  This paper investigates the achievable region of a $K$-user discrete
memoryless (DM) multiple access wiretap (MAC-WT) channel, where each user
transmits both secret and open messages. All these messages are intended for
Bob, while Eve is only interested in the secret messages. In the achievable
coding strategy, the confidential information is protected by open messages and
also by the introduction of auxiliary messages. When introducing an auxiliary
message, one has to ensure that, on one hand, its rate is large enough for
protecting the secret message from Eve and, on the other hand, the resulting
sum rate (together with the secret and open message rate) does not exceed Bob's
decoding capability. This yields an inequality structure involving the rates of
all users' secret, open, and auxiliary messages. To obtain the rate region, the
auxiliary message rates must be eliminated from the system of inequalities. A
direct application of the Fourier-Motzkin elimination procedure is elusive
since a) it requires that the number of users $K$ is explicitly given, and b)
even for small $K = 3, 4, \ldots$, the number of inequalities becomes extremely
large. We prove the result for general $K$ through the combined use of
Fourier-Motzkin elimination procedure and mathematical induction. This paper
adopts the strong secrecy metric, characterized by information leakage. To
prove the achievability under this criterion, we analyze the resolvability
region of a $K$-user DM-MAC channel. In addition, we show that users with zero
secrecy rate can play different roles and use different strategies in encoding
their messages. These strategies yield non-redundant rate inequalities. By
considering all possible coding strategies, we provide a new achievable region
for the considered channel, and show that it strictly improves those already
known in the existing literature by considering a specific example.
