Paper 2025/1178

Engel p-adic Supersingular Isogeny-based Cryptography over Laurent series

Abstract

This paper builds the foundation for a cryptosystem based on p-adic representations of supersingular elliptic curve isogenies generated through Engel expansions of Laurent series. This mathematical framework manifests as a lightweight encryption scheme implemented on ESP32 microcontrollers for IoT applications. Efficient isogeny paths are constructed for quantum-resistant primitives secured against Shor's algorithm by decomposing elements into Engel sequences. Performance analysis confirms linear computational scaling with message size and speed gain at a higher clock rate, along with power trace signatures corroborating theoretical computational models. Consequently, we confirm the practical feasibility of our proposed p-adic isogeny cryptography on resource-constrained embedded systems while offering rigorous post-quantum security assurances.