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Vaudenay recently proposed a message authentication protocol which is interactive and based on short authenticated strings (SAS). We study here SAS-based non-interactive message authentication protocols (NIMAP). We start by the analysis of two popular non-interactive message authentication protocols. The first one is based on a collision-resistant hash function and was presented by Balfanz et al. The second protocol is based on a universal hash function family and was proposed by Gehrmann, Mitchell, and Nyberg. It uses much less authenticated bits but requires a stronger authenticated channel. We propose a protocol which can achieve the same security as the first protocol but using less authenticated bits, without any stronger communication model, and without requiring a hash function to be collision-resistant.