Grafhen: Group-Based Homomorphic Encryption Without Noise (arxiv.org)

Researchers have introduced GRAFHEN, a novel fully homomorphic encryption (FHE) scheme that eliminates the traditional need for noise and bootstrapping by encoding plaintexts as elements of algebraic groups. Instead of lattice/noise-based encodings, GRAFHEN represents groups in software via rewriting systems so that breaking the scheme reduces to solving a subgroup membership problem in those representations. The authors claim this makes cryptanalysis “maximally hard” while retaining practical performance; their prototype includes benchmarks reportedly several orders of magnitude faster than current FHE standards. The paper also catalogues likely attack vectors and proposes countermeasures for each, and provides code, demos and data alongside the manuscript. Significance for the AI/ML community is clear: if secure, a noise-free, group-theoretic FHE could drastically lower the computational cost of privacy-preserving model evaluation and training, removing the expensive bootstrapping step that currently limits real-world deployment. Key technical implications are that security now hinges on new group-theoretic assumptions (subgroup membership hardness in specific rewriting-system representations) rather than lattice or number-theoretic hardness, so rigorous cryptanalysis and independent benchmarking are essential. GRAFHEN could be a practical leap for secure ML inference and federated analytics, but its novel foundations mean the community should treat performance claims with cautious optimism until broader peer review and attacks have been performed.