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In wireless sensor networks (WSN), message authentication is crucial to prevent false response that may be evoked by a message. There is a need for a strong cryptographic mechanism to mitigate attacks like false message injection and denial of service. Public key cryptography is resource intensive while symmetric key cryptography does not meet the demands of scalability, simultaneous broadcasts from nodes etc. To address the problem of authentication in resource limited WSN, a Multivariate Rainbow signature scheme is proposed. Rainbow signature is based on layered unbalanced oil and vinegar multivariate signature in which linear equations are solved to obtain successive sets of central variables. The small computation and memory requirement seems to make the scheme viable for message and source verification. The Rainbow scheme was simulated for large scale WSN. Results show that the throughput of the network is large with low average delay even for large number of nodes. Moreover, the queue size at the nodes is small with low jitter which indicates that memory requirement is a small percentage of memory available at the nodes. These indicate the efficacy of Rainbow signature for WSN.