From Watermarks to Fuzzy Extractors: a Practical Construction

Fuzzy extractors are a powerful tool to extract randomness from noisy data. A fuzzy extractor can extract randomness only if the source data is discrete while in practice source data is continuous. Using quantizers to transform continuous data into discrete data is a commonly used solution. However, as far as we know no study has been made of the effect of the quantization strategy on the performance of fuzzy extractors. We use an unexplored parallel between watermarking theory and fuzzy extractors to study the effects of quantization. We construct the encoder and the decoder function of a fuzzy extractor using quantization index modulation (QIM) and we express performance properties of a fuzzy extractor in terms of geometric properties of the used QIM. In the end we present and analyze, as an exercise, two constructions in the two dimensional space. Our 6-hexagonal tiling construction offers ( log2 6 2 − 1) ≈ 0.3 extra bits per dimension of the space compared to the known square quantization based fuzzy extractor. The other construction turns out to be optimal from resilience to noise perspective.