The Internet of Nano Things (IoNT) is increasingly recognized as a superior alternative to the Internet of Things (IoT) due to its inherent benefits. However, the security of IoNT remains an open challenge that needs to be addressed at various levels. Given the highly sensitive data shared in IoNT, the development of security protocols becomes imperative. Despite the emergence of some methodologies, many security aspects have been overlooked, and no concrete cryptosystems have been developed. In this paper, we propose an Identity-Based Encryption (IBE) scheme built on the Learning With Errors (LWE) assumption. We design a lightweight protocol with the consideration of resource-constrained devices involved in the IoNT network. The proposed scheme is resistant to various attacks, including side-channel analysis, replay attacks, man-in-the-middle attacks, plaintext and ciphertext attacks, ensuring unforgeability. Additionally, performance evaluation indicates that the proposed scheme outperforms existing ones in terms of computational and communication costs.