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Edwards-bls12

Edwards-bls12-point->u

The function \mathcal{U} in TODO

Signature
(edwards-bls12-point->u point) → u
Arguments: point — Guard (edwards-bls12-pointp point).
Returns: u — Type (natp u).

This function can be defined on any finite point (in fact, on any pair), but it is only used on Edwards-BLS12 points.

This is always below the Edwards-BLS12 field prime.

Definitions and Theorems

Function: edwards-bls12-point->u

(defun edwards-bls12-point->u (point)
  (declare (xargs :guard (edwards-bls12-pointp point)))
  (let ((acl2::__function__ 'edwards-bls12-point->u))
    (declare (ignorable acl2::__function__))
    (point-finite->x point)))

Theorem: natp-of-edwards-bls12-point->u

(defthm natp-of-edwards-bls12-point->u
  (b* ((u (edwards-bls12-point->u point)))
    (natp u))
  :rule-classes :type-prescription)

Theorem: edwards-bls12-point->u-upper-bound

(defthm edwards-bls12-point->u-upper-bound
  (implies (edwards-bls12-pointp point)
           (b* ((acl2::?u (edwards-bls12-point->u point)))
             (< u (edwards-bls12-q))))
  :rule-classes :linear)