be determined from the rate functions of optimally guessing individual users' strings; if all users' selection statistics are identical, the exponential growth rate of the average guesswork as the string-length increases is determined by the specific Rényi entropy of the string-source with parameter (V-U+1)/(V-U+2), generalizing the known V=U=1 case; and that the Shannon entropy of the source is a lower bound on the average guesswork growth rate for all U and V, thus providing a bound on computational security for multi-user systems. Examples are presented to illustrate these results and their ramifications for systems design