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Secure group communication with efficient self-organising key agreement protocol and small broadcast ciphertext is essential to many collaborative and distributed applications in mobile ad-hoc networks (MANETs). In this study, the authors propose a Chinese Remainder Theorem-based secure group communication scheme which is able to provide confidentiality service and non-repudiation service simultaneously. In the proposed scheme, all group members contribute their own public keys to negotiate a shared encryption public key, which corresponds to all different decryption keys. By using the shared public key and the respective secret key, confidentiality and non-repudiation can be obtained, respectively. Both are essential to secure group communication in MANETs. Compared with the exiting signcryption schemes for multiple recipients, the proposed self-organising scheme has much smaller ciphertext that does not increase with the size of the group. Accordingly, it is quite suitable to secure group communication in self-organising, distributed and resource-constrained MANETs.