Deniable authentication is an essential cryptography paradigm, which enables a receiver to identify the source of a given message, but the receiver cannot prove the source of the message to any third party over an insecure network. In this paper, we propose a novel noninteractive deniable authentication quantum bits-based scheme, named NIDAQ, aiming to require one ciphertext with non-interactive process for achieve mutual authentication, deniability and the message transmission secretly without a central node, and at the same time, wiping out the stubborn flaws in traditional communication. Our proposed protocols’ security are mainly based on quantum-verifiable and chaotic maps. In contrast to the recent literatures, our proposed scheme not only cares about security and efficiency, but also provides privacy protection which is a very important property in the modern social network. Finally, we give the security proof and the efficiency analysis of our proposed scheme.