Efficient construction of secure hyperelliptic discrete logarithm problems

Hyperelliptic curves have been used to define discrete logarithm problems as cryptographic one-way functions. However, no efficient algorithm for construction of secure hyperelliptic curves is known until now. In this paper, efficient algorithms are presented to construct secure discrete logarithm problems on hyperelliptic curves whose Jacobian varieties are either simple or isogenous to a product of simple abelian varieties.

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