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Identity based key agreement protocol affords a natural way to authenticate the participants in a key agreement protocol.However,most existing work cannot work in the multiple PKG environment where PKGs have both different secret master keys and different public parameters.In addition,they cannot securely support the public computation,which enables some of the time-consuming calculation to be submitted to public computing resources.In this paper,we propose a new extensible and efficient identity based key agreement protocol E2IBK.Its private key extraction method comes directly from a typical IBE (Identity Based Encryption) scheme,making it have a common and firm security basis.Through combining two participants values with different items of a proper bilinear pairing,E2IBK can be used with PKGs having both different secret master keys and different public parameters.Moreover,it supports public computation to greatly reduce the user terminals cost on computing the session key.Through theoretical analysis,we demonstrate that E2IBK has all the security properties needed by a key agreement protocol,and prove that its extensibility and efficiency outperform existing identity based key agreement protocols.