This study aims to examine the computational efficiency of blockchain-based digital signature technologies with respect to healthcare data security. When thinking about the revolutionary opportunities and risks posed by healthcare data digitization, concerns regarding data privacy and security have come to the forefront. Blockchain technology, which is both decentralised and immutable, offers a promising alternative. Two of its primary uses, data integrity and identity authentication, are made possible by digital signature systems. We conducted a comprehensive analysis to find out how efficient different protocols are in healthcare computing. Among these protocols were EdDSA, ECDSA, and Schnorr signatures. Our research indicates that efficiency is significantly affected by protocol selection. Despite the strong security it provides, data validation delays may occur due to the increased processing expense generated by ECDSA. Schnorr signatures and EdDSA are viable solutions that offer a reasonable compromise between security and efficiency. By delving into optimization methodologies and associated difficulties, this research paved the road for the ethical application of blockchain technology in healthcare. The healthcare industry, policymakers, and IT developers all benefit from our study when it comes to selecting and improving methods for secure and efficient data storage. This study uniquely examines the computational efficiency of blockchain-based digital signature protocols in healthcare data security, addressing optimization methodologies and highlighting the suitability of Schnorr signatures and EdDSA.