Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with (ell,ell,ell)-isogenies
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math.AG
cs.CR
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curveshyperellipticjacobiansproblemcurvediscretegenusisogenies
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We give an algorithm to compute $(\ell,\ell,\ell)$-isogenies from the Jacobians of genus three hyperelliptic curves to the Jacobians of non-hyperelliptic curves. 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.
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