TreePIR: Efficient Private Retrieval of Merkle Proofs via Tree Colorings with Fast Indexing and Zero Storage Overhead
Bibliographic record
Abstract
A Batch Private Information Retrieval (batch-PIR) scheme allows a client to retrieve multiple data items from a database without revealing them to the storage server(s). Most existing approaches for batch - Pirare based on batch codes, in particular, probabilistic batch codes (PBC) (Angel et al. S&P'18), which incur large storage overheads. In this work, we show that zero storage overhead is achievable for tree-shaped databases. In particular, we develop TreePIR, a novel approach tailored made for private retrieval of the set of nodes along an arbitrary root-to-leaf path in a Merkle tree with no storage redundancy. This type of tree has been widely implemented in many real-world systems such as Amazon DynamoDB, Google's Certificate Transparency, and blockchains. Tree nodes along a root-to-leaf path forms the well-known Merkle proof. TreePIR, which employs a novel tree coloring, outperforms PBC, a fundamental component in state-of-the-art batch-PIR schemes (Angel et al. S&P'18, Mughees-Ren S&P'23, Liu et al. S&P'24), in all metrics, achieving 3 ×lower total storage and 1.5-3 ×lower computation and communication costs. Most notably, TreePIR has 8-160× lower setup time and its polylog-complexity indexing algorithm is 19–160 ×faster than PBC for trees of 210_224leaves.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".