  We present a secret key agreement (SKA) protocol for a multi-user
time-division duplex system where a base-station (BS) with a large antenna
array (LAA) shares secret keys with users in the presence of non-colluding
eavesdroppers. In the system, when the BS transmits random sequences to
legitimate users for sharing common randomness, the eavesdroppers can attempt
the pilot contamination attack (PCA) in which each of eavesdroppers transmits
its target user's training sequence in hopes of acquiring possible information
leak by steering beam towards the eavesdropper. We show that there exists a
crucial complementary relation between the received signal strengths at the
eavesdropper and its target user. This relation tells us that the eavesdropper
inevitably leaves a trace that enables us to devise a way of measuring the
amount of information leakage to the eavesdropper even if PCA parameters are
unknown. To this end, we derive an estimator for the channel gain from the BS
to the eavesdropper and propose a rate-adaptation scheme for adjusting the
length of secret key under the PCA. Extensive analysis and evaluations are
carried out under various setups, which show that the proposed scheme
adequately takes advantage of the LAA to establish the secret keys under the
PCA.
