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Third Point operation on elliptic curves people explore is the point doubling for any point being lying on the elliptic curve point doubling is similar to point addition with the difference that there are no two distinct points but only one instead of using a line that would connect the two points we use a tangent line at given point this time the second point where this tangent line crosses the elliptic curve is the negation of the result labeled minus R s with Edison we have this point over the x-axis and there lies the resulting point R which is the double of the original point P on elliptic curve over a finite field the situation looks more complex as you can see there are many smooth elliptic curves with the Kuban coefficients which produce the rational points over the finite field this comes from the fact that not only the x and y coordinate values wrapped around the finite field but also the values of the elliptic function get read we can see this third wrapping if we add multip
