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Translating the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves with $(\ell ,\ell ,\ell )$-Isogenies
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Abstract: | We give an algorithm to compute $$(\ell ,\ell ,\ell )$$ ( ℓ , ℓ , ℓ ) -isogenies from the Jacobians of genus three hyperelliptic curves to the Jacobians of non-hyperelliptic curves over a finite field of characteristic different from 2 in time $$\tilde{O}(\ell ^3)$$ O ~ ( ℓ 3 ) , where $$\ell $$ ℓ is an odd prime which is coprime to the characteristic. An important application is to reduce the discrete logarithm problem in the Jacobian of a hyperelliptic curve to the corresponding problem in the Jacobian of a non-hyperelliptic curve. |
BibTeX
@article{jofc-2021-31761, title={Translating the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves with $$(\ell ,\ell ,\ell )$$-Isogenies}, journal={Journal of Cryptology}, publisher={Springer}, volume={34}, doi={10.1007/s00145-021-09401-3}, author={Song Tian}, year=2021 }