I am not sure how comfortable you are with mathematics (and algebra in particular), but my courses in algebraic geometry were among the hardest I have taken so far (and the study of elliptic curves is a specialisation of the study of algebraic geometry). After studying algebra for 4 years I can now finally understand most of the introductory chapter of my book on elliptic curves, though not all of it. Since you want to learn about a specific algorithm rather than all of elliptic curves I think it shouldn't take you the 4/5 years that it is taking me, but be warned that acquiring a deep understanding might prove to be very hard.