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Identity-based encryption is a public key-based method of encryption that enables communicating identities to use some individual and unique information, such as their physical IP addresses and MAC addresses, to identify them and as public keys. The scheme does not require the extra device to store long-term public keys. So, it is convenient for use in practical applications, including smart industry and smart manufacturing. This study develops a novel, efficient, and secure identity-based encryption scheme using an extended Chebyshev chaotic map that has recently been demonstrated to outperform traditional cryptography, including modular exponential computations or scalar multiplications on elliptic curves. Besides demonstrating that the proposed scheme satisfies the security requirements of identity-based encryption, the simulation results of this study show that the proposed scheme requires less response time than related identity-based encryption schemes. Due to hardware limitations, not all industrial devices can load heavy computations. Therefore, the proposed identity-based encryption scheme outperforms related identity-based encryption approaches, and is suitable for industrial environment.