Efficient Deterministic Truncation and RMFE-Native Fixed-Point Operators for Private Neural Network Training

Fixed-point arithmetic is widely used in privacy-preserving neural network training, but securely restoring the target scale of intermediate values remains costly. In the semi-honest, honest-majority setting with general $n$-party Shamir sharing, existing mask-and-reveal deterministic truncation approaches either introduce a statistical security parameter $\kappa$ to prevent modular wraparound or explicitly correct wraparound at the cost of sequential secure comparisons. In this work, we develop a more efficient deterministic truncation protocol for Shamir secret sharing over Galois rings. We revisit modular wraparound in the mask-and-reveal paradigm and incorporate its correction directly into the truncation relation. For Galois rings of characteristic $2^k$, the formulation further simplifies, yielding a $\kappa$-free deterministic truncation protocol that requires only one online secure comparison. We further integrate this truncation protocol into the RMFE-based training framework and develop new protocols for efficient fixed-point multiplication and gradient aggregation, two key components of RMFE-based private neural network training for general $n$ parties. Experiments on fully connected and convolutional neural networks demonstrate up to a $1.70\times$ speedup in the LAN setting, together with substantial communication savings over the existing RMFE-based training framework.