Achieving Tight Space-Time Tradeoff and Practical Performance in Preprocessing PIR with Multi-level Recursion

Client-specific preprocessing PIR supports sublinear online private queries after a linear-time offline phase that prepares client-specific hints. The relevant lower bound is tight: any scheme with $S$ bits of client storage and online cost $T$ must satisfy $S \cdot T = \Omega(n)$. Most practical random-set schemes fall short by a $\kappa$ factor in client storage, while the known constant-factor-optimal schemes, WR-PIR (Eurocrypt 2025) and Balanced PIR (S&P 2026), rely on complex hint-manag