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Data communication over intermittently connected mobile ad hoc networks (ICMANs) can be carried out by opportunistically employment of mobility nature of nodes and the storage space of all nodes. However, due to intermittent connectivity, security schemes introduced for the conventional mobile ad hoc networks (MANETs) cannot be directly deployed over ICMANs for node authentication. Therefore, this paper adopts the nodes' mobilities to implement the (t, n) threshold secret sharing and identity-based cryptography (IBC) over ICMANs. Such (t, n) based IBC can subsequently be utilized to facilitate node authentication to defend against the malicious attacks in the ICMANs context. In the proposed security scheme, the master private key of IBC is shared by n distributed private key generators (PKGs), while each node needs to employ its mobility nature to contact at least t-out-of-n PKGs to reconstruct its own private key. To overcome the routing-security interdependence cycle, only face-to-face based node authentication is employed. In other words, authentication and key establishment between nodes and distributed PKGs is only allowed whenever they encounter each other directly. Delay performance of such (t, n) based IBC in the ICMANs context is accordingly modeled and evaluated.