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A k-connected wireless sensor network (WSN) allows messages to be routed via one (or more) of at least k node-disjoint paths, so that even if some nodes along one of the paths fail, or are compromised, the other paths can still be used. This is a much desired feature in fault tolerance and security, k-connectivity in this context is largely a well-studied subject. When we apply the random key pre-distribution scheme to secure a WSN however, and only consider the paths consisting entirely of secure (encrypted and/or authenticated) links, we are concerned with the secure k-connectivity of the WSN. This notion of secure k-connectivity is relatively new and no results are yet available. The random key pre-distribution scheme has two important parameters: the key ring size and the key pool size. While it has been determined before the relation between these parameters and 1-connectivity, our work in k-connectivity is new. Using a recently introduced random graph model called kryptograph, we derive mathematical formulae to estimate the asymptotic probability of a WSN being securely k-connected, and the expected secure k-connectivity, as a function of the key ring size and the key pool size. Finally, our theoretical findings are supported by simulation results.