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In this paper, a constrained random perturbation based pairwise keY establishment (CARPY) scheme and its variant, a CARPY+ scheme, for Wireless Sensor Networks (WSNs), are presented. Compared to all existing schemes which satisfy only some requirements in so-called sensor-key criteria, including: 1) resilience to the adversary's intervention, 2) directed and guaranteed key establishment, 3) resilience to network configurations, 4) efficiency, and 5) resilience to dynamic node deployment, the proposed CARPY+ scheme meets all requirements. In particular, to the best of our knowledge, CARPY+ is the first non-interactive key establishment scheme with great resilience to a large number of node compromises designed for WSNs. We examine the CARPY and CARPY+ schemes from both the theoretical and experimental aspects. Our schemes have also been practically implemented on the TelosB compatible mote to evaluate the corresponding performance and overhead.