Post-quantum digital signature schemes are critical for securing digital communications against the emerging threat of quantum computing, which can break traditional digital signature systems. Among the Post-quantum signature candidates, hash-based signatures, particularly the Merkle Signature Scheme, provide strong security guarantees. Merkle Signature Scheme uses a Merkle tree to generate a large number of one-time digital signatures from a single public key. However, computing the authentication paths in the Merkle Signature Scheme, which are necessary for verifying signatures, can be computationally expensive, especially for large trees. This paper presents an optimized algorithm for computing these authentication paths, leveraging techniques such as lazy evaluation and efficient tree hash management. The improved algorithm reduces redundant computations and memory usage, thereby enhancing the efficiency and scalability of the Merkle Signature Scheme. Experimental results demonstrate significant improvements in computation time, making the Merkle Signature Scheme more practical for real-world applications.