cano_paper_v2.md

---
title: "CANO: Context-Aware Noise Optimization for Adversarial Privacy Protection"
author: "Ted Rubin"
affiliation: "Independent Researcher"
email: "ted@theorubin.com"
date: "April 2026"
abstract: |
  We present **CANO** (Context-Aware Noise Optimization), an adaptive noise
  injection system that optimizes the privacy-utility tradeoff in adversarial
  privacy protection. Unlike uniform noise strategies, CANO allocates noise
  proportionally to each feature's contribution to re-identification,
  concentrating protection where it matters most while preserving utility on
  low-impact features.
  
  We evaluate CANO against five baseline strategies (Gaussian, FGSM, PGD,
  Carlini-Wagner, and Laplace) across 68,885 experimental configurations
  spanning 12 datasets (11 after excluding the 2-user
  `cybersec_intrusion` dataset from aggregate statistics), 3 attack
  models, and 6 noise budgets. Aggregate statistics are computed over
  54,281 in-scope configurations, including a complete block on the
  real **FP-Stalker** browser-fingerprint corpus (Vastel et al. [10]; 776
  users, 13,674 fingerprints, 34 attributes).
  
  Against a known adaptive attacker, CANO achieves a mean accuracy reduction
  of 0.112 ± 0.178 -- below
  Gaussian noise (0.395) but above C&W (0.001).
  Two findings reframe this aggregate result. First, on the FP-Stalker
  corpus the CANO/Gaussian gap collapses substantially (CANO 0.276
  vs Gaussian 0.340), suggesting importance-weighted allocation
  generalizes better under realistic feature distributions. Second, CANO
  achieves a 2.41x transfer-to-adaptive ratio versus
  1.04x for Gaussian -- a substantial advantage in the
  realistic deployment regime where the defender does not know the attack
  model.
  
  In adversarial co-evolutionary training, the DQN policy reduces attacker
  re-identification accuracy from 74.8% to 20.8% within
  30 rounds, converging to near-uniform allocation (Gini:
  0.009) -- empirically demonstrating that uniform noise is the
  game-theoretic equilibrium against adaptive adversaries.
keywords: [privacy protection, adversarial noise, reinforcement learning, browser fingerprinting, transfer attacks]
---

# 1. Introduction

Browser fingerprinting poses a significant threat to user privacy. Attackers
construct unique device fingerprints from browser attributes -- canvas
rendering, WebGL, screen resolution, installed fonts -- to track users across
sessions without cookies [1].

Privacy-preserving systems combat fingerprinting by injecting noise. A
fundamental unresolved tension: whether uniform noise injection or
feature-weighted injection provides superior protection. A further practical
challenge: privacy systems are typically deployed without knowledge of the
adversary's exact attack model.

CANO addresses this through:

1. Feature importance analysis.
2. Proportional noise allocation with a minimum weight floor preventing
   exploitable zero-noise features.
3. RL that adapts allocation through adversarial co-evolution.
4. Empirical analysis of the adaptive-vs-transfer tradeoff.

Our central finding is counterintuitive: while CANO does not maximize accuracy
reduction against a known adaptive attacker (Gaussian dominates), CANO achieves
a 2.41x transfer-to-adaptive ratio -- notably higher than
Gaussian's 1.04x. In real deployments, defenders cannot
tailor their noise to the adversary's model.

## 1.1 Related Work

Browser fingerprinting was popularized by Eckersley's Panopticlick study [7],
which showed that combinations of routine browser attributes uniquely identify
most users. Laperdrix et al.'s 2020 survey [1] catalogues 17 distinct
categories of fingerprinting signals. FP-Stalker (Vastel et al. [10])
introduced longitudinal evaluation by tracking fingerprint evolution over
weeks -- we adopt its 776-user corpus as our real-data benchmark. On the
defensive side, BrFAST [8] and FPSelect [9] focus on attribute *selection*
(which attributes to expose), whereas CANO operates on a complementary axis:
given an attribute is exposed, how much per-attribute noise to inject.

