With the continuous development of the internet of things (IoT) technology, large amount of data has been generated by lots of IoT devices which require large-scale data processing technologies and storage technologies. Cloud computation is a paradigm for handling such massive data. With the help of cloud computing, IoT devices can utilize the data more efficiently, conveniently and faster. Therefore, how to promote the better integration of the IoT and cloud computing is an interesting research problem. In the big data era, group sum evaluation over outsourced data stream collected by IoT devices is an essential building block in many stream applications, such as statistical monitoring, data mining, machine learning and so on. Thus it is very valuable to design a mechanism to verify the correctness of the group sum evaluation over the outsourced data streams, especially when the data streams are originated from multiple data sources. Recently, Liu et al. proposed such a scheme to solve this problem. However in this paper, we show their scheme is not secure. Concretely, the adversary can easily forge tags for outsourced data, thus the correctness of the group sum evaluation can not be guaranteed anymore. Furthermore, we give two improved schemes which can resist our attack and analyze their security. Finally, we roughly evaluate the performance of our two improved schemes. Our first scheme almost shares the same efficiency as Liu et al.’s proposal but with no security flaw, the second scheme shares the same structure with Liu et al.’s proposal and can be compatible with the existing composite order bilinear pairing cryptosystem. © 2018, Springer-Verlag GmbH Austria, part of Springer Nature.