177 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
On the Optimality of Secret Key Agreement via Omniscience
For the multiterminal secret key agreement problem under a private source
model, it is known that the maximum key rate, i.e., the secrecy capacity, can
be achieved through communication for omniscience, but the omniscience strategy
can be strictly suboptimal in terms of minimizing the public discussion rate.
While a single-letter characterization is not known for the minimum discussion
rate needed for achieving the secrecy capacity, we derive single-letter lower
and upper bounds that yield some simple conditions for omniscience to be
discussion-rate optimal. These conditions turn out to be enough to deduce the
optimality of omniscience for a large class of sources including the
hypergraphical sources. Through conjectures and examples, we explore other
source models to which our methods do not easily extend
On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model
The focus of this paper is on the public communication required for
generating a maximal-rate secret key (SK) within the multiterminal source model
of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the
two-terminal scenario, we derive a lower bound on the communication complexity,
, defined to be the minimum rate of public communication needed
to generate a maximal-rate SK. It is well known that the minimum rate of
communication for omniscience, denoted by , is an upper bound on
. For the class of pairwise independent network (PIN) models
defined on uniform hypergraphs, we show that a certain "Type "
condition, which is verifiable in polynomial time, guarantees that our lower
bound on meets the upper bound. Thus, PIN
models satisfying our condition are -maximal, meaning that the
upper bound holds with equality. This allows
us to explicitly evaluate for such PIN models. We also give
several examples of PIN models that satisfy our Type condition.
Finally, we prove that for an arbitrary multiterminal source model, a stricter
version of our Type condition implies that communication from
\emph{all} terminals ("omnivocality") is needed for establishing a SK of
maximum rate. For three-terminal source models, the converse is also true:
omnivocality is needed for generating a maximal-rate SK only if the strict Type
condition is satisfied. Counterexamples exist that show that the
converse is not true in general for source models with four or more terminals.Comment: Submitted to the IEEE Transactions on Information Theory. arXiv admin
note: text overlap with arXiv:1504.0062
On the Communication Complexity of Secret Key Generation in the Multiterminal Source Model
Communication complexity refers to the minimum rate of public communication
required for generating a maximal-rate secret key (SK) in the multiterminal
source model of Csiszar and Narayan. Tyagi recently characterized this
communication complexity for a two-terminal system. We extend the ideas in
Tyagi's work to derive a lower bound on communication complexity in the general
multiterminal setting. In the important special case of the complete graph
pairwise independent network (PIN) model, our bound allows us to determine the
exact linear communication complexity, i.e., the communication complexity when
the communication and SK are restricted to be linear functions of the
randomness available at the terminals.Comment: A 5-page version of this manuscript will be submitted to the 2014
IEEE International Symposium on Information Theory (ISIT 2014
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