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Approximate Message Authentication Code (AMAC) is a recently introduced cryptographic primitive with several applications in the areas of cryptography and coding theory. Briefly speaking, AMACs represent a way to provide data authentication that is tolerant to acceptable modifications of the original message. Although constructs had been proposed for this primitive, no security analysis or even modeling had been done. In this paper we propose a rigorous model for the design and security analysis of AMACs. We then present two AMAC constructions with desirable efficiency and security properties. AMAC is a useful primitive with several applications of different nature. A major one, that we study in this paper, is that of entity authentication via biometric techniques or passwords over noisy channels. We present a formal model for the design and analysis of biometric entity authentication schemes and show simple and natural constructions of such schemes starting from any AMAC.