  A set of m terminals, observing correlated signals, communicate interactively
to generate common randomness for a given subset of them. Knowing only the
communication, how many direct queries of the value of the common randomness
will resolve it? A general upper bound, valid for arbitrary signal alphabets,
is developed for the number of such queries by using a query strategy that
applies to all common randomness and associated communication. When the
underlying signals are independent and identically distributed repetitions of m
correlated random variables, the number of queries can be exponential in signal
length. For this case, the mentioned upper bound is tight and leads to a
single-letter formula for the largest query exponent, which coincides with the
secret key capacity of a corresponding multiterminal source model. In fact, the
upper bound constitutes a strong converse for the optimum query exponent, and
implies also a new strong converse for secret key capacity. A key tool,
estimating the size of a large probability set in terms of Renyi entropy, is
interpreted separately, too, as a lossless block coding result for general
sources. As a particularization, it yields the classic result for a discrete
memoryless source.
