Consider a scenario where several mutually distrustful enterprises need to collaboratively train an artificial intelligence model. Due to the need for data privacy protection, the comparison operations involved in the model training process must not disclose the compared data or the results of the comparisons. Currently, the open-source implementation MP-SPDZ supports dishonest majority settings, and its most efficient secure comparison protocol is primarily based on the framework proposed by Catrina and Hoogh in 2010. Protocols within this framework are mainly implemented using secret sharing techniques, especially for the basic multiplication operation, with communication overhead being a significant technical challenge. This paper firstly introduces fully homomorphic encryption technology into this framework, leveraging its single instruction multiple data (SIMD) capabilities to improve the random number generation and bit comparison protocols. This results in reduced communication overhead and enhanced protocol efficiency. Experimental data demonstrates that when the vector dimension is 8192 and the number of parties is 7, the communication overhead of the improved protocol is 37% of that in MP-SPDZ, and the overall comparison time is 41% of the time required by that in MP-SPDZ. This advantage increases as the number of users decreases.