To simplify the certificate management in public key infrastructure, key management protocols for wireless sensor networks typically use identity‐based cryptography for negotiating the shared key. However, current identity‐based key management protocols are mainly based on the bilinear map technique, which requires high computation costs on sensor nodes, resulting in short lifetimes of sensor nodes. To address this issue, we present a novel identity‐based key management protocol called Identity‐Based Key Management using Lagrange Interpolation (IBKML). Similar to the protocols of this field, IBKML can provide confidentiality and integrity protections for the negotiated key. However, compared to other well‐known approaches, IBKML is based on Lagrange interpolation instead of bilinear map, which employs only a few modular multiplication operations. Because modular multiplication is much more efficient than bilinear pairing, IBKML can reduce the computation costs on sensor nodes significantly. Experimental results show that the proposed protocol is feasible for real applications. Copyright © 2016 John Wiley & Sons, Ltd.