As users increasingly interact with large language models (LLMs) using private information, secure and encrypted communication becomes essential. Homomorphic encryption (HE) provides a principled solution by enabling computation directly on encrypted data. Although prior work has explored aspects of running LLMs under HE, the challenge of text generation, particularly next-token prediction, has received limited attention and remains a key obstacle to practical encrypted interaction. In this work, we propose a TSP-based token reordering strategy to address the difficulties of encrypted text generation, together with a post-processing step that further reduces approximation error. Theoretical analysis and experimental results demonstrate that our method prevents collapse, improves coherence in generated text, and preserves data privacy throughout. Overall, our contributions advance the feasibility of practical and privacy-preserving LLM inference.