When data is transmitted through the network, it is vulnerable to network attacks such as eavesdropping and tampering. Therefore, data confidentiality and data integrity should be guaranteed which can be achieved with the signcryption schemes. Based on the elliptic curve, a multi-receiver multi-message signcryption scheme is proposed, which can be effectively adapted to many scenarios such as broadcast systems. Multiple key distribution centers are used to manage the system master key, and the secrets of each center can be updated periodically to resist the APT attacks. In addition, users registered in different periods can communicate with each other to improve the availability. A secret update strategy based on the public blockchain is proposed, and the update operation is triggered based on the block height and the block timestamp. Blockchain, with its non-tampering feature, can guarantee security of the proposed scheme. In addition, the new scheme does not need to send transactions and is therefore free. Based on the computational Diffie-Hellman problem and the discrete logarithm problem, confidentiality and unforgeability of the proposed scheme are analyzed on the random oracle model. The proposed scheme also has the following security attributes:key escrow security, forward and backward compatibility, and non-repudiation. Performance analysis shows that the proposed scheme has a shorter ciphertext length and higher efficiency. In the simulation part, influence of the number of key distribution centers and the threshold on the system performance is analyzed. Without considering the network delay and other disturbing factors, the performance loss is less than 5% for the proposed scheme compared with those with a single key distribution center. The time errors incurred by the update strategy based on blockchain decrease with the increasing periods. When the period is set more than 550s, the time error percentage is less than 1%. The time errors make it more difficult for the attackers to predict the update time and launch the attacks.