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Bio-cryptographic systems, such as Fuzzy Vault and Fuzzy Extractor, can not only verify a person but also protect a pre-stored user feature template. Nearly all of the existing bio-cryptographic systems work in encrypted domain, and hence all biometric features should be transformed from biometric domain to encrypted domain, usually referred to the encoding and decoding process. The selection of biometric features play a vitally important role for the system. Minutia local structure features are considered as one of the most promising biometric features since they are stable, discriminating, alignment free, easy to be encoded and with large feature space. Unfortunately, although this category of features have been proposed for years, very few deep investigations, such as mathematical proof, appear in exisiting literature. In this paper, a comprehensive and detailed analysis of the minutia local structure is provided, covering the following topics: statistical test and analysis, theoretical matching performance estimation and security strength analysis.