Information security is a concern in integrated electronic health record systems (EHRs). This paper discusses the development of a mathematical model to secure the access of EHRs. In this paper, we incorporate the notion of a broadcast encryption scheme for securing EHRs. We present a novel solution to allow a secure access to the EHRs whilst minimising the number of the encrypted ciphertexts. In a nutshell, our proposed solution enjoys shorter ciphertexts compared to having multiple ciphertexts encrypted for several different participants. Our proposed solution is applicable in practice to solve an existing open problem in the effort of securing EHRs.