829 research outputs found
Expurgation Exponent of Leaked Information in Privacy Amplification for Binary Sources
We investigate the privacy amplification problem in which Eve can observe the
uniform binary source through a binary erasure channel (BEC) or a binary
symmetric channel (BSC). For this problem, we derive the so-called expurgation
exponent of the information leaked to Eve. The exponent is derived by relating
the leaked information to the error probability of the linear code that is
generated by the linear hash function used in the privacy amplification, which
is also interesting in its own right. The derived exponent is larger than
state-of-the-art exponent recently derived by Hayashi at low rate.Comment: 5 pages, 7 figures, to be presented at IEEE Information Theory
Workshop (ITW) 201
Converses for Secret Key Agreement and Secure Computing
We consider information theoretic secret key agreement and secure function
computation by multiple parties observing correlated data, with access to an
interactive public communication channel. Our main result is an upper bound on
the secret key length, which is derived using a reduction of binary hypothesis
testing to multiparty secret key agreement. Building on this basic result, we
derive new converses for multiparty secret key agreement. Furthermore, we
derive converse results for the oblivious transfer problem and the bit
commitment problem by relating them to secret key agreement. Finally, we derive
a necessary condition for the feasibility of secure computation by trusted
parties that seek to compute a function of their collective data, using an
interactive public communication that by itself does not give away the value of
the function. In many cases, we strengthen and improve upon previously known
converse bounds. Our results are single-shot and use only the given joint
distribution of the correlated observations. For the case when the correlated
observations consist of independent and identically distributed (in time)
sequences, we derive strong versions of previously known converses
Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy
This paper investigates the privacy amplification problem, and compares the
existing two bounds: the exponential bound derived by one of the authors and
the min-entropy bound derived by Renner. It turns out that the exponential
bound is better than the min-entropy bound when a security parameter is rather
small for a block length, and that the min-entropy bound is better than the
exponential bound when a security parameter is rather large for a block length.
Furthermore, we present another bound that interpolates the exponential bound
and the min-entropy bound by a hybrid use of the Renyi entropy and the
inf-spectral entropy.Comment: 6 pages, 4 figure
Information Geometry Approach to Parameter Estimation in Markov Chains
We consider the parameter estimation of Markov chain when the unknown
transition matrix belongs to an exponential family of transition matrices.
Then, we show that the sample mean of the generator of the exponential family
is an asymptotically efficient estimator. Further, we also define a curved
exponential family of transition matrices. Using a transition matrix version of
the Pythagorean theorem, we give an asymptotically efficient estimator for a
curved exponential family.Comment: Appendix D is adde
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