<p>Multi-Key fully homomorphic encryption (MKFHE) is a promising technique that allows computations on ciphertexts encrypted by different parties, with the potential to break down data silos. However, when users’ ciphertexts are uploaded to the cloud, the cloud decides which user set is involved in a computation task rather than the user. This raises privacy concerns as users lose control over their data. Furthermore, many MKFHE schemes produce non-compact ciphertexts whose size increases linearly or quadratically with the number of users. We propose an authorized MKFHE scheme with compact ciphertext, called AMKFHE, to address the above issues. In our scheme, homomorphic computations between a user’s ciphertext and the ciphertexts of other users or user sets are not permitted unless the user has authorized those users or user sets. This approach enables users to maintain control over their ciphertexts, ensuring their privacy. Additionally, our scheme produces compact ciphertexts. We construct and implement our scheme based on the residue number system (RNS) variant of the CKKS17 scheme. We demonstrate the applicability of our scheme by presenting a privacy-preserving statistical power of genome-wide association studies (GWAS) for multi-party with AMKFHE. Our experiment shows that AMKFHE can homomorphically implement the Cochran-Armitage trend test (CATT) for a candidate allele with a specific disease for 10 parties on average in 0.012&#xa0;ms.</p>