ScoreShield: Differentially Private Release of Similarity Scores

Differential privacy (DP) is increasingly deployed to limit membership inference risk in machine-learning systems. Prior work has shown that DP-SGD can widen accuracy disparities across demographic groups, but this framing treats fairness as a purely outcome-side concern. We argue that privacy cost, the information leakage borne by each group, is itself a form of harm, and adopt a compensatory-fairness framework in which a group that involuntarily bears greater privacy exposure is owed proportionally greater benefit from the system. From this principle we derive the \emph{Privacy-Cost Equity Ratio} (PCER), a group fairness metric defined as a group's positive prediction rate normalized by its per-group overfitting gap. By a standard membership inference bound, this overfitting gap upper-bounds each group's vulnerability to inference attacks, making PCER a conservative measure of benefit relative to exposure. PCER needs only per-group train and test accuracy (no shadow models), making it a practical post-hoc audit tool. We evaluate PCER alongside standard fairness metrics across six benchmark--attribute combinations spanning tabular and NLP domains, under DP-SGD at a range of privacy budgets, and validate the overfitting-gap proxy against a direct threshold membership-inference attack. The results reveal patterns that outcome-based metrics miss. On COMPAS, PCER uncovers a persistent double disadvantage: the protected group bears both greater privacy exposure and worse predictive outcomes, something demographic parity gap masks entirely. Sensitivity analysis shows very strong privacy guarantees collapse both groups' overfitting to a numerical floor, rendering exposure-based audits uninformative in that regime. Together, these findings show that fairness audits of privacy-preserving systems must account for who bears the cost of protection, not only who benefits from its outcomes.

Applying differential privacy (DP) via DP-SGD to Low-Rank Adaptation (LoRA) is a natural approach for privacy-preserving fine-tuning. However, LoRA's low-rank parameterization poses a fundamental challenge. In LoRA, each trainable update is represented as a low-rank matrix $Z = AB^\top$, but this factorization is inherently non-identifiable: many factor pairs $(A,B)$ represent the same update $Z$. As a result, applying DP-SGD directly to the factors induces gauge-dependent perturbations on $Z$, and we show that this naive DP-LoRA can lead to unbounded noise amplification. We propose PRISM, an intrinsic DP mechanism for LoRA that is gauge invariant by construction, avoids bilinear noise amplification, and admits an efficient low-dimensional noise sampler. Moreover, PRISM yields a closed-form characterization of the effective intrinsic noise induced on $Z$, enabling stable privacy-utility trade-offs through bounded, gauge-invariant perturbations. We establish standard $(ε,δ)$-DP guarantees for PRISM and introduce a DP-aware, gauge-invariant adaptive update rule that prevents adaptive optimization from amplifying injected privacy noise, improving numerical stability in practice.

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.