Trapdoor Computational Fuzzy Extractors

We describe a method of cryptographically-secure key extraction from a noisy biometric source. The computational security of our method can be clearly argued through hardness of Learning Parity With Noise (LPN). We use a fuzzy commitment scheme so the extracted key is chosen by definition to have uniformly random bits. The biometric source is used as the noise term in the LPN problem. A key idea in our construction is to use additional ‘confidence’ information produced by the source for polynomial-time key recovery even under high-noise settings, i.e., Θ(m) errors, where m is the number of biometric bits. The confidence information is never exposed and is used as a noise-avoiding trapdoor to exponentially reduce key recovery complexity. Previous computational fuzzy extractors were unable to correct Θ(m) errors or would run in exponential time in m. A second key result is that we relax the requirement on the noise in the LPN problem, which relaxes the requirement on the biometric source. Through a reduction argument, we show that in the LPN problem, correlation in the bits generated by the biometric source can be viewed as a bias on the bits, which affects the security parameter, but not the security of the overall construction. Using a silicon Physical Unclonable Function (PUF) as a concrete example, we show how keys can be extracted securely and efficiently even under extreme environmental variation.