Embedding Renewable Cryptographic Keys into Continuous Noisy Data

Fuzzy extractor is a powerful but theoretical tool to extract uniform strings from discrete noisy data. Before it can be used in practice, many concerns need to be addressed in advance, such as making the extracted strings renewable and dealing with continuous noisy data. We propose a primitive fuzzy embedder as a practical replacement for fuzzy extractor. Fuzzy embedder naturally supports renewability because it allows a randomly chosen string to be embedded. Fuzzy embedder takes continuous noisy data as input and its performance directly links to the property of the input data. We give a general construction for fuzzy embedder based on the technique of Quantization Index Modulation (QIM) and derive the performance result in relation to that of the underlying QIM. In addition, we show that quantization in 2-dimensional space is optimal from the perspective of the length of the embedded string. We also present a concrete construction for fuzzy embedder in 2-dimensional space and compare its performance with that obtained by the 4-square tiling method of Linnartz, et al. [13].