Genome-wide association studies are pivotal in understanding the genetic underpinnings of complex traits and diseases. Collaborative, multi-site GWAS aim to enhance statistical power but face obstacles due to the sensitive nature of genomic data sharing. Current state-of-the-art methods provide a privacy-focused approach utilizing computationally expensive methods such as Secure Multi-Party Computation and Homomorphic Encryption. In this context, we present a novel algorithm PP-GWAS designed to improve upon existing standards in terms of computational efficiency and scalability without sacrificing data privacy. This algorithm employs randomized encoding within a distributed architecture to perform stacked ridge regression on a Linear Mixed Model to ensure rigorous analysis. Experimental evaluation with real world and synthetic data indicates that PP-GWAS can achieve computational speeds twice as fast as similar state-of-the-art algorithms while using lesser computational resources, all while adhering to a robust security model that caters to an all-but-one semi-honest adversary setting. We have assessed its performance using various datasets, emphasizing its potential in facilitating more efficient and private genomic analyses.