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In recent years, data generated by Internet of Things (IoT) devices has become increasingly massive. The amount of data stored in the cloud is also enormous and needs to be processed in a timely, efficient, secure, and private manner. While data stored on the cloud is guaranteed to be available, this does not mean that the secrecy and privacy of the sender are guaranteed. Moreover, sharing data on the cloud may sometimes lead to unpleasant surprises, such as undeniable disputes due to the shared content. Our certificateless signcryption (CLSC) scheme is proposed to address the above issues. It provides unforgeability, indistinguishability, non-transferability, and privacy of sender identity to ensure secrecy and privacy of the sender. Our contributions are not only limited to solving the aforementioned issues. The security model of non-transferability and privacy of sender identity for the signcryption scheme is first proposed. This is followed by a concrete simulation of the proof. In addition, our CLSC scheme does not use bilinear pairing, which is significantly lowers its computational cost and makes it suitable for IoT devices in wireless sensor networks (WSNs).