Robust fuzzy extractors and authenticated key agreement from close secrets

Consider two parties holding correlated random variables W and W', respectively, that are within distance t of each other in some metric space. These parties wish to agree on a uniformly distributed secret key R by sending a single message over an insecure channel controlled by an all-powerful adversary. We consider both the keyless case, where the parties share no additional secret information, and the keyed case, where the parties share a long-term secret SK that they can use to generate a sequence of session keys {R_j}using multiple pairs {(W_j, W_j′)}. The former has applications to, e.g., biometric authentication, while the latter arises in, e.g., the bounded storage model with errors. Our results improve upon previous work in several respects: - The best previous solution for the keyless case with no errors (i.e., t = 0) requires the min-entropy of W to exceed 2|W|/3. We show a solution when the min-entropy of W exceeds the minimal threshold |W|/2. - Previous solutions for the keyless case in the presence of errors (i.e., t > 0) required random oracles. We give the first constructions (for certain metrics) in the standard model. - Previous solutions for the keyed case were stateful. We give the first stateless solution.