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In this paper, we propose a strongly resilient polynomial-based random key pre-distribution scheme for multiphase wireless sensor networks (RPoK): a private sub-key is not directly stored in each sensor node by applying the polynomial-based scheme to the RoK scheme. Such a polynomial is linearly transformed using forward and backward keys in order to achieve the forward and backward security of polynomials. As a result, our scheme achieves a large reduction of the ratio of compromised links by enhancing the security of the previous RoK scheme. The results obtained analytically and by simulations show that our scheme can dramatically improve the ratio of compromised links compared with the RoK scheme.