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Information Theoretic Analysis of PUF-Based Tamper Protection

Georg Maringer, Matthias Hiller

TL;DR

The paper develops an information-theoretic framework for PUF-based tamper protection, modeling enrollment and reconstruction as a wiretap channel with zero leakage helper data. It provides asymptotic lower bounds on secrecy capacities under digital and analog attacker models and derives finite-blocklength achievability and converse bounds that translate to practical requirements on the number of PUF cells and quantization levels. A key finding is that 128-bit security can be achieved with a finite, practical number of PUF cells under realistic erasure scenarios, but existing schemes that leak helper data fail to meet these security targets. The results offer fundamental design benchmarks for PUF-based tamper protection, highlighting that coarse quantization and carefully constructed zero-leakage helper data can reduce hardware requirements while maintaining strong security guarantees.

Abstract

Physical Unclonable Functions (PUFs) enable physical tamper protection for high-assurance devices without needing a continuous power supply that is active over the entire lifetime of the device. Several methods for PUF-based tamper protection have been proposed together with practical quantization and error correction schemes. In this work we take a step back from the implementation to analyze theoretical properties and limits. We apply zero leakage output quantization to existing quantization schemes and minimize the reconstruction error probability under zero leakage. We apply wiretap coding within a helper data algorithm to enable a reliable key reconstruction for the legitimate user while guaranteeing a selectable reconstruction complexity for an attacker, analogously to the security level for a cryptographic algorithm for the attacker models considered in this work. We present lower bounds on the achievable key rates depending on the attacker's capabilities in the asymptotic and finite blocklength regime to give fundamental security guarantees even if the attacker gets partial information about the PUF response and the helper data. Furthermore, we present converse bounds on the number of PUF cells. Our results show for example that for a practical scenario one needs at least 459 PUF cells using 3 bit quantization to achieve a security level of 128 bit.

Information Theoretic Analysis of PUF-Based Tamper Protection

TL;DR

The paper develops an information-theoretic framework for PUF-based tamper protection, modeling enrollment and reconstruction as a wiretap channel with zero leakage helper data. It provides asymptotic lower bounds on secrecy capacities under digital and analog attacker models and derives finite-blocklength achievability and converse bounds that translate to practical requirements on the number of PUF cells and quantization levels. A key finding is that 128-bit security can be achieved with a finite, practical number of PUF cells under realistic erasure scenarios, but existing schemes that leak helper data fail to meet these security targets. The results offer fundamental design benchmarks for PUF-based tamper protection, highlighting that coarse quantization and carefully constructed zero-leakage helper data can reduce hardware requirements while maintaining strong security guarantees.

Abstract

Physical Unclonable Functions (PUFs) enable physical tamper protection for high-assurance devices without needing a continuous power supply that is active over the entire lifetime of the device. Several methods for PUF-based tamper protection have been proposed together with practical quantization and error correction schemes. In this work we take a step back from the implementation to analyze theoretical properties and limits. We apply zero leakage output quantization to existing quantization schemes and minimize the reconstruction error probability under zero leakage. We apply wiretap coding within a helper data algorithm to enable a reliable key reconstruction for the legitimate user while guaranteeing a selectable reconstruction complexity for an attacker, analogously to the security level for a cryptographic algorithm for the attacker models considered in this work. We present lower bounds on the achievable key rates depending on the attacker's capabilities in the asymptotic and finite blocklength regime to give fundamental security guarantees even if the attacker gets partial information about the PUF response and the helper data. Furthermore, we present converse bounds on the number of PUF cells. Our results show for example that for a practical scenario one needs at least 459 PUF cells using 3 bit quantization to achieve a security level of 128 bit.

Paper Structure

This paper contains 34 sections, 20 theorems, 102 equations, 8 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Main Results
  4. Outline
  5. State of the Art
  6. PUF-Based Tamper Protection
  7. Quantization
  8. Equiprobable Quantization
  9. Equidistant Quantization
  10. Error Correction
  11. Preliminaries
  12. Notation
  13. The Wiretap Channel
  14. Secret Sharing using Common Randomness
  15. Helper Data Algorithm
  16. ...and 19 more sections

Key Result

theorem 1

Let the output of an arbitrary list decoder $\mathcal{L}$ given Eve's observation $E$ be denoted by $\mathcal{L}(E)$. Let $\delta$ be the secrecy parameter of the implemented secrecy code for the respective wiretap channel. Then the probability that the transmitted codeword is not in the output list

Figures (8)

  • Figure 2.1: Sketch of PUF-based envelope IOK+18 with two conducting electrode layers in red and blue, and two shielding layers in black
  • Figure 3.1: Degraded wiretap channel (top), wiretap channel (bottom)
  • Figure 3.2: Secret Sharing using Common Randomness
  • Figure 3.3: Simplified schematic of a key generation scheme based on a PUF.
  • Figure 3.4: Key enrollment and key reconstruction for analog PUFs
  • ...and 3 more figures

Theorems & Definitions (58)

  • definition 1
  • theorem 1: yang2016finite Thm. 8
  • definition 2
  • remark 1
  • theorem 2: wyner1975wire
  • theorem 3: csiszar1978broadcast
  • remark 2
  • definition 3
  • theorem 4
  • corollary 1: bloch2011physical, Corollary 4.1
  • ...and 48 more