With the rapid development of machine learning, decision trees have become an important predictive model in statistics and data mining due to their intuitiveness and efficiency. However, existing schemes suffer from high communication overhead and are vulnerable to quantum attacks. To address this problem, we propose a secure non-interactive decision tree evaluation protocol based on fully homomorphic encryption. The protocol does not rely on the interaction between entities. It performs classification tasks in a cryptographic domain by the model owner and does not require the client to remain online continuously, which greatly reduces the cost of communication between entities. Experimental evaluations on UCI datasets demonstrate that our protocol significantly reduces communication overhead, requiring only 23.9%, 24.8%, and 33.7% of the bandwidth used by existing protocols on the Heart-Disease, Breast-Cancer, and Spambase datasets, respectively. In addition, we designed a new secure comparison protocol based on a bitwise encoding method. This encoding mechanism represents numerical values hierarchically by converting data into binary strings, providing structured input for subsequent secure comparisons through bitwise homomorphic operations. Furthermore, the protocol adopts a lattice-based fully homomorphic encryption scheme, which greatly enhances the protocol to resist against quantum attacks.