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Serial Polar Automorphism Ensemble Decoders for Physical Unclonable Functions

Marvin Rübenacke, Sebastian Cammerer, Michael Sullivan, Alexander Keller

TL;DR

The paper tackles the challenge of reliable key extraction from physical unclonable functions (PUFs) under high raw bit error rates by proposing a serial Automorphism Ensemble Decoder (AED) for Polar codes. It reuses a single successive cancellation (SC) decoder across multiple decoding attempts and introduces cascaded and recursive interleavers to scale AED candidates with minimal hardware, aided by aggressive 3-bit quantization. The approach achieves the same block error rate of $10^{-6}$ as a BCH baseline while using $1.75\times$ fewer codeword bits for $K=312$, translating into reduced helper data and chip area, and it extends naturally to biased PUFs with debiasing. Overall, the work demonstrates a practical, area-efficient, soft-decision-capable coding scheme for PUFs that preserves reliability in ultra-low-rate regimes.

Abstract

Physical unclonable functions (PUFs) involve challenging practical applications of error-correcting codes (ECCs), requiring extremely low failure rates on the order of $10^{-6}$ and below despite raw input bit error rates as high as 22%. These requirements call for an efficient ultra-low rate code design. In this work, we propose a novel coding scheme tailored for PUFs based on Polar codes and a low-complexity version of automorphism ensemble decoding (AED). Notably, our serial AED scheme reuses a single successive cancellation (SC) decoder across multiple decoding attempts. By introducing cascaded and recursive interleavers, we efficiently scale the number of AED candidates without requiring expensive large multiplexers. An aggressive quantization strategy of only 3 bits per message further reduces the area requirements of the underlying SC decoder. The resulting coding scheme achieves the same block error rate of $10^{-6}$ as our baseline based on Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes while requiring 1.75x fewer codeword bits to encode the same K = 312 payload bits. This reduction translates directly into 1.75x less helper data storage and, consequently, a smaller overall chip area.

Serial Polar Automorphism Ensemble Decoders for Physical Unclonable Functions

TL;DR

The paper tackles the challenge of reliable key extraction from physical unclonable functions (PUFs) under high raw bit error rates by proposing a serial Automorphism Ensemble Decoder (AED) for Polar codes. It reuses a single successive cancellation (SC) decoder across multiple decoding attempts and introduces cascaded and recursive interleavers to scale AED candidates with minimal hardware, aided by aggressive 3-bit quantization. The approach achieves the same block error rate of as a BCH baseline while using fewer codeword bits for , translating into reduced helper data and chip area, and it extends naturally to biased PUFs with debiasing. Overall, the work demonstrates a practical, area-efficient, soft-decision-capable coding scheme for PUFs that preserves reliability in ultra-low-rate regimes.

Abstract

Physical unclonable functions (PUFs) involve challenging practical applications of error-correcting codes (ECCs), requiring extremely low failure rates on the order of and below despite raw input bit error rates as high as 22%. These requirements call for an efficient ultra-low rate code design. In this work, we propose a novel coding scheme tailored for PUFs based on Polar codes and a low-complexity version of automorphism ensemble decoding (AED). Notably, our serial AED scheme reuses a single successive cancellation (SC) decoder across multiple decoding attempts. By introducing cascaded and recursive interleavers, we efficiently scale the number of AED candidates without requiring expensive large multiplexers. An aggressive quantization strategy of only 3 bits per message further reduces the area requirements of the underlying SC decoder. The resulting coding scheme achieves the same block error rate of as our baseline based on Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes while requiring 1.75x fewer codeword bits to encode the same K = 312 payload bits. This reduction translates directly into 1.75x less helper data storage and, consequently, a smaller overall chip area.

Paper Structure

This paper contains 20 sections, 1 theorem, 12 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model and Background
  3. Physical Unclonable Functions
  4. Helper Data Algorithms
  5. Polar Codes
  6. Successive Cancellation Decoding
  7. Permutation Automorphism Group
  8. Automorphism Ensemble Decoding
  9. Non-Uniform Quantization
  10. Serial Automorphism Ensemble Decoding
  11. Serial Architecture
  12. Cascaded Interleavers
  13. Recursive Interleavers
  14. Block Interleavers
  15. Results
  16. ...and 5 more sections

Key Result

Theorem 1

Let $\boldsymbol{P}(\boldsymbol{A})$ denote the $N\times N$ permutation matrix of codeword bits corresponding to the linear transformation matrix $\boldsymbol{A}$. For any block profile $\boldsymbol{s} = [s_0, s_1, \dots, s_{t-1}]$, and $\boldsymbol{A} = \operatorname{diag}(\boldsymbol{A}_0, \boldsy

Figures (7)

  • Figure 1: Overview of the PUF key extraction pipeline using the fuzzy commitment scheme. The debiasing (yellow) is an optional component.
  • Figure 2: Simplified SC decoding factor tree of a $(64,17)$ Polar code with LLR bit widths annotated; max. bit width is 3 bits.
  • Figure 3: Serial implementation of AED with a single constituent decoder and switchable permutations.
  • Figure 4: Different interleaver architectures to realize the permutations in a serial AED implementation. The recursive de-interleaver requires multiple cycles which are not shown.
  • Figure 5: Comparison of BCH and Polar-based coding schemes for $K \approx 312$.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Example 1
  • Example 2