Robustly reusable fuzzy extractor from isogeny

Abstract

Robustly reusable Fuzzy Extractor (rrFE) allows multiple extractions from the same fuzzy source in a reproducible way. The reusability of rrFE asks the pseudo-randomness of the extracted keys, while robustness of rrFE makes sure that active attacks can be detected during the reproduction of the extracted key. With rrFE, we are able to produce cryptographic keys for our cryptosystems from fuzzy sources, like biometrics, physical unclonable functions, etc. There are rrFE schemes from the DDH, LWE and LPN assumptions. However there is no rrFE scheme from isogeny-based assumptions up to now.In this paper, we construct the first rrFE from isogeny. To obtain such an rrFE, we propose a new framework for constructing rrFE with a core technical tool, named Enhanced Effective Group Action (EEGA). EEGA is built upon the basic Effective Group Action (EGA), and is equipped with a sampling algorithm and a derivation algorithm. With such an EEGA, the same random input can be derived to produce different pseudo-random and unpredictable outputs. The EEGA, together with other routine building blocks like secure sketch and extractor, leverages an FE to achieve reusability and robustness. We construct EEGA based on CSI-FiSh, which admits the first rrFE scheme from isogeny. Besides, we also propose another two EEGA instantiations from the DDH assumption, and this provides another approach to DDH-based rrFE, which may be of independent interest.