# What are unified addition and differential addition in elliptic curve point arithmetic?

A lot of papers use these terms but I do not find a proper explanation of them. Can somebody tell the meaning / difference / intuition / application and if possible with an example.

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Unified addition means that the formula you use for adding two points doesn't depend on whether they are equal. Simplifying point addition in the Weierstrass form somewhat $s=(y_A-y_b)/(x_A-x_b)$ when $A\neq B$ - this is "Adding". Otherwise $s=(3x_A^2-p)/{2y_A}$ when doubling a point.