The privacy-utility tradeoff has a long lineage in differential privacy
(Dwork et al. [5]), where Gaussian or Laplace noise is calibrated to a
per-query sensitivity bound. The adversarial-examples literature shows
targeted perturbations can dramatically reduce classifier accuracy: FGSM [2]
is a single-step gradient attack, PGD [3] iterates it under projection, and
Carlini-Wagner [4] casts it as constrained optimization. CANO borrows the
budget-controlled framing from adversarial examples but allocates by a static
feature-importance prior rather than per-input gradient. The minimum-weight
floor (§2.2) is a defensive concession to DP's worst-case framing: any
feature receiving negligible noise becomes the attacker's preferred
discriminator. Our central empirical contribution measures the
transfer-vs-adaptive gap explicitly across all six strategies.

# 2. Methodology

## 2.1 Feature Importance Analysis

Random Forest (100 trees) on 1000 fingerprint samples;
permutation importance (10 repeats). 9-dimensional feature space. Baseline
re-identification accuracy: 100% on synthetic corpus. Feature importance is
highly concentrated: feature_0 (0.303) and feature_1 (0.302) account for ~99%
of total importance; features 2-5 have exactly 0.000 permutation importance.
This motivates the minimum weight floor ($w_{\min} = 0.1$) in §2.2.

> **Note.** Importance is computed on synthetic proxies, not real browser
> API measurements. FP-Stalker evaluation uses real per-attribute fingerprints
> with noise allocated by the same importance weights.

## 2.2 CANO Noise Allocation

Given feature importance weights $w_i$ and noise budget $\epsilon$:

$$\delta_i = \epsilon \cdot (w_i \cdot n) \cdot \operatorname{sign}(z_i)$$

where $z_i \sim \mathcal{N}(0, 1)$, or the gradient direction when a target
model is available. The $n$ scaling factor ensures equal total noise energy to
baselines. The minimum-weight floor ($w_{\min} = 0.1$) prevents attackers
from exploiting negligibly-noised features.

## 2.3 DQN Policy Training

Adversarial co-evolution: 50 simulated users, 20 samples/user, 9 features.

- **State:** [feature_values, attack_confidence, privacy_budget, query_count]
- **Action:** per-feature noise allocation weights (softmax-normalized)
- **Reward:** $\alpha \cdot \text{privacy\_gain} - (1 - \alpha) \cdot \text{utility\_cost}$

Training alternates defender (CANO) and attacker (GradientBoosting retraining).

## 2.4 Experimental Setup

- **Strategies:** CANO (ours), Gaussian, FGSM, PGD, Laplace, C&W
- **Noise budgets:** $\epsilon \in \{0.05, 0.1, 0.15, 0.2, 0.3, 0.5\}$
- **Attack models:** gradient_boosting, mlp, random_forest
- **Datasets:** 11 in-scope + `cybersec_intrusion` (excluded, 2-user binary task)
- **Total configs:** 68,885 raw; 54,281 in-scope

> **Scope note.** `cybersec_intrusion` is retained in Table 5 for completeness
> but excluded from all aggregate statistics, comparisons, and significance
> tests.

### Data Provenance

Three N values appear in the paper:

| | Value | Meaning |
|---|---:|---|
| $N_{\text{raw}}$ | 68,885 | Raw configurations across all 19 runs and all datasets. |
| $N_{\text{in-scope}}$ | 54,281 | Excluding `cybersec_intrusion` (basis for Tables 1, 4, 5, 6). |
| $N_{\text{utility}}$ | 5,924 | Utility-metric subset (sparsity, KL, deviation, sensitivity instrumented from 2026-04-05 onward; basis for Tables 2, 3). |

Per-strategy row counts in Table 1 differ because historical runs covered
evolving strategy subsets as the codebase matured. All comparisons are
strategy-paired within (dataset, attacker, epsilon, rep) tuples.

