A major challenge in distributed mobile networks is network integrity, resulting from short link duration and severe transmission collisions. This paper analyzes the impact of link duration and transmission collisions on a range of on-the-fly authentication protocols, which operate based on predistributed keys and can instantly verify and forward messages. All unexpired messages within a link duration can be verified retrospectively, once the keys are matched on-the-air. We develop a new general 4D Markov model which, apart from the first three dimensions modeling a cycle of the protocols, is able to unprecedentedly capture unexpired messages between cycles in the fourth dimension. Validated by simulation, our analysis reveals that the on-the-fly authentication is efficient under short link duration, but is susceptible to transmission collisions. The authentication requires holistic cross-layer designs of retransmission and rekeying. The proposed model is able to facilitate the design of the protocol parameters, which allows the protocols to significantly outperform the state of the art.
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