The smart healthcare system (SHS), a significant medical domain underpinning the Internet of Things (IoT), which collects and analyzes health data from many sources to provide better medical treatment. The smart healthcare system is a combination of hardware and software used in the medical care field, providing remote diagnosis and treatment via a patient‐based health data‐sharing system. To increase security, a large variety of authenticated techniques have been developed over the past several decades, most of which are based on conventional number‐theoretic assumptions such as discrete logarithms and integer factorization problems. However, Shor's method is capable of solving number‐theory‐based problems. As a result, Shor's technique might be used to resolve challenging number theory problems on a quantum computer effectively. Therefore, this article presents blockchain‐based healthcare record solutions with lattice RLWE‐based key exchange protocol using a smart card. Blockchain applications may correctly detect errors, including those that are risky, in the medical industry. It can also improve the efficiency, security, and transparency of transferring medical data throughout the healthcare protocol. The formal security of this protocol is shown under the ROM (random oracle model), and the informal security is also given in this article against well‐known attacks. The presented protocol outperforms related earlier mechanisms in terms of communication and computational cost overheads, according to the performance study.