  Strong secrecy communication over a discrete memoryless state-dependent
multiple access channel (SD-MAC) with an external eavesdropper is investigated.
The channel is governed by discrete memoryless and i.i.d. channel states and
the channel state information (CSI) is revealed to the encoders in a causal
manner. An inner bound of the capacity is provided. To establish the inner
bound, we investigate coding schemes incorporating wiretap coding and secret
key agreement between the sender and the legitimate receiver. Two kinds of
block Markov coding schemes are studied. The first one uses backward decoding
and Wyner-Ziv coding and the secret key is constructed from a lossy
reproduction of the CSI. The other one is an extended version of the existing
coding scheme for point-to-point wiretap channels with causal CSI. We further
investigate some capacity-achieving cases for state-dependent multiple access
wiretap channels (SD-MAWCs) with degraded message sets. It turns out that the
two coding schemes are both optimal in these cases.
