In this paper, we consider an authentication framework for independent modalities based on binary hypothesis testing using source coding jointly with the random projections. The source coding ensures the multimodal signals reconstruction at the decoder based on the authentication data. The random projections are used to cope with the security, privacy, robustness and complexity issues. Finally, the authentication performance is investigated for both direct and random projections domains. The asymptotic performance approximation is derived and compared with the exact solutions. The impact of modality fusion on the authentication system performance is demonstrated.