Compressed FHE: Accelerating Encrypted Matrix Multiplication in CKKS with Precision-Balanced Low-Rank Factor Chains

This work establishes cFHE (compressed FHE), a unified analytical and empirical framework that integrates low-rank matrix factorization techniques into the CKKS homomorphic encryption scheme. Theoretical bounds are derived for the accumulation of relative error across sequences of factorized matrices, leading to an explicit expression for the attainable computation depth as a function of target accuracy, norm amplification behavior, and per-layer approximation quality. Extensions to tree-based