Let K be a field of characteristic # 2 and let E : y = x + ax + b be an elliptic curve defined over K. Show that if P1 =

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Let K Be A Field Of Characteristic 2 And Let E Y X Ax B Be An Elliptic Curve Defined Over K Show That If P1 1 (34.81 KiB) Viewed 26 times

I need to show P1 = (x1, y1), P2 = (x2, y2) ∈ E(K) are such that P1 ̸= −P2, taking into account the "Hints" or "comments" which give an idea of ​​what to do
Let K be a field of characteristic # 2 and let E : y = x + ax + b be an elliptic curve defined over K. Show that if P1 = (x1, yı), P2 = (x2,42) E(K) are such that P1 * -P2, then: P1+ P2 = (m? – #1 – 12,-41 - m(m? - 261 – 22)), where 3ata if P = P2, m = 2y1 VI-V2 if Pi + P2 11-22 Deduce that for every P = (x,y) such that 2P #0, we have P(x) 2. P= '( p' (ac) 2., -y (1+ 3.0 4p(2) 2p( 4p(2) (1 2007 (% - ))) Hint: If P, and P2 if are distinct, write an equation for the line through P and P2, and find the x-coordinate of the third point of intersection of this line with E. If the points P and P2 coincide, repeat the argument with the tangent to E at P.