{"ID":2837076,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20533","arxiv_id":"2511.20533","title":"Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation","abstract":"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.","short_abstract":"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 knowledg...","url_abs":"https://arxiv.org/abs/2511.20533","url_pdf":"https://arxiv.org/pdf/2511.20533v1","authors":"[\"Ilias Cherkaoui\",\"Indrakshi Dey\"]","published":"2025-11-25T17:35:54Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"cs.IT\"]","methods":"[\"Large Language Model\"]","has_code":false}