Dynamic graph updates for Fragment Tree and BlindGES

Extend both the Fragment Tree attack and the BlindGES graph-encryption scheme to support dynamic graph updates in which vertices and edges may be added or removed over time, rather than assuming a static graph.

Background

The report analyzes structural leakage in PathGES and presents the Fragment Tree attack for recovering shortest-path queries from leaked token relationships. It also introduces BlindGES, which uses a Merge-and-Divide mechanism and a two-level multimap index to reduce one-to-one token-to-path mappings and suppress path-length leakage.

Both approaches are presented under a static-graph assumption: the encrypted indexes, shortest-path trees, heavy-light decompositions, path fragments, and leakage analyses are constructed for a fixed graph. Supporting insertions and deletions of vertices or edges would therefore require methods for updating these structures and preserving the intended security and query-efficiency properties without rebuilding the entire scheme or attack model.