With the rapid developments in embedded sensor technology, the internet of things (IoT) becomes the most focused research trend in the recent years. However, the integration of such technology into mobile crowdsensing networks results in many security challenges. Data confidentiality and authenticity are the two key privacy concerns in any IoT‐based crowdsensing environment. Focusing on these security issues, we present a new cryptographic protocol to meet those challenges. Our protocol is based on two new schemes; first is an encryption scheme, which utilizes the idea of identity‐based encryption, and the second is a designated verifier signature scheme. Here, we design a pairing‐free and random oracle‐free encryption scheme with a small‐size public parameter where the anonymity of IoT‐recipient is maintained. Besides, the proposed designated verifier signature scheme facilitates the signatory to send a signature without sending the original message. The security of the encryption and signature schemes are proven in the standard security model based on the difficulty of proposed modified interactive quadratic residuosity “(MIQR)” assumption. Moreover, the schemes are compared with other relevant schemes and found several merits in terms of functionality. Thus, the proposed protocol is applicable in many IoT‐enabled crowdsourcing environments where the authenticity of confidential data is the major concern.