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The three critical resources in any cluster based Wireless Sensor Networks (WSN) are Sensor Nodes (SN), Cluster Head (CH) and Base Station (BS). The main job of Cluster Head is to send all the aggregated data collected from multiple sensor Nodes to the Base Station. But before sending the data, the Cluster Head must be perfectly sure about the actual identity of Base Station. If any intruder acts as Base Station and receives the aggregated data the entire security of the network is spoiled. To avoid this, the authenticity of the base station needs to be checked by cluster head before sending any data. Many asymmetric authentication techniques like digital signatures are difficult to implement in resource constraint sensor Nodes. A zero-knowledge proof protocol is a powerful cryptographic system that can be applied in many cryptographic applications and operations such as identification, authentication, key exchange and others, but many of the existing zero knowledge proof of identity involves exponential calculations which are not suitable for WSN. To overcome the limitations of the existing techniques, the proposed protocol provides Zero knowledge proof identity using congruence equations. Here, Triplet simultaneous linear congruence equations are used to subdivide a whole secret into three shares. A part of a secret is used as identity of the base station and stored in it. The Base Station won't reveal the part of secret stored in it to the Cluster Head but the Cluster Head confirms the true identity without getting the actual secret from Base Station. In this scheme, the Cluster Heads need to solve only congruence equations which need only limited computation and memory. When the proposed protocol is compared with existing protocols it shows that it provide instant authentication, with minimum memory utilization and withstand many attacks.