[Paper Review] On Burst Error Correction and Storage Security of Noisy Data

Felix Fontein, Kyle Marshall+3 more|arXiv (Cornell University)|May 23, 2012

Biometric Identification and Security5 references3 citations

TL;DR

This paper proposes a novel syndrome fuzzy hashing framework for securing noisy biometric data by leveraging burst error-correcting codes, particularly Reed-Solomon and concatenated codes in two-dimensional array structures. It demonstrates that tailored code constructions can efficiently correct both burst and random errors while minimizing information leakage, with decoding complexity optimized via field representation and interleaving schemes.

ABSTRACT

Secure storage of noisy data for authentication purposes usually involves the use of error correcting codes. We propose a new model scenario involving burst errors and present for that several constructions.

Motivation & Objective

• To address the challenge of securing biometric data subject to burst errors during storage and retrieval.
• To improve upon existing fuzzy commitment and syndrome hashing schemes by reducing information leakage and enhancing error resilience.
• To design efficient, practical code constructions that correct burst errors in two-dimensional data arrays while maintaining low decoding complexity.
• To evaluate the trade-offs between error-correcting capability, code rate, and computational cost across different code structures.
• To provide a systematic comparison of six code constructions for burst error correction in the context of fuzzy hashing for noisy data.

Proposed method

• Uses syndrome fuzzy hashing as the core framework, where a data vector is stored as a hash and its syndrome under a parity-check matrix.
• Represents codewords as two-dimensional arrays (e.g., $n_1 \times n_2$) to exploit spatial error patterns, particularly burst errors.
• Applies base field representations of Reed-Solomon codes over $\mathbb{F}_q$ to enable burst error correction in the expanded domain.
• Employs concatenated coding schemes with outer Reed-Solomon codes and inner $q$-ary codes (e.g., BCH or cyclic codes) to correct both burst and random errors.
• Designs specific interleaving patterns (e.g., diagonal or block-wise) to isolate burst errors and limit their impact on inner codes.
• Analyzes decoding complexity using standard and advanced algorithms (e.g., Gorenstein-Peterson-Zierler and $O(\sqrt{n}\log n)$-complexity methods) in extension fields.

Experimental results

Research questions

• RQ1 How can burst error-correcting codes be effectively integrated into syndrome fuzzy hashing to improve security and robustness for noisy biometric data?
• RQ2 What are the trade-offs between code rate, error-correcting capability, and decoding complexity when using different code constructions for burst errors?
• RQ3 How do various interleaving patterns (e.g., row-wise, diagonal) affect the correction of rectangular and diagonal burst errors in two-dimensional arrays?
• RQ4 In what scenarios do concatenated codes outperform single-code constructions in terms of burst error correction and random error resilience?
• RQ5 What is the impact of field representation (e.g., $\mathbb{F}_{q^m}$ vs. $\mathbb{F}_q^m$) on decoding efficiency and error correction performance?

Key findings

• Construction I (base field Reed-Solomon) achieves $O(q^{2m})$ decoding complexity using standard Gorenstein-Peterson-Zierler decoding, with improved $O(mq^{3/2m})$ complexity via advanced algorithms.
• Construction II (trivial inner code) offers fast decoding with good burst error correction, suitable for embedded systems, though limited in random error tolerance.
• Construction III (polynomial basis representation) provides comparable burst correction to Construction II but with faster decoding due to optimized field operations.
• Construction IV (row-wise interleaving) efficiently corrects multiple large bursts but is sensitive to high random error density.
• Construction V (adaptive block interleaving) corrects up to $((s_1-1)(n/b)+1) \times ((s_2-1)b+1)$ rectangular bursts when submatrices contain at most $t$ errors per block.
• Construction VI (diagonal interleaving) is optimal for long, narrow bursts (e.g., $k \times \ell$ with $k \ll \ell$), treating diagonal bursts as single errors in the outer code.