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A double large prime variation for small genus hyperelliptic index calculus
Authors: P. Gaudry, E. Thomë, N. Thëriault, C. DiemAbstract:
In this article, we examine how the index calculus approach for computing
discrete logarithms in small genus hyperelliptic curves can be improved
by introducing a double large prime variation. Two algorithms are
presented. The first algorithm is a rather natural adaptation of the
double large prime variation to the intended context. On heuristic and
experimental grounds, it seems to perform quite well but lacks a
complete and precise analysis. Our second algorithm is a considerably
simplified variant, which can be analyzed easily. The resulting
complexity improves on the fastest known algorithms. Computer experiments
show that for hyperelliptic curves of genus three, our first algorithm
surpasses Pollard’s Rho method even for rather small field sizes.
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