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Point compression does not lose information; that's the point. Technical details: suppose we are working in field Zp for a big prime p. The curve equation is: Y2 = X3 + aX + b for two constants a and b which define the curve. For a point (X,Y) on the curve, you can use the equation to recover Y2 from X alone. Since we are working in a field, Y2 can have ...

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