  This paper studies the problem of secure communication over a K-transmitter
multiple access channel in the presence of an external eavesdropper, subject to
a joint secrecy constraint (i.e., information leakage rate from the collection
of K messages to an eavesdropper is made vanishing). As a result, we establish
the joint secrecy achievable rate region. To this end, our results build upon
two techniques in addition to the standard information-theoretic methods. The
first is a generalization of Chia-El Gamal's lemma on entropy bound for a set
of codewords given partial information. The second is to utilize a compact
representation of a list of sets that, together with properties of mutual
information, leads to an efficient Fourier-Motzkin elimination. These two
approaches could also be of independent interests in other contexts.
