Efficient Authenticated Data Structures for Graph Connectivity and Geometric Search Problems

TL;DR

This paper introduces efficient cryptographic techniques for authenticating graph connectivity and geometric search queries, ensuring data integrity even when managed by untrusted hosts.

Contribution

It presents the path hash accumulator, a novel primitive for authenticating structured data, enabling secure and efficient graph and geometric data queries.

Findings

Efficient authenticated data structures for graph connectivity.

Secure geometric search query authentication.

Introduction of the path hash accumulator primitive.

Abstract

Authenticated data structures provide cryptographic proofs that their answers are as accurate as the author intended, even if the data structure is being controlled by a remote untrusted host. We present efficient techniques for authenticating data structures that represent graphs and collections of geometric objects. We introduce the path hash accumulator, a new primitive based on cryptographic hashing for efficiently authenticating various properties of structured data represented as paths, including any decomposable query over sequences of elements. We show how to employ our primitive to authenticate queries about properties of paths in graphs and search queries on multi-catalogs. This allows the design of new, efficient authenticated data structures for fundamental problems on networks, such as path and connectivity queries over graphs, and complex queries on two-dimensional geometric objects, such as intersection and containment queries.