  We consider the problem where a group of n nodes, connected to the same
broadcast channel (e.g., a wireless network), want to generate a common secret
bitstream, in the presence of an adversary Eve, who tries to obtain information
on the bitstream. We assume that the nodes initially share a (small) piece of
information, but do not have access to any out-of-band channel. We ask the
question: can this problem be solved without relying on Eve's computational
limitations, i.e., without using any form of public-key cryptography?
  We propose a secret-agreement protocol, where the n nodes of the group keep
exchanging bits until they have all agreed on a bit sequence that Eve cannot
reconstruct with very high probability. In this task, the nodes are assisted by
a small number of interferers, whose role is to create channel noise in a way
that bounds the amount of information Eve can overhear. Our protocol has
polynomial-time complexity and requires no changes to the physical or MAC layer
of network devices.
  First, we formally show that, under standard theoretical assumptions, our
protocol is information-theoretically secure, achieves optimal
secret-generation rate for n = 2 nodes, and scales well to an arbitrary number
of nodes. Second, we adapt our protocol to a small wireless 14-square-meter
testbed; we experimentally show that, if Eve uses a standard wireless physical
layer and is not too close to any of the nodes, 8 nodes can achieve a
secret-generation rate of 38 Kbps. To the best of our knowledge, ours is the
first experimental demonstration of information-theoretic secret exchange on a
wireless network at a rate beyond a few tens of bits per second.
