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Provable Performance Guarantees of Copy Detection Patterns

Joakim Tutt, Slava Voloshynovskiy

TL;DR

This paper aims to establish a theoretical framework to derive optimal criteria for the analysis, optimization, and future development of CDP authentication technologies, ensuring their reliability and effectiveness in diverse security scenarios.

Abstract

Copy Detection Patterns (CDPs) are crucial elements in modern security applications, playing a vital role in safeguarding industries such as food, pharmaceuticals, and cosmetics. Current performance evaluations of CDPs predominantly rely on empirical setups using simplistic metrics like Hamming distances or Pearson correlation. These methods are often inadequate due to their sensitivity to distortions, degradation, and their limitations to stationary statistics of printing and imaging. Additionally, machine learning-based approaches suffer from distribution biases and fail to generalize to unseen counterfeit samples. Given the critical importance of CDPs in preventing counterfeiting, including the counterfeit vaccines issue highlighted during the COVID-19 pandemic, there is an urgent need for provable performance guarantees across various criteria. This paper aims to establish a theoretical framework to derive optimal criteria for the analysis, optimization, and future development of CDP authentication technologies, ensuring their reliability and effectiveness in diverse security scenarios.

Provable Performance Guarantees of Copy Detection Patterns

TL;DR

This paper aims to establish a theoretical framework to derive optimal criteria for the analysis, optimization, and future development of CDP authentication technologies, ensuring their reliability and effectiveness in diverse security scenarios.

Abstract

Copy Detection Patterns (CDPs) are crucial elements in modern security applications, playing a vital role in safeguarding industries such as food, pharmaceuticals, and cosmetics. Current performance evaluations of CDPs predominantly rely on empirical setups using simplistic metrics like Hamming distances or Pearson correlation. These methods are often inadequate due to their sensitivity to distortions, degradation, and their limitations to stationary statistics of printing and imaging. Additionally, machine learning-based approaches suffer from distribution biases and fail to generalize to unseen counterfeit samples. Given the critical importance of CDPs in preventing counterfeiting, including the counterfeit vaccines issue highlighted during the COVID-19 pandemic, there is an urgent need for provable performance guarantees across various criteria. This paper aims to establish a theoretical framework to derive optimal criteria for the analysis, optimization, and future development of CDP authentication technologies, ensuring their reliability and effectiveness in diverse security scenarios.
Paper Structure (13 sections, 4 theorems, 21 equations, 3 figures, 1 table)

This paper contains 13 sections, 4 theorems, 21 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Information flow in Copy Detection Patterns
  3. A statistical viewpoint
  4. Hamming distance test
  5. Posterior likelihood approach
  6. Neymann-Pearson optimal bound
  7. Channels aggregation strategies
  8. Experimental results
  9. 1x1 Indigo base smartphone dataset
  10. Reliability and authentication performance
  11. Aggregation strategies
  12. Final classification performance
  13. Conclusion

Key Result

Proposition 3.1

The average log-likelihood is given by: where the right-hand side designates the cross-entropy between the unknown probe distribution $P_b^{{\bf y}}({\bf \omega})$ and the reference distribution $P_b({\bf \omega})$.

Figures (3)

  • Figure 1: An illustration of the theoretical framework under study. Given a fixed pattern ${\bf \omega}$ and a CDP probe ${\bf y}$, one identifies all appearances of the pattern ${\bf \omega}$ (left) in the digital template ${\bf t}$. For each location $(i,j)$ of ${\bf \omega}$ in ${\bf t}$, one can associate a random bit-flipping $\delta_{i,j}$. The Hamming distance $D^{{\bf \omega}}$ between ${\bf t}$ and $\tilde{{\bf t}}$ for the pattern ${\bf \omega}$ follows a Binomial distribution which is compared with the reference Binomial distributions of originals and fakes CDP. Based on the reference distributions, an optimal separation bound $\gamma_{crit}$ is computed which minimizes the average probability of error.
  • Figure 2: Average probability of error between originals and fakes samples as a function of the probability of bit-flipping of each channel. The optimal probability of error is computed using the theoretical model (in red) and empirically on the test set (in blue). Both curves show a close match.
  • Figure 3: A plot of the final classification error probability based on the final score $S_{final}$ for each aggregation strategy as a function of the number of channels aggregated. Continuous curves correspond to (AD) and dashed curves correspond to (DA). The best $k$ channels are different for each strategy and depend on the optimality criterion.

Theorems & Definitions (7)

  • Proposition 3.1
  • proof
  • Corollary 1
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • proof