In Wireless Sensor Network (WSN), when the compromised sensor nodes disturb network data and transmission, it is particularly important to determine the compromised sensor nodes in time and take appropriate measures to ensure the security of the entire network. Therefore, a data aggregation scheme for wireless sensor network was proposed to timely determine the compromised sensor nodes. First, the state public key encryption, the symmetric public key encryption, the pseudo random function and the message authentication code were used to encrypt the plaintext twice. Secondly, the cluster head node authenticated the ciphertext and filtered false data. Then, the cluster head node decrypted the ciphertext, and the numbers of the compromised nodes were sent to the base station. At last, the base station decrypted the ciphertext to recover the plaintext and authenticated the data. The proposed scheme solves the problem of the error aggregation value problem caused by the compromised nodes, filters the false data in time and determines the compromised sensor nodes. The analysis shows that the proposed scheme is secure under the secure one-way hash function, the message authentication code and the assumption of the Discrete Logarithm Problem (DLP), and also greatly reduces the communication cost and computational cost. Simulation result shows that, compared with the secure aggregation scheme for WSN using stateful public key cryptography, the computational cost, the communication cost and the time consumption of determining the compromised sensor nodes of the proposed scheme is decreased by at least 19.96%, 36.81% and 28.10%, respectively.

Since the broadcast authentication of public-key cryptography based on digital signatures in Wireless Sensor Network (WSN) costs large amounts of energy, and the sensor nodes have limited resources, so a broadcast authentication scheme based on mutual cooperation of sensor nodes was proposed to save the energy consumption of sensor nodes and speed up the digital signature authentication of sensor nodes. First of all, a user broadcasted his signature information into the group network of WSN, but did not broadcast the y-coordinate of the point in the signature. Then, according to the x-coordinate of the point and elliptic curve equation, the high-energy nodes in group network computed the y-coordinate and broadcasted it to the normal nodes in the group; at the same time, using vBNN-IBS (a variant of Bellare-Namprempre-Neben-Identity-based Signature) digital signature, the high-energy nodes authenticated the signature information broadcasted by user and rebroadcasted the effective signature information. Finally, after receiving the y-coordinate, the normal nodes in group network utilized elliptic curve equation to verify the correctness and reliability of y-coordinate, and implemented the same signature authentication as the high-energy nodes, and then rebroadcasted the effective signature information. In addition, the proposed scheme minimized the length of Authorization Revocation List (ARL) by integrating immediate revocation and automation revocation. Simulation results show that compared with another improved vBNN-IBS scheme accelerated by using mutual cooperation of sensor nodes, the energy consumption and the total certification time of the proposed scheme decreases 41% and 66% respectively when the amount of data packets received by the authentication node from its neighbour nodes is up to a certain number.