TreePIR: Efficient Private Retrieval of Merkle Proofs via Tree Colorings with Fast Indexing and Zero Storage Overhead

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-PIR are 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 \textit{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 trees 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 $3\times$ lower total storage and $1.5$-$2\times$ lower computation and communication costs. Most notably, TreePIR has $8$-$160\times$ lower setup time and its polylog-complexity indexing algorithm is $19$-$160\times$ faster than PBC for trees of $2^{10}$-$2^{24}$ leaves.