In the context of Internet of Things (IoT) and embedded and low power wireless systems, lightweight key establishment mechanisms are essential for secure communications. This paper proposes an algebraic curve-based light weight key establishment scheme, which has high cryptographic security and low computation complexity. The method proposed combines optimized constructions of algebraic curves over finite fields and efficient scalar multiplication and memory-aware arithmetic to enable secure generation of shared secrets at constrained devices. A low-load protocol structure is presented for the generation of public keys, derivation of session keys and secure authentication between communicating entities. Experimental testing shows that the proposed framework requires a 28.6% less computation time and a 22.4% less amount of energy when compared with the traditional lightweight cryptography algorithms at the same level of security. The framework is designed for an extensible next-generation security applications for Internet of Things (IoT).