Drug counterfeiting is one of the most serious public health problems in the world, reducing consumer trust and costing hundreds of billions of dollars annually. However, the pharmaceutical supply chain monitoring system lacks traceability, is prone to unauthorized distribution, or has weak regulatory enforcement. While frameworks leveraging the advantages of blockchains have great promise, they primarily depend on the Rivest-Shamir-Adleman (RSA) and elliptic curve digital signature (ECDSA) algorithms. These algorithms lead to high computational costs and long processing times. They are also susceptible to side-channel attacks. This paper presents an Edwards-curve Digital Signature Algorithm (EdDSA) enabled blockchain-based framework for the pharmaceutical supply chain. It combines a decentralized ledger acting as an immutable and auditable record of the payments, and a QR-code verification module allowing consumers to verify products on the spot. The EdDSA algorithm enhances the functionality of the system with fast signature generation and verification. In addition, it has a higher resilience and efficiency against cryptographic attacks and is resource-efficient. Through experimental evaluation, it is shown that the proposed framework achieves superior performance in transaction throughput, execution time, and energy efficiency in comparison to state-of-the-art methods while obtaining a comparable level of security guarantees. Finally, the EdDSA-based framework not only improves transparency and security by mitigating threats to public health safety but also encourages stakeholders to make the right decisions, paving the way for a counterfeit-free global market for pharmaceuticals.