Paper 2025/1907

Introducing GRAFHEN: GRoup-bAsed Fully Homomorphic Encryption without Noise

Auguste Hoang Duc, Ravel Technology

Michel Koskas, Ravel Technology

Florian Méhats, Ravel Technology

Abstract

We present GRAFHEN, a new cryptographic scheme which offers Fully Homomorphic Encryption without the need for bootstrapping (or in other words, without noise). Building on the work of Nuida and others, we achieve this using encodings in groups. The groups are represented on a machine using rewriting systems. In this way the subgroup membership problem, which an attacker would have to solve in order to break the scheme, becomes maximally hard, while performance is preserved. In fact we include a simple benchmark demonstrating that our implementation runs several orders of magnitude faster than existing standards. We review many possible attacks against our protocol and explain how to protect the scheme in each case.

@misc{cryptoeprint:2025/1907,
      author = {Pierre Guillot and Auguste Hoang Duc and Michel Koskas and Florian Méhats},
      title = {Introducing {GRAFHEN}: {GRoup}-{bAsed} Fully Homomorphic Encryption without Noise},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1907},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1907}
}