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Are there any elliptic curves, that require computing GCD for point addition? I've an algorithm, that apparently adds two points on an elliptic curve, but it uses GCD, which is strange, because I never saw it being used for addition on any kind of curve.

Are there any formulas for point operations on EC that involve GCD, or perhaps are sped up by using GCD?

By GCD I also mean extended GCD.

  • 1
    Are these elliptic curves over $\mathbb F_p$? Extended gcd is commonly used to find modular reciprocals.2011-09-09
  • 0
    Curve is over polynomials with coefficients modulo a prime. For example, x coord. of result is divided by gcd, so it isn't used just for reciprocals.2011-09-09
  • 1
    Could it be a step intended to simplify *projective* coordinates of a point?2011-09-10
  • 0
    The group law on primitive integer points of $x^2 - d y^2 = 4 z^3$ uses $\gcd$. Some elliptic curves are on this surface but their group laws don't coincide.2012-02-23

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