Quantum direct communication (QDC) uses the basic principle of quantum mechanics to realize the secure communication between legal parties. Deterministic secure quantum communication (DSQC), as a branch of QDC, is a way to transmit secret message with the aid of classical bits. In this paper, a multi-party DSQC based on [Formula: see text]-dimension [Formula: see text]-particles GHZ states is proposed, in which unitary operation is not required. On the basis of [Formula: see text]-dimension single-photon measurement results, the communication parties encode and decode the message through performing modulo addition and subtraction. In addition, the scheme uses the added [Formula: see text]-dimension single photon for eavesdropping detection. The scheme has expansibility and universality. It can scale to as many parties in any dimension as required. Based on the star-shaped communication structure, it can be extended to a network to achieve the rapid communication of secret message across regions.

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