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Bio-cryptography is a new security technology which combines cryptography with biometrics. Fuzzy extractors are effective in terms of binding a cryptographic key to biometric features. However, most existing fuzzy extractors require fingerprint registration prior to the application of fuzzy extractors, and depend on error-correction codes to rectify the biometric uncertainty. This is not operative in practice due to low matching performance. In this paper, by taking full advantage of a Delaunay triangulation net, e.g. local structural stability, we propose a new registration-free Delaunay triangle-based fuzzy extractor. The new fuzzy extractor not only can mitigate biometric uncertainty but also eliminate the feature pre-alignment process in fingerprint authentication. Experimental results show that the proposed scheme achieves a better performance than those of the those of existing registration-based fuzzy extractor methods.