Fully Homomorphic Encryption (FHE) enables secure eligibility verification by allowing computations on encrypted data without decryption. In applications like voting systems, financial services, or healthcare, FHE ensures privacy while verifying criteria (e.g., age, income, or medical status). Users submit encrypted data to a verifier, who performs computations (e.g., threshold checks) directly on ciphertexts, producing an encrypted result. Only the user can decrypt the outcome, confirming eligibility without exposing sensitive information. FHE supports complex verification logic, maintaining data confidentiality and integrity. Challenges include computational overhead and key management, but advancements in FHE schemes (e.g., CKKS, BGV) improve efficiency. FHE’s non-interactive nature suits decentralized systems, enhancing trust in privacy-preserving eligibility checks.