Abstract Electronic health information exchange (HIE) allows doctors, nurses, pharmacists, other health care providers and patients to appropriately access and securely share a patient’s vital medical information electronically—improving the speed, quality, safety and cost of patient care. At present, public key cryptography (PKC) is the most secure and practical cryptographic techniques to achieve this function in healthcare information exchange for medical IoT systems. ElGamal cryptosystem is one of the most well-known public key cryptosystems (they are also called asymmetric key cryptosystems), which is based on the discrete logarithm problem. At present, with the development of quantum computer technology, the ElGamal cryptosystem may be attacked by quantum algorithms. At the same time, since ElGamal requires several secure random integers to resist cryptographic analysis and ensure communication security and securing data sharing. Especially, when the encrypted information is large, multiple random numbers need to be used for grouping encryption, which makes the efficiency of ElGamal need to be improved. It is necessary to construct an alternative cryptographic algor
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