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elliptic-curve at the point ⊖R. You then flip this point over x-axis to get the point R = P⊕Q (resp. R = P⊕P). Mathematically speaking, the rules for adding two points P and Q over an elliptic-curve E(F11) are defined as follows: P⊕O = P, where O is the point-at-infinity. If P = (Xp, Yp), then