In this paper we propose an OFDM (Orthogonal Frequency Division Multiplexing) wireless communication system that introduces mutual authentication and encryption at the physical layer, without impairing spectral efficiency, exploiting some freedom degrees of the base-band signal, and using encrypted-hash algorithms. FEC (Forward Error Correction) is instead performed through variable-rate Turbo Codes. To avoid false rejections, i.e. rejections of enrolled (authorized) users, we designed and tested a robust hash algorithm. This robustness is obtained both by a segmentation of the hash domain (based on BCH codes) and by the FEC capabilities of Turbo Codes.