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A Framework for the Security and Privacy of Biometric System Constructions under Defined Computational Assumptions

Sam Grierson, William J Buchanan, Craig Thomson, Baraq Galeb, Chris Eckl

TL;DR

This paper introduces a formal framework for constructing secure and privacy-preserving biometric systems by leveraging the principles of universal composability, which enables the modular analysis and verification of individual system components.

Abstract

Biometric systems, while offering convenient authentication, often fall short in providing rigorous security assurances. A primary reason is the ad-hoc design of protocols and components, which hinders the establishment of comprehensive security proofs. This paper introduces a formal framework for constructing secure and privacy-preserving biometric systems. By leveraging the principles of universal composability, we enable the modular analysis and verification of individual system components. This approach allows us to derive strong security and privacy properties for the entire system, grounded in well-defined computational assumptions.

A Framework for the Security and Privacy of Biometric System Constructions under Defined Computational Assumptions

TL;DR

This paper introduces a formal framework for constructing secure and privacy-preserving biometric systems by leveraging the principles of universal composability, which enables the modular analysis and verification of individual system components.

Abstract

Biometric systems, while offering convenient authentication, often fall short in providing rigorous security assurances. A primary reason is the ad-hoc design of protocols and components, which hinders the establishment of comprehensive security proofs. This paper introduces a formal framework for constructing secure and privacy-preserving biometric systems. By leveraging the principles of universal composability, we enable the modular analysis and verification of individual system components. This approach allows us to derive strong security and privacy properties for the entire system, grounded in well-defined computational assumptions.

Paper Structure

This paper contains 15 sections, 3 theorems, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Metric Spaces
  4. Learning Framework
  5. Deep Neural Networks
  6. The Biometric System Setting
  7. Biometric System Overview
  8. Biometric System Modules.
  9. Accuracy and Correctness
  10. Feature Extraction with Representation Learning
  11. Biometric Verification
  12. Biometric Verification Formulation
  13. Biometric Identification
  14. Biometric Identification Formulation
  15. Conclusions

Key Result

Lemma 2.1

Let $C_n = (V, E)$ be a Boolean circuit of depth $d \in \mathbb{N}$ that computes the function $f$. There exists an MLP of depth $d$ that computes $f$.

Figures (3)

  • Figure 1: A common biometric system architecture, adapted from work by Jain et al.JFR07.
  • Figure 2: A biometric verification system model with indications of the generic information flows based on work by Jain et al.JFR07 and Construction \ref{['cons:2.1']}. In the above figure, we assume that the $\mathsf{init}$ method of Construction \ref{['cons:2.1']} has already been run.
  • Figure 3: A biometric identification system model with indications of the generic information flows based on work by Jain et al.JFR07 and Construction \ref{['cons:2.2']}. In the above figure, we assume that the $\mathsf{init}$ method of Construction \ref{['cons:2.2']} has already been run.

Theorems & Definitions (20)

  • Definition 2.1: Metric Space
  • Example 2.1: Hamming Metric
  • Example 2.2: Levenshtein Metric
  • Example 2.3: Euclidean Metric
  • Example 2.4: Chebyshev Metric
  • Definition 2.2: PPT Training Algorithm
  • Definition 2.3: Feedforward Neural Network
  • Definition 2.4: Multi-Layer Perception
  • Lemma 2.1
  • Definition 3.1: False Match Rate
  • ...and 10 more