Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910905181143040 |
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| author | Baraka, Mohammed El Ezzouak, Siham |
| author_facet | Baraka, Mohammed El Ezzouak, Siham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography Baraka, Mohammed El Ezzouak, Siham Number Theory 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. |
| title | Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.04559 |