Smart Connected Health Systems (SCHSs) belong to health systems that provide services of health care remotely. They provide the doctors with access to electronic medical records with the aid of medical sensors, smart wearable devices and smart medical instruments. Although SCHSs have many applications in the area of health care, securing massive amount of valuable and sensitive data of the patients and preserving the privacy are challenging. User authentication based on public key cryptographic techniques is playing a crucial role in SCHSs for protecting the privacy of patients. However, quantum computers will break such techniques. Rainbow signature is one of the candidates of the next generation of cryptographic algorithms which can resist attacks on quantum computers. However, it is vulnerable to Differential Power Analysis (DPA) attacks, which is based on information gained from the cryptographic implementations. We present techniques to exploit the countermeasures to protect Rainbow against DPA attacks. We propose a variant of Rainbow with resistance to DPA attacks. First, we take a random vector to randomize the power consumption of private keys during computing the first affine transformation; Second, random variables are adopted during computing central map transformation; Third, we take two random vectors during computing the second affine transformation to randomize the power consumption of private keys. We analyze the efficiency and implement the scheme on hardware. Compared with the related implementations, our scheme is efficient and suitable for signature generations on hardware. Besides, we propose a secure authentical scheme based on the implementation for protecting record of patients in SCHSs.