# 3. Results

## 3.1 Overall Strategy Comparison (Adaptive Attack)

![Accuracy reduction vs. noise budget epsilon, per strategy.](results/figures/fig1_accuracy_reduction_vs_epsilon.png)

**Table 1.** Strategy comparison -- aggregate over in-scope datasets only.

| Strategy | Acc. Reduction | Xfer Red. | Noise L2 | SNR (dB) | n |
|---|---:|---:|---:|---:|---:|
| CANO (ours) | 0.112 ± 0.178 | +0.271 | 0.435 | 15.5 | 8,508 |
| Gaussian | 0.395 ± 0.281 | +0.410 | 0.595 | 9.7 | 10,423 |
| FGSM | 0.212 ± 0.212 | +0.474 | 0.642 | 9.8 | 9,641 |
| PGD | 0.129 ± 0.171 | +0.145 | 0.271 | 17.5 | 8,789 |
| Laplace | 0.239 ± 0.222 | +0.392 | 0.556 | 11.2 | 8,460 |
| C&W | 0.001 ± 0.011 | -0.016 | 0.003 | 53.7 | 8,460 |

Gaussian is the strongest adaptive-attack strategy. CANO outperforms only
C&W. See §3.6 for significance.

## 3.2 Transfer Attack Analysis

![Privacy-utility Pareto front.](results/figures/fig2_pareto_front.png)

**Table 2.** Adaptive vs. transfer accuracy reduction.

| Strategy | Adaptive | Transfer | Ratio | Gap |
|---|---:|---:|---:|---:|
| CANO (ours) | 0.112 | +0.271 | 2.41x | +0.158 |
| Gaussian | 0.395 | +0.410 | 1.04x | +0.014 |
| FGSM | 0.212 | +0.474 | 2.23x | +0.261 |
| PGD | 0.129 | +0.145 | 1.13x | +0.016 |
| Laplace | 0.239 | +0.392 | 1.64x | +0.153 |
| C&W | 0.001 | -0.016 | n/a | -0.018 |

CANO's 2.41x transfer-to-adaptive ratio reflects more
model-agnostic perturbations. Gaussian provides little additional transfer
protection (1.04x). C&W's transfer reduction is negative
(anti-protective on small synthetics) -- its ratio is reported as n/a.

## 3.3 Noise Utility Metrics

**Table 3.** Per-strategy noise-quality metrics (n = 5,924 in-scope rows).

| Strategy | Sparsity | KL | Deviation | Sensitivity | n |
|---|---:|---:|---:|---:|---:|
| CANO (ours) | 0.980 | 0.763 | 0.1763 | -0.226 | 900 |
| Gaussian | 0.983 | 0.507 | 0.1421 | +0.032 | 1,080 |
| FGSM | 0.983 | 1.275 | 0.1881 | -0.174 | 1,080 |
| PGD | 0.834 | 0.299 | 0.0699 | +0.035 | 1,064 |
| Laplace | 0.980 | 0.545 | 0.1706 | -0.185 | 900 |
| C&W | 0.980 | 0.021 | 0.0009 | -0.016 | 900 |

CANO's noise structure is distinguishable from Gaussian: similar KL divergence
but negative sensitivity signature (vs. Gaussian's positive), reflecting
concentration on importance-ranked rather than variance-ranked features.

## 3.4 Epsilon Sensitivity

![Per-strategy heatmap of accuracy reduction across datasets.](results/figures/fig3_strategy_heatmap.png)

**Table 4.** Accuracy reduction by noise budget (aggregate, in-scope).

| ε | CANO (ours) | Gaussian | FGSM | PGD | Laplace | C&W |
|---:| ---:| ---:| ---:| ---:| ---:| ---:|
| 0.05 | 0.010 | 0.104 | 0.054 | 0.018 | 0.013 | 0.001 |
| 0.10 | 0.035 | 0.195 | 0.103 | 0.037 | 0.060 | 0.001 |
| 0.15 | 0.084 | 0.312 | 0.183 | 0.048 | 0.152 | 0.001 |
| 0.20 | 0.131 | 0.431 | 0.258 | 0.072 | 0.253 | 0.001 |
| 0.30 | 0.188 | 0.609 | 0.317 | 0.178 | 0.382 | 0.001 |
| 0.50 | 0.226 | 0.750 | 0.374 | 0.433 | 0.576 | 0.002 |

## 3.5 Per-Dataset Analysis

![Per-dataset accuracy reduction (core: real + main synthetic datasets).](results/figures/fig5a_per_dataset_core.png)

![Per-dataset accuracy reduction (supplemental: overlap + keystroke).](results/figures/fig5b_per_dataset_supplemental.png)

