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-Require Import Crypto.Tactics.VerdiTactics.
-Require Import Crypto.Spec.CompleteEdwardsCurve Crypto.Util.IterAssocOp.
-Require Import Crypto.CompleteEdwardsCurve.CompleteEdwardsCurveTheorems.
-Require Import Coq.Numbers.BinNums Coq.NArith.NArith Coq.NArith.Nnat Coq.ZArith.ZArith.
-
-Section EdwardsDoubleAndAdd.
- Context {prm:TwistedEdwardsParams}.
- Definition doubleAndAdd (bound n : nat) (P : E.point) : E.point :=
- iter_op E.add E.zero N.testbit_nat (N.of_nat n) P bound.
-
- Lemma scalarMult_double : forall n P, E.mul (n + n) P = E.mul n (P + P)%E.
- Proof.
- intros.
- replace (n + n)%nat with (n * 2)%nat by omega.
- induction n; simpl; auto.
- rewrite E.add_assoc.
- f_equal; auto.
- Qed.
-
- Lemma doubleAndAdd_spec : forall bound n P, N.size_nat (N.of_nat n) <= bound ->
- E.mul n P = doubleAndAdd bound n P.
- Proof.
- induction n; auto; intros; unfold doubleAndAdd;
- rewrite iter_op_spec with (scToN := fun x => x); (
- unfold Morphisms.Proper, Morphisms.respectful, Equivalence.equiv;
- intros; subst; try rewrite Nat2N.id;
- reflexivity || assumption || apply E.add_assoc
- || rewrite E.add_comm; apply E.add_0_r).
- Qed.
-End EdwardsDoubleAndAdd. \ No newline at end of file