Privacy computing receives increasing attention but writing privacy computing code remains challenging for developers due to limited library functions that necessitate extensive function implementation from scratch as well as the data-oblivious requirement which contradicts intuitive thinking and usual practices of programmers. Large language models (LLMs) have demonstrated surprising capabilities in coding tasks and achieved state-of-the-art performance across many benchmarks. However, even with extensive prompting, existing LLMs struggle with code translation task for privacy computing, such as translating Python to MP-SPDZ, due to the scarcity of MP-SPDZ data required for effective pre-training or fine-tuning. To address the limitation, this paper proposes SPDZCoder, a rule-based framework to teach LLMs to synthesize privacy computing code without asking experts to write tons of code and by leveraging the instruction-following and in-context learning ability of LLMs. Specifically, SPDZCoder decouples the translation task into the refactoring stage and the generation stage, which can mitigate the semantic-expressing differences at different levels. In addition, SPDZCoder can further improve its performance by a feedback stage. SPDZCoder does not require fine-tuning since it adopts an in-context learning paradigm of LLMs. To evaluate SPDZCoder, we manually created a benchmark dataset, named SPDZEval, containing six classes of difficult tasks to implement in MP-SPDZ. We conduct experiments on SPDZEval and the experimental results shows that SPDZCoder achieves the state-of-the-art performance in pass@1 and pass@2 across six data splits. Specifically, SPDZCoder achieves an overall correctness of 85.94% and 92.01% in pass@1 and pass@2, respectively, significantly surpassing baselines (at most 30.35% and 49.84% in pass@1 and pass@2, respectively) by a large margin.

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