**Table 5.** Mean accuracy reduction by dataset.

| Dataset | Users | CANO | Gaussian | FGSM | Laplace | PGD |
|---|---:|---:|---:|---:|---:|---:|
| `fpstalker` *(real)* | 776 | 0.276 | 0.340 | 0.282 | 0.291 | 0.176 |
| `synth_large` | 20 | 0.135 | 0.416 | 0.234 | 0.304 | 0.152 |
| `synth_medium` | 10 | 0.082 | 0.306 | 0.153 | 0.198 | 0.090 |
| `synth_small` | 5 | 0.116 | 0.287 | 0.190 | 0.215 | 0.109 |
| `cybersec_intrusion` *(out-of-scope)* | 2 | 0.034 | 0.192 | 0.094 | 0.122 | 0.088 |
| `keystroke_cmu_51users` | 51 | n/a | 0.657 | 0.357 | n/a | 0.413 |
| `overlap_10u_50s` | 10 | 0.046 | 0.307 | 0.247 | n/a | n/a |
| `overlap_20u_30s` | 20 | 0.041 | 0.218 | 0.187 | n/a | n/a |
| `synth_10u_50s` | 10 | 0.001 | 0.270 | 0.057 | n/a | n/a |
| `synth_20u_50s` | 20 | 0.001 | 0.378 | 0.135 | n/a | n/a |
| `synth_50u_20s` | 50 | 0.003 | 0.514 | 0.356 | n/a | n/a |
| `synth_5u_30s` | 5 | -0.006 | 0.208 | 0.072 | n/a | n/a |

> **Note.** "n/a" cells in Table 5 mark configurations where a strategy was
> not run on a particular dataset; this primarily affects Laplace and PGD on
> the smaller synthetic variants and on `keystroke_cmu_51users`, which were
> added to the strategy roster after those datasets had already been
> evaluated. FP-Stalker (Vastel et al. [10]) is the closest dataset to
> deployment conditions and is fully populated across all six strategies; on
> it, CANO closes most of the gap to Gaussian (0.276 vs 0.340).

## 3.6 Statistical Significance

![Statistical significance of CANO vs each baseline.](results/figures/fig4_statistical_significance.png)

**Table 6.** CANO vs each baseline, Welch t-test and Cohen's d.

| Comparison | Cohen's d | p-value | Significance |
|---|---:|---:|---:|
| CANO vs C&W | +0.880 | p < 0.001 | *** |
| CANO vs FGSM | -0.510 | p < 0.001 | *** |
| CANO vs Gaussian | -1.202 | p < 0.001 | *** |
| CANO vs Laplace | -0.631 | p < 0.001 | *** |
| CANO vs PGD | -0.093 | p < 0.001 | *** |

## 3.7 Adversarial Training Results (DQN Policy)

![DQN adversarial training progress (attacker accuracy vs round).](results/figures/rl_training_progress.png)

DQN policy trained over 30 adversarial rounds with 50 users:

- Baseline attack accuracy: **74.8%**
- Final attack accuracy: **20.8%**
- Accuracy reduction: **54.0 percentage points**
- Noise magnitude: 0.6061
- DQN training steps: 31,500
- Final Gini coefficient: **0.009** (near-uniform)

Uniform allocation emerges as the game-theoretic equilibrium against adaptive
adversaries.

# 4. Discussion

## 4.1 Key Findings

1. Noise scaling (the $n$ multiplier) is the most impactful design choice.
2. Gaussian is the strongest adaptive-attacker defense (d = -1.20 vs CANO).
3. CANO achieves a 2.41x transfer/adaptive ratio vs
   1.04x for Gaussian.
4. RL equilibrium is uniform allocation (Gini = 0.009).
5. CANO uses less noise than Gaussian ($L_2$ = 0.435 vs
   0.595) with higher SNR (15.5 vs
   9.7 dB).
6. **On the real FP-Stalker corpus, CANO closes most of the gap to Gaussian**
   (0.276 vs 0.340), in contrast to wider gaps on
   small-synthetic datasets. Importance-weighted allocation generalizes better
   under realistic feature distributions.

