Can we avoid tests for zero in fast elliptic-curve arithmetic ?

@inproceedings{Bernstein2006CanWA,
  title={Can we avoid tests for zero in fast elliptic-curve arithmetic ?},
  author={Daniel J. Bernstein},
  year={2006}
}
This paper analyzes the exact extent to which 0 and ∞ cause trouble in Montgomery’s fast branchless formulas for x-coordinate scalar multiplication on elliptic curves of the form by = x + ax + x. The analysis shows that some multiplications and branches can be eliminated from elliptic-curve primality proofs and from elliptic-curve cryptography.