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Montgomery-curve

Montgomery-curvep

Recognizer for montgomery-curve structures.

Signature
(montgomery-curvep x) → *

Definitions and Theorems

Function: montgomery-curvep

(defun montgomery-curvep (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'montgomery-curvep))
    (declare (ignorable acl2::__function__))
    (and (mbe :logic (and (alistp x)
                          (equal (strip-cars x) '(p a b)))
              :exec (fty::alist-with-carsp x '(p a b)))
         (b* ((?p (cdr (std::da-nth 0 x)))
              (?a (cdr (std::da-nth 1 x)))
              (?b (cdr (std::da-nth 2 x))))
           (and (dm::primep p)
                (> p 2)
                (fep a p)
                (fep b p)
                (not (equal a 2))
                (not (equal a (mod -2 p)))
                (not (equal b 0)))))))

Theorem: consp-when-montgomery-curvep

(defthm consp-when-montgomery-curvep
  (implies (montgomery-curvep x)
           (consp x))
  :rule-classes :compound-recognizer)