1,170 research outputs found
On the Shannon Cipher System With a Wiretapper Guessing Subject to Distortion and Reliability Requirements
In this paper we discuss the processes in the Shannon cipher system with
discrete memoryless source and a guessing wiretapper. The wiretapper observes a
cryptogram of -vector of ciphered messages in the public channel and tries
to guess successively the vector of messages within given distortion level
and small probability of error less than with positive
reliability index . The security of the system is measured by the expected
number of guesses which wiretapper needs for the approximate reconstruction of
the vector of source messages. The distortion, the reliability criteria and the
possibility of upper limiting the number of guesses extend the approach studied
by Merhav and Arikan. A single-letter characterization is given for the region
of pairs (of the rate of the maximum number of guesses
and the rate of the average number of guesses) in dependence on key rate
, distortion level and reliability .Comment: 14 pages, 3 figures, Submitted to IEEE Transactions on Information
Theor
Some Useful Integral Representations for Information-Theoretic Analyses
This work is an extension of our earlier article, where a well-known integral
representation of the logarithmic function was explored, and was accompanied
with demonstrations of its usefulness in obtaining compact, easily-calculable,
exact formulas for quantities that involve expectations of the logarithm of a
positive random variable. Here, in the same spirit, we derive an exact integral
representation (in one or two dimensions) of the moment of a nonnegative random
variable, or the sum of such independent random variables, where the moment
order is a general positive noninteger real (also known as fractional moments).
The proposed formula is applied to a variety of examples with an
information-theoretic motivation, and it is shown how it facilitates their
numerical evaluations. In particular, when applied to the calculation of a
moment of the sum of a large number, , of nonnegative random variables, it
is clear that integration over one or two dimensions, as suggested by our
proposed integral representation, is significantly easier than the alternative
of integrating over dimensions, as needed in the direct calculation of the
desired moment.Comment: Published in Entropy, vol. 22, no. 6, paper 707, pages 1-29, June
2020. Available at: https://www.mdpi.com/1099-4300/22/6/70
Tight Bounds on the R\'enyi Entropy via Majorization with Applications to Guessing and Compression
This paper provides tight bounds on the R\'enyi entropy of a function of a
discrete random variable with a finite number of possible values, where the
considered function is not one-to-one. To that end, a tight lower bound on the
R\'enyi entropy of a discrete random variable with a finite support is derived
as a function of the size of the support, and the ratio of the maximal to
minimal probability masses. This work was inspired by the recently published
paper by Cicalese et al., which is focused on the Shannon entropy, and it
strengthens and generalizes the results of that paper to R\'enyi entropies of
arbitrary positive orders. In view of these generalized bounds and the works by
Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and
lossless data compression of discrete memoryless sources.Comment: The paper was published in the Entropy journal (special issue on
Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding),
vol. 20, no. 12, paper no. 896, November 22, 2018. Online available at
https://www.mdpi.com/1099-4300/20/12/89
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
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