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.