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I am studying this paper about an index calculus attack in hyperelliptic curves for genus $3, 4, 5, \dots, 9$.

The paper has a lot of big-O's. On page 17, it has a table that shows the big-O for the current attack on many genuses. Generally, in order to crack any cryptographic scheme takes many years as far as I know, so it is practically infeasible. Because I am not sure, is the index calculus attack in hyperelliptic curves attack feasible with a common 2-core, 4-core intel laptop? In other words is that something that it can be accomplished in, let's say, genus-3 HCC ?

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    $\begingroup$ Those algorithms are (unfortunately) largely theoretical: The constants hidden in the asymptotic complexities are huge. I don't think anyone has ever run them on "serious", non-toy instances. $\endgroup$
    – yyyyyyy
    Oct 24 at 8:45

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