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.

翻译：批量隐私信息检索方案允许客户端从数据库中检索多个数据项，同时不向存储服务器泄露这些项的信息。现有的大多数批量隐私信息检索方法基于批量编码，特别是概率批量编码，但这类方法会产生巨大的存储开销。在本工作中，我们证明了对于树形结构的数据库，可以实现零存储开销。具体而言，我们提出了TreePIR，这是一种专为默克尔树中任意根到叶路径上节点集合的隐私检索而设计的新方法，且无需任何存储冗余。此类树结构已在许多实际系统中得到广泛应用，例如Amazon DynamoDB、Google证书透明度以及区块链。根到叶路径上的树节点构成了众所周知的默克尔证明。TreePIR采用了一种新颖的树着色方法，在各项指标上均优于概率批量编码这一现有先进批量隐私信息检索方案中的核心组件，实现了总存储降低3倍，计算与通信成本降低1.5至2倍。尤为突出的是，TreePIR的初始化时间降低了8至160倍，并且其多对数复杂度的索引算法在叶子节点数为2^{10}至2^{24}的树结构上比概率批量编码快19至160倍。