Securing Systems with Scarce Entropy: LWE-Based Lossless Computational Fuzzy Extractor for the IoT

With the advent of the Internet of Things, lightweight devices necessitate secure and cost-efficient key storage. Since traditional secure storage is expensive, the valuable entropy could originate from noisy sources, for which fuzzy extractors allow strong key derivation. While providing information-theoretic security, fuzzy extractors require large amount of input entropy to account for entropy loss in the key extraction process. It has been shown by Fuller et al. [20] that the entropy loss can be reduced if the requirement is relaxed to computational security based on the hardness of the Learning with Errors problem. Using this computational fuzzy extractor, we show how to construct a device-server authentication system providing outsider chosen perturbation security and pre-application robustness. We present the first implementation of a lossless computational fuzzy extractor where the entropy of the source equals the entropy of the key on a constrained device. The implementation needs only 1.45KB of SRAM and 9.8KB of Flash memory on an 8-bit microcontroller. We compare our implementation to existing work in terms of security, while achieving no entropy loss.