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# 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} }

- Published 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.