Transformer-based large language models are becoming critical technological infrastructure, but their rapid deployment has turned privacy leakage from a localized concern into a systemic risk spanning the entire model lifecycle. These risks restrict adoption in sensitive and heavily regulated domains.

Cryptographic techniques such as fully homomorphic encryption and secure multi-party computation offer provable security guarantees and are increasingly used in key stages including data selection, fine-tuning, and inference. Nevertheless, work on cryptography-based privacy-preserving LLMs remains fragmented.

This survey systematically reviews and classifies existing frameworks and methods, providing a structured basis for coordinating optimization strategies and designing efficient privacy-preserving LLM algorithms. It also identifies limitations in current research and outlines promising directions for future exploration.