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    • Jubjub

    Jubjub-point-abscissa-is-not-1

    A Jubjub point cannot have abscissa 1.

    The reason is that, if we set u = 1 in the curve equation, we obtain that v^2 is equal to the non-square (1-a)/(1-d), an impossibility (the fact that (1-a)/(1-d), which has a known value, is not a square, can be seen using Euler's criterion. A more detailed proof is in Theorem 5.4.5 in [ZPS:5.4.8.2].

    Definitions and Theorems

    Theorem: jubjub-point-abscissa-is-not-1

    (defthm jubjub-point-abscissa-is-not-1
      (implies (jubjub-pointp point)
               (not (equal (jubjub-point->u point) 1))))