Torsion points and bilinear pairing

if you have a point P where mP=O, then you have a point of order m in the group E
If you have a set of points E[m]={P belongs to E:[m]P=O}
these points are points of finite order, they are called torsion points!

E[m] is a subgroup af E

the great "news" ;Bilinear pairing, is that every point P can be written as a linear combination
P = aP1 + bP2 for unique choice of a and b (in Z/mZ)

If m is large its difficult to find a and b. If b=0, then finding a is solving ECDLP!
P=aP1.