I am studying this paper about an index calculus attack in hyperelliptic curves for genus $3, 4, 5, \dots, 9$.
- Nicolas Thériault, Index calculus attack for hyperelliptic curves of small genus, 2003.
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 ?