19 research outputs found
Secret Key Agreement under Discussion Rate Constraints
For the multiterminal secret key agreement problem, new single-letter lower
bounds are obtained on the public discussion rate required to achieve any given
secret key rate below the secrecy capacity. The results apply to general source
model without helpers or wiretapper's side information but can be strengthened
for hypergraphical sources. In particular, for the pairwise independent
network, the results give rise to a complete characterization of the maximum
secret key rate achievable under a constraint on the total discussion rate
Compressed Secret Key Agreement: Maximizing Multivariate Mutual Information Per Bit
The multiterminal secret key agreement problem by public discussion is
formulated with an additional source compression step where, prior to the
public discussion phase, users independently compress their private sources to
filter out strongly correlated components for generating a common secret key.
The objective is to maximize the achievable key rate as a function of the joint
entropy of the compressed sources. Since the maximum achievable key rate
captures the total amount of information mutual to the compressed sources, an
optimal compression scheme essentially maximizes the multivariate mutual
information per bit of randomness of the private sources, and can therefore be
viewed more generally as a dimension reduction technique. Single-letter lower
and upper bounds on the maximum achievable key rate are derived for the general
source model, and an explicit polynomial-time computable formula is obtained
for the pairwise independent network model. In particular, the converse results
and the upper bounds are obtained from those of the related secret key
agreement problem with rate-limited discussion. A precise duality is shown for
the two-user case with one-way discussion, and such duality is extended to
obtain the desired converse results in the multi-user case. In addition to
posing new challenges in information processing and dimension reduction, the
compressed secret key agreement problem helps shed new light on resolving the
difficult problem of secret key agreement with rate-limited discussion, by
offering a more structured achieving scheme and some simpler conjectures to
prove
Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory
It is known that the mutual information, in the sense of Kolmogorov
complexity, of any pair of strings x and y is equal to the length of the
longest shared secret key that two parties can establish via a probabilistic
protocol with interaction on a public channel, assuming that the parties hold
as their inputs x and y respectively. We determine the worst-case communication
complexity of this problem for the setting where the parties can use private
sources of random bits. We show that for some x, y the communication complexity
of the secret key agreement does not decrease even if the parties have to agree
on a secret key whose size is much smaller than the mutual information between
x and y. On the other hand, we discuss examples of x, y such that the
communication complexity of the protocol declines gradually with the size of
the derived secret key. The proof of the main result uses spectral properties
of appropriate graphs and the expander mixing lemma, as well as information
theoretic techniques.Comment: 33 pages, 6 figures. v3: the full version of the MFCS 2020 pape