Analyzing IND-CPA Security of HQC Codes Using k-Nearest Neighbors

Hamming Quasi-Cyclic (HQC) codes, recently selected by NIST for post-quantum cryptography standardization, rely on the hardness of the 2-QCSD problem. While typically analyzed through algebraic methods, we apply AI-driven techniques to explore their IND-CPA security. Using manifold learning (e.g., Isomap), we reveal geometric structure in high-dimensional embeddings of code instances.We then apply k-Nearest Neighbors (KNN) to assess separability and potential learnability within this space. To scale this analysis, we incorporate Hierarchical Navigable Small World (HNSW) graphs, enabling efficient nearest-neighbor search. Our results suggest that geometric and learning-based techniques may offer new insights into the hardness assumptions of HQC-based cryptography.