Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914170914471936 |
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| author | Cherkaoui, Ilias Dey, Indrakshi |
| author_facet | Cherkaoui, Ilias Dey, Indrakshi |
| contents | Securing the Internet of Things (IoT) against quantum attacks requires public-key cryptography that (i) remains compact and (ii) runs efficiently on microcontrollers, capabilities many post-quantum (PQ) schemes lack due to large keys and heavy arithmetic. We address both constraints simultaneously with, to our knowledge, the first-ever isogeny framework that encodes super-singular elliptic-curve isogeny data via novel Engel expansions over the p-adic Laurent series. Engel coefficients compress torsion information, thereby addressing the compactness constraint, yielding public keys of ~1.1 - 16.9 kbits preserving the hallmark small sizes of isogeny systems. Engel arithmetic is local and admits fixed-precision p-adic operations, enabling micro-controller efficiency with low-memory, branch-regular kernels suitable for embedded targets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation Cherkaoui, Ilias Dey, Indrakshi Cryptography and Security Information Theory Securing the Internet of Things (IoT) against quantum attacks requires public-key cryptography that (i) remains compact and (ii) runs efficiently on microcontrollers, capabilities many post-quantum (PQ) schemes lack due to large keys and heavy arithmetic. We address both constraints simultaneously with, to our knowledge, the first-ever isogeny framework that encodes super-singular elliptic-curve isogeny data via novel Engel expansions over the p-adic Laurent series. Engel coefficients compress torsion information, thereby addressing the compactness constraint, yielding public keys of ~1.1 - 16.9 kbits preserving the hallmark small sizes of isogeny systems. Engel arithmetic is local and admits fixed-precision p-adic operations, enabling micro-controller efficiency with low-memory, branch-regular kernels suitable for embedded targets. |
| title | Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation |
| topic | Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2511.20533 |