Large language models (LLMs) are increasingly used for code generation, but their ability to program specialized cryptographic systems remains poorly understood. Cheon-Kim-Kim-Song (CKKS), a fully homomorphic encryption (FHE) scheme supporting approximate arithmetic over packed real- and complex-valued vectors, is particularly relevant to machine-learning workloads. Prior work has not systematically examined the CKKS-specific challenges of LLM-generated encrypted programs. To address this gap, we introduce FHE-CodeEval, a 46-case benchmark that evaluates three core challenges: packing, nonlinear approximation, and level/scale management, as well as how models coordinate decisions across them. We further introduce communication-aware efficiency, an FHE-specific metric comparing generated programs with compiler baselines using server-side runtime and ciphertext footprint.

We evaluate eight recent proprietary and open-weight LLMs on FHE-CodeEval. Across all 46 cases, the best observed scores reach 51.7% Pass@1 and 69.6% Pass@5 with iterative execution feedback, but only 7.8% Pass@1 and 13.0% Pass@5 in the one-shot setting. For efficiency, even the best-performing model achieves a geometric-mean communication-aware efficiency of only 0.44 over its valid rollouts in the compiler-comparable subset. These results reveal a substantial gap between functional correctness and efficiency in LLM-generated CKKS programs. Code is available at https://github.com/qiuchuy/FHE-CodeEval.

In professional financial-legal consulting services, accurately and efficiently retrieving and answering legal questions is crucial. Although some breakthroughs have been made in information retrieval and answer generation, few frameworks have successfully integrated these tasks. Therefore, we propose RIRAG (Retrieval-In-the-loop Response and Answer Generation), a bi-directional retrieval-enhanced framework for financial-legal question answering in ObliQA Shared Task. The system introduces BDD-FinLegal, which means Bi-Directional Dynamic finance-legal, a novel retrieval mechanism specifically designed for financial-legal documents, combining traditional retrieval algorithms with modern neural network methods. Legal answer generation is implemented through large language models retrained on expert-annotated datasets. Our method significantly improves the professionalism and interpretability of the answers while maintaining high retrieval accuracy. Experiments on the ADGM dataset show that the system achieved a significant improvement in the Recall@10 evaluation metric and was recognized by financial legal experts for the accuracy and professionalism of the answer generation. This study provides new ideas for building efficient and reliable question-answering systems in the financial-legal domain.