message: [book] added more to pasta spec
diff: @@ -13,7 +13,12 @@ But in our code, because of the cycles:
  * Fp refers to the base field of Pallas, and the scalar field of Vesta
  * Fq refers to the base field of Vesta, and the scalar field of Pallas
  -TODO: change the naming of Fp and Fq to avoid ambiguity with the conventional Fq and Fr.
  +Note that $|F_q| > |F_p|$.
  +
  +In pickles:
  +
  +* Vesta is also referred to as the step curve, or the tick curve.
  +* Pallas is also referred to as the wrap curve, or the tock curve.
  ## Pallas
  @@ -23,6 +28,13 @@ TODO: change the naming of Fp and Fq to avoid ambiguity with the conventional Fq
  * mina generator: $(1, 12418654782883325593414442427049395787963493412651469444558597405572177144507)$
  * arkworks generator: $(-1, 2)$
  +You can use [sage](https://www.sagemath.org/) to test this:
  +
  +```py
  +Fp = GF(28948022309329048855892746252171976963363056481941560715954676764349967630337)
  +Pallas = EllipticCurve(Fp, [0, 5])
  +Pallas.count_points()
  +```
  ## Vesta
  @@ -31,3 +43,11 @@ TODO: change the naming of Fp and Fq to avoid ambiguity with the conventional Fq
  * scalar field: $28948022309329048855892746252171976963363056481941560715954676764349967630337$
  * mina generator: $(1, 11426906929455361843568202299992114520848200991084027513389447476559454104162)$
  * arkworks generator: $(-1, 2)$
  +
  +You can use [sage](https://www.sagemath.org/) to test this:
  +
  +```py
  +Fq = GF(28948022309329048855892746252171976963363056481941647379679742748393362948097)
  +Vesta = EllipticCurve(Fq, [0, 5])
  +Vesta.count_points()
  +```
  