SHARD: cell-keyed residual splitting for alignment-resistant private dense retrieval
arXiv:2606.27976
The paper introduces SHARD, a technique that divides PCA‑derived document vectors into a short public prefix and a residual encrypted with cell‑specific orthogonal keys, aiming to limit alignment attacks on dense retrieval while keeping ranking performance unchanged.
Abstract
Dense retrieval systems expose document geometry when vector stores are compromised, and a global protective transform can often be aligned from known pairs. We study SHARD, which splits PCA coordinates into a short routing prefix and a residual protected by independent cell-local orthogonal keys. It supports CKKS ciphertext--plaintext reranking but is evaluated as a leakage trade-off, not a cryptographic document-privacy guarantee. Corrected scoring uses centered document coordinates and an uncentered scoring query, preserving raw ranking up to a query-dependent constant. Across ten BEIR/MIRACL configurations it reproduces raw nDCG@10 and recall, whereas centering both sides loses up to 0.080 nDCG. Cell keys spread diffuse known-pair evidence across compartments, but minimum-norm alignment recovers useful signal far below full key rank, so there is no hard de-anonymization threshold. Real CKKS has maximum score error 2.29e-6 and no top-1 flips; block packing cuts query upload by 74--87% but raises in-process p50 latency by 14--26%. In a strengthened GTR case, an unknown key lowers token-F1 from 0.665 to 0.242; a wide prefix and eight pairs restore much. Under 25--90% release overlap, the unchanged prefix and clean residual norm link persistent rows with R@1 at least 0.9996, although cell-Gram linkage degrades under churn. A formally calibrated Gaussian release gives nDCG@10 at most 0.011 at epsilon=1; its only three strict utility matches occur at epsilon=32768 with linkage R@1 at least 0.995. SHARD preserves retrieval and compartmentalizes alignment evidence, but does not provide DP, unlinkability, or cancellable templates.