Introducing GRAFHEN: Group-based Fully Homomorphic Encryption without Noise
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912668944695296 |
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| author | Guillot, Pierre Duc, Auguste Hoang Koskas, Michel Méhats, Florian |
| author_facet | Guillot, Pierre Duc, Auguste Hoang Koskas, Michel Méhats, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introducing GRAFHEN: Group-based Fully Homomorphic Encryption without Noise Guillot, Pierre Duc, Auguste Hoang Koskas, Michel Méhats, Florian Cryptography and Security Group Theory E.3 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. |
| title | Introducing GRAFHEN: Group-based Fully Homomorphic Encryption without Noise |
| topic | Cryptography and Security Group Theory E.3 |
| url | https://arxiv.org/abs/2510.21483 |