Functional Encryption ( \(\textsf{FE} \) ) has emerged as a new paradigm for public-key encryption in recent years, making the efficiency of \(\textsf{FE} \) schemes crucial for many practical constructions. In this work, we propose a more efficient two-stage sampling method that improves the efficiency of the prior two-stage sampling method introduced by Lai, Liu, and Wang [15]. By leveraging our new two-stage sampling method, we can significantly boost the efficiency of existing functional encryption constructions while simultaneously enhancing the security of the scheme. This improvement is achieved because we can now rely on a weaker security assumption. To be more precise, our efficient two-stage sampling method leads to an adaptively secure Identity-Based Inner Product Functional Encryption ( \(\textsf{IB} \) - \(\textsf{FEIP} \) ) scheme with smaller parameters and higher efficiency. We believe that our advancements will contribute to the deployment of compact and efficient \(\textsf{FE} \) constructions in various real-world applications.