600 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
Reconciliation of a Quantum-Distributed Gaussian Key
Two parties, Alice and Bob, wish to distill a binary secret key out of a list
of correlated variables that they share after running a quantum key
distribution protocol based on continuous-spectrum quantum carriers. We present
a novel construction that allows the legitimate parties to get equal bit
strings out of correlated variables by using a classical channel, with as few
leaked information as possible. This opens the way to securely correcting
non-binary key elements. In particular, the construction is refined to the case
of Gaussian variables as it applies directly to recent continuous-variable
protocols for quantum key distribution.Comment: 8 pages, 4 figures. Submitted to the IEEE for possible publication.
Revised version to improve its clarit
On privacy amplification, lossy compression, and their duality to channel coding
We examine the task of privacy amplification from information-theoretic and
coding-theoretic points of view. In the former, we give a one-shot
characterization of the optimal rate of privacy amplification against classical
adversaries in terms of the optimal type-II error in asymmetric hypothesis
testing. This formulation can be easily computed to give finite-blocklength
bounds and turns out to be equivalent to smooth min-entropy bounds by Renner
and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a
bound in terms of the divergence by Yang, Schaefer, and Poor
[arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy
amplification based on linear codes can be easily repurposed for channel
simulation. Combined with known relations between channel simulation and lossy
source coding, this implies that privacy amplification can be understood as a
basic primitive for both channel simulation and lossy compression. Applied to
symmetric channels or lossy compression settings, our construction leads to
proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing
to the notion of channel duality recently detailed by us in [IEEE Trans. Info.
Theory 64, 577 (2018)], we show that linear error-correcting codes for
symmetric channels with quantum output can be transformed into linear lossy
source coding schemes for classical variables arising from the dual channel.
This explains a "curious duality" in these problems for the (self-dual) erasure
channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and
partly anticipates recent results on optimal lossy compression by polar and
low-density generator matrix codes.Comment: v3: updated to include equivalence of the converse bound with smooth
entropy formulations. v2: updated to include comparison with the one-shot
bounds of arXiv:1706.03866. v1: 11 pages, 4 figure
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