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.