The theoretical limits of watermark spread spectrum sequence

Area of Science:

• Digital Watermarking
• Spread Spectrum Communications
• Information Security

Background:

• Spread spectrum (SS) sequences, commonly used in watermarking, originate from SS communications and i.i.d. random sequences.
• The suitability of these traditional SS sequences for digital watermarking has been largely overlooked by researchers.
• A critical difference exists between SS watermark channels and traditional SS communication channels, particularly concerning correlation properties.

Purpose of the Study:

• To compare the correlation properties of SS watermark channels and traditional SS communication channels.
• To define watermark auto- and cross-correlation properties suitable for SS watermarking, considering cropping and translation attacks.
• To propose new correlation properties, Loose Autocorrelation and Tight Cross-Correlation (LAC&TCC), for enhanced SS watermark robustness.

Main Methods:

• Comparison of SS watermark channel and traditional SS communication channel correlation properties.
• Definition of watermark auto- and cross-correlation metrics.
• Introduction and theoretical establishment of Loose Autocorrelation (LAC) and Tight Cross-Correlation (TCC) properties.
• Derivation of the lower bound for peak cross-correlation (Rc(l)) and the higher bound for peak autocorrelation (Ra(l)).

Main Results:

• Identified distinct correlation properties between SS watermark and communication channels.
• Proposed LAC&TCC properties, requiring autocorrelation close to 1 and cross-correlation close to 0, irrespective of synchronization.
• Established theoretical bounds for peak autocorrelation (Ra(l)) and peak cross-correlation (Rc(l)).
• Demonstrated that a detection threshold can reliably distinguish auto- and cross-correlations, even with minimal cover data.

Conclusions:

• The proposed LAC&TCC properties offer a robust framework for spread spectrum digital watermarking.
• The established bounds guarantee the theoretical possibility of distinguishing authentic watermarks from false positives, even under adverse conditions.
• This research addresses a gap in understanding SS sequence suitability for watermarking, enhancing security against common attacks.