Secure aggregation of user update vectors (e.g. gradients) has become a critical issue in the field of federated learning. Many Secure Aggregation Protocols (SAPs) face exorbitant computation costs, severely constraining their applicability. Given the observation that a considerable portion of SAP's computation burden stems from processing each entry in the private vectors, we propose \textbf{P}artial \textbf{V}ector \textbf{F}reezing (\textbf{PVF}), a portable module for compressing computation costs without introducing additional communication overhead. \textbf{$\bmλ$-SecAgg}, which integrates SAP with PVF, ``freezes'' a substantial portion of the private vector through specific transformations, requiring only $\frac{1}λ$ of the original vector to participate in SAP. Eventually, users can ``thaw'' the public sum of the ``frozen entries'' by the result of SAP. To avoid potential privacy leakage, we devise Disrupting Variables Extension for PVF. We demonstrate that PVF can seamlessly integrate with various SAPs and it poses no threat to user privacy in the semi-honest and active adversary settings. We include $7$ baselines, encompassing $5$ distinct types of masking schemes, and explore the acceleration effects of PVF on these SAPs. Empirical investigations indicate that when $λ=100$, PVF yields up to $99.5\times$ speedup and up to $32.3\times$ communication reduction.