User authentication is a crucial service in wireless sensor networks (WSNs) that is becoming increasingly common in WSNs because wireless sensor nodes are typically deployed in an unattended environment, leaving them open to possible hostile network attack. The main research goal of the paper is to securely authenticate remote user in a convenient and user friendly manner. In this paper, we propose a RSA (asymmetric Rivest, Shamir, Adleman cryptographic algorithm for encryption based remote user authentication using smart cards in hierarchical wireless sensor networks. Usually, the proposed scheme includes three phases for user authentication such as registration phase, login phase and authentication phase. First an asymmetric Rivest, Shamir, Adleman(RSA) cryptographic algorithm that resolves security weaknesses. The RSA method is suitable for applications with higher security requirements. Finally, we present a comparison of security and computation time for the proposedmethod. Our proposed scheme achieves better security against attacks and less computational time as compared to those for other existing cryptographic approaches.