  We consider a single-cell downlink massive MIMO communication in the presence
of an adversary capable of jamming and eavesdropping simultaneously. We show
that massive MIMO communication is naturally resilient to no training-phase
jamming attack in which the adversary jams only the data communication and
eavesdrops both the data communication and the training. Specifically, we show
that the secure degrees of freedom (DoF) attained in the presence of such an
attack is identical to the maximum DoF attained under no attack. Further, we
evaluate the number of antennas that base station (BS) requires in order to
establish information theoretic security without even a need for Wyner
encoding. Next, we show that things are completely different once the adversary
starts jamming the training phase. Specifically, we consider an attack, called
training-phase jamming in which the adversary jams and eavesdrops both the
training and the data communication. We show that under such an attack, the
maximum secure DoF is equal to zero. Furthermore, the maximum achievable rates
of users vanish even in the asymptotic regime in the number of BS antennas. To
counter this attack, we develop a defense strategy in which we use a secret key
to encrypt the pilot sequence assignments to hide them from the adversary,
rather than encrypt the data. We show that, if the cardinality of the set of
pilot signals are scaled appropriately, hiding the pilot signal assignments
from the adversary enables the users to achieve secure DoF, identical to the
maximum achievable DoF under no attack. Finally, we discuss how computational
cryptography is a legitimate candidate to hide the pilot signal assignments.
Indeed, while information theoretic security is not achieved with cryptography,
the computational power necessary for the adversary to achieve a non-zero
mutual information leakage rate goes to infinity.
