In the Internet of Medical Things (IoMT), medical devices are connected to the Internet of Things (IoT), allowing better tailored healthcare, faster hospital treatments, more affordable medical solutions, and more patient comfort. The most serious threat to the safety and confidentiality of patient’s medical records is the possibility of attacks on the IoMT environment. In order to address these problems, researchers have proposed several approaches and methodologies. None of these protocols presents a low-computing-overhead method that combines authentication with privacy preservation. This research proposes a protocol for secure authentication of IoMT devices while protecting user privacy. The proposed approach ensures the confidentiality of the IoMT devices connected to the patient’s body while communicating. In addition, the proposed protocol is validated using the widely recognized formal validation tool Automated Validation of Internet Security Protocols and Applications (AVISPA). The suggested protocol resolves existing protocols’ vulnerabilities and is resistant to many well-known security issues. Compared with existing protocols that use public cryptosystems, such ElGamal and RSA, the suggested protocol stands out due to its smaller key size and reduced computational overhead. A comparison with the well-known protocols revealed that the combined method for “lightweight authentication and privacy preservation” is computationally 5 to 6 times more efficient. However, this research has significant real-world implications from various social, economic, and business viewpoints, both locally and globally.

We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one as well as the first derivative in our analysis. We also provide computable radius of convergence, error estimates, and uniqueness of the solution results not given in earlier studies. Hence, we expand the applicability of these methods. The dynamical analysis of the discussed family is also presented. Numerical experiments complete this article.

The convergence balls as well as the dynamical characteristics of two sixth order Jarratt-like methods (JLM1 and JLM2) are compared. First, the ball analysis theorems for these algorithms are proved by applying generalized Lipschitz conditions on derivative of the first order. As a result, significant information on the radii of convergence and the regions of uniqueness for the solution are found along with calculable error distances. Also, the scope of utilization of these algorithms is extended. Then, we compare the dynamical properties, using the attraction basin approach, of these iterative schemes. At the end, standard application problems are considered to demonstrate the efficacy of our theoretical findings on ball convergence. For these problems, the convergence balls are computed and compared. From these comparisons, it is confirmed that JLM1 has the bigger convergence balls than JLM2. Also, the attraction basins for JLM1 are larger in comparison to JLM2. Thus, for numerical applications, JLM1 is better than JLM2.