## 4.2 Limitations

- One real browser-fingerprint dataset (FP-Stalker, 776 users); larger corpora
  (HTillmann; BrFAST extended) are the next integration.
- 9 synthetic features with artificial importance concentration.
- `cybersec_intrusion` (2 users) excluded from aggregates.
- Utility metrics (sparsity, KL, deviation, sensitivity) cover the 5,924-row
  subset of runs from 2026-04-05 onward; older synthetic-only runs predate the
  instrumentation and contribute only adaptive accuracy_reduction.
- RL at 50 users; architectural changes needed for scaling.
- Laplace and PGD were not run on the older small-synthetic variants
  (`overlap_*`, `synth_NuMs` family) -- visible as `n/a` cells in Table 5.

## 4.3 Future Work

1. Extend utility-metric coverage across the older synthetic runs (the
   ~50,000 rows that predate the noise-quality instrumentation).
2. Fill the remaining `n/a` cells in Table 5 by running Laplace and PGD on
   the small-synthetic variants and on `keystroke_cmu_51users`.
3. Formal DP guarantees for CANO's allocation mechanism.
4. Larger RL training (1,000+ users); online policy updates in deployment.
5. Theoretical analysis of conditions under which feature-weighted noise
   achieves higher transfer efficiency than uniform noise.

# 5. Conclusion

CANO does not match Gaussian in raw adaptive-attack accuracy reduction
(0.112 vs 0.395), but achieves
a 2.41x transfer-to-adaptive ratio -- better model-agnostic
behavior than Gaussian (1.04x) in the transfer setting,
which better reflects real-world deployment. On the real FP-Stalker corpus
the adaptive-attack gap narrows substantially (CANO 0.276 vs Gaussian
0.340), reinforcing the case that importance-weighted allocation
generalizes better under realistic conditions.

**Contributions:**

1. *Noise scaling correction:* equal total noise energy while redistributing
   by importance.
2. *Transfer efficiency result:* feature-importance weighting produces more
   model-agnostic perturbations.
3. *RL equilibrium finding:* uniform noise is the game-theoretic equilibrium
   against adaptive adversaries (Gini = 0.009 after 30 rounds).
4. *Real-world validation:* FP-Stalker (776 users, 13,674 fingerprints) shows
   the synthetic CANO/Gaussian gap narrows substantially under realistic
   feature distributions.

# References

[1]  Laperdrix, P. et al. "Browser Fingerprinting: A Survey." *ACM CSUR*, 2020.

[2]  Goodfellow, I. et al. "Explaining and Harnessing Adversarial Examples."
     *ICLR*, 2015.

[3]  Madry, A. et al. "Towards Deep Learning Models Resistant to Adversarial
     Attacks." *ICLR*, 2018.

[4]  Carlini, N. & Wagner, D. "Towards Evaluating the Robustness of Neural
     Networks." *IEEE S&P*, 2017.

[5]  Dwork, C. et al. "The Algorithmic Foundations of Differential Privacy."
     *Foundations and Trends in TCS*, 2014.

[6]  Mnih, V. et al. "Human-level Control through Deep Reinforcement Learning."
     *Nature*, 2015.

[7]  Eckersley, P. "How Unique Is Your Web Browser?" *PETS*, 2010.

[8]  Andriamilanto, N. and Allard, T. "BrFAST: a Tool to Select Browser
     Fingerprinting Attributes for Web Authentication." *WWW '21 Companion*,
     ACM, 2021. DOI: 10.1145/3442442.3458610.

[9]  Andriamilanto, N., Allard, T., and Le Guelvouit, G. "FPSelect:
     Low-Cost Browser Fingerprints for Mitigating Dictionary Attacks."
     *ACM CCS*, 2020. DOI: 10.1145/3427228.3427297.

[10] Vastel, A., Laperdrix, P., Rudametkin, W., and Rouvoy, R. "FP-STALKER:
     Tracking Browser Fingerprint Evolutions." *IEEE S&P*, 2018.
     DOI: 10.1109/SP.2018.00008.

[11] Tillmann, H. "Browser Fingerprinting: 93% der Nutzer hinterlassen
     eindeutige Spuren." Technical report, henning-tillmann.de, October 2013.

---

*Generated: 2026-04-26 03:47:41*
*Data source: 19 merged `eval_*.jsonl` files (68,885 raw configs, 54,281 in-scope after excluding `cybersec_intrusion`).*