The Internet of Bio-Nano Things concept (IoBNT) emerged from the need to establish connections between biological nanomachines, the intra-body nanonetwork, and the cyber internet to facilitate information exchange. While extensive research has concentrated on optimizing communication efficiency among nanodevices within networks, challenges such as IoBNT security and the interface linking nanonetwork to the internet have remained unaddressed. Consequently, this study introduces a privacy scheme designed to operate atop the Physical Cyber Interface (pHCI) within the IoBNT framework. Our proposed chaotic system derives its foundation from the command signals issued by medical personnel to pHCI devices implanted within the human body. It employs a concealed version of features generated through a Modified Quadratic Map (MQM) to enhance the privacy of patient information and to ensure a precise dosage release. Additionally, our scheme incorporates Binary Phase Shifting Key (BPSK) modulation through the incorporation of a carrier wave, along with feature extraction with zero-crossing rates. This privacy scheme significantly amplifies the key space, thereby guaranteeing an accurate right dose release with the protection of patient privacy. To assess the performance of our proposed scheme, we evaluate its operation on top of the pHCI device using various performance metrics. Subsequently, we study its performance by employing multi-compartmental models in both the forward and reverse pHCI directions of the IoBNT paradigm. The results from our simulation model clearly illustrate that the IoBNT-based privacy scheme has potential to enhance the delivery of therapeutic drugs to target cells while effectively addressing privacy concerns. An evaluation of performance metrics for two binary codes (thermal and light) reveals sensitivity and specificity rates of 95.333% and 95%, 100%, and 100%, respectively. Furthermore, the performance of our proposed privacy scheme, as measured by EER, accuracy, NPV, and PPV, has proven to be highly satisfactory. Hence, our proposed scheme makes significant role in enhancing the security of the physical cyber interface device while remaining cost-effective, and ensuring the safety of patients' life and confidentiality.