  Secure aggregation of user vectors has become a critical issue in the field
of federated learning. Many Secure Aggregation Protocols (SAP) face exorbitant
computation costs, which severely limit their applicability. We uncover that
current endeavors to reduce computation costs tend to overlook a crucial fact:
a considerable portion of SAP's computation burden stems from processing each
entry in the private vectors. Given this observation, we propose PVF, a
portable module for compressing computation costs. PVF is able to ``freeze'' a
substantial portion of the private vector through specific linear
transformations, only requiring $\frac{1}{\lambda}$ 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 enhance functionality, we introduce
extensions that can enforce consistency constraints on users' original vectors,
verify aggregated results, and enhance security when a portion of the private
vector is known to the server. We demonstrate that PVF can seamlessly integrate
with various SAP and prove that it poses no threat to user privacy in the
semi-honest and active adversary settings. We select $8$ baselines,
encompassing $6$ distinct types of SAP, and explore the acceleration effects of
PVF on these SAP. Empirical investigations indicate that when $\lambda=100$,
PVF yields up to $99.5\times$ speedup and up to $32.3\times$ communication
reduction, with the potential to approach nearly $1000\times$ acceleration as
$\lambda$ increases.
