Editing Index calculus algorithm (section)

=== Applications in other groups ===

The lack of the notion of ''prime elements'' in the group of points on [[elliptic curves]] makes it impossible to find an efficient ''factor base'' to run index calculus method as presented here in these groups. Therefore this algorithm is incapable of solving discrete logarithms efficiently in elliptic curve groups. However: For special kinds of curves (so called [[supersingular elliptic curve]]s) there are specialized algorithms for solving the problem faster than with generic methods. While the use of these special curves can easily be avoided, in 2009 it has been proven that for certain fields the discrete logarithm problem in the group of points on ''general'' elliptic curves over these fields can be solved faster than with generic methods. The algorithms are indeed adaptations of the index calculus method.<ref>{{cite journal|last=Diem|first=C|title=On the discrete logarithm problem in elliptic curves|journal=Compositio Mathematica|year=2010}}</ref>