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arXiv · 2504.04559

Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography

Mohammed El Baraka·Siham Ezzouak
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Abstract

We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny computations from O(g4) to O(g3) operations for genus 2 curves, achieving significant ciency gains over traditional elliptic curve methods. Detailed pseudocode and comprehensive complexity analyses demonstrate these improvements both theoretically and empirically. Additionally, we provide a thorough security analysis, including proofs of resistance to quantum attacks such as Shor's and Grover's algorithms. Our findings establish hyperelliptic isogeny-based cryptography as a promising candidate for secure and e cient post-quantum cryptographic systems.

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Mohammed El Baraka, Siham Ezzouak. 2025-04-06. Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography. https://arxiv.org/abs/2504.04559

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