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arXiv · 2511.20533

Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation

Ilias Cherkaoui·Indrakshi Dey
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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.

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Ilias Cherkaoui, Indrakshi Dey. 2025-11-25. Engel p-adic Isogeny-based Cryptography over Laurent Series: Foundations, Security, and an ESP32 Implementation. https://arxiv.org/abs/2511.20533

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