16 research outputs found
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
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
Achieving SK Capacity in the Source Model: When Must All Terminals Talk?
In this paper, we address the problem of characterizing the instances of the
multiterminal source model of Csisz\'ar and Narayan in which communication from
all terminals is needed for establishing a secret key of maximum rate. We give
an information-theoretic sufficient condition for identifying such instances.
We believe that our sufficient condition is in fact an exact characterization,
but we are only able to prove this in the case of the three-terminal source
model. We also give a relatively simple criterion for determining whether or
not our condition holds for a given multiterminal source model.Comment: A 5-page version of this paper was submitted to the 2014 IEEE
International Symposium on Information Theory (ISIT 2014
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
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
The Communication Complexity of Achieving SK Capacity in a Class of PIN Models
The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csiszar and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by R-CO, is an upper bound on the communication complexity, denoted by R-SK. A source model for which this upper bound is tight is called R-SK-maximal. In this paper, we establish a sufficient condition for R-SK-maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute R-SK exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee R-SK-maximality for sources beyond PIN models