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Require Coq.ZArith.ZArith Coq.ZArith.Znumtheory.
Require Coq.Numbers.Natural.Peano.NPeano.
Require Crypto.Encoding.EncodingTheorems.
Require Crypto.CompleteEdwardsCurve.CompleteEdwardsCurveTheorems.
Require Crypto.ModularArithmetic.PrimeFieldTheorems.
Require Bedrock.Word.
Require Crypto.Tactics.VerdiTactics.
Require Crypto.Encoding.PointEncodingPre.
Obligation Tactic := eauto; exact PointEncodingPre.point_encoding_canonical.
Require Import Crypto.Spec.Encoding Crypto.Spec.ModularWordEncoding.
Require Import Crypto.Spec.CompleteEdwardsCurve Crypto.Spec.ModularArithmetic.
Local Open Scope F_scope.
Section PointEncoding.
Context {prm: TwistedEdwardsParams} {sz : nat} {sz_nonzero : (0 < sz)%nat}
{bound_check : (BinInt.Z.to_nat q < NPeano.Nat.pow 2 sz)%nat} {q_5mod8 : (q mod 8 = 5)%Z}
{sqrt_minus1_valid : (@ZToField q 2 ^ BinInt.Z.to_N (q / 4)) ^ 2 = opp 1}
{FqEncoding : canonical encoding of (F q) as (Word.word sz)}
{sign_bit : F q -> bool} {sign_bit_zero : sign_bit 0 = false}
{sign_bit_opp : forall x, x <> 0 -> negb (sign_bit x) = sign_bit (opp x)}.
Existing Instance prime_q.
Definition point_enc (p : E.point) : Word.word (S sz) := let '(x,y) := proj1_sig p in
Word.WS (sign_bit x) (enc y).
Program Definition point_dec_with_spec :
{point_dec : Word.word (S sz) -> option E.point
| forall w x, point_dec w = Some x -> (point_enc x = w)
} := @PointEncodingPre.point_dec _ _ _ sign_bit.
Definition point_dec := Eval hnf in (proj1_sig point_dec_with_spec).
Definition point_encoding_valid : forall p : E.point, point_dec (point_enc p) = Some p :=
@PointEncodingPre.point_encoding_valid _ _ q_5mod8 sqrt_minus1_valid _ _ sign_bit_zero sign_bit_opp.
Definition point_encoding_canonical : forall x_enc x, point_dec x_enc = Some x -> point_enc x = x_enc :=
PointEncodingPre.point_encoding_canonical.
Instance point_encoding : canonical encoding of E.point as (Word.word (S sz)) := {
enc := point_enc;
dec := point_dec;
encoding_valid := point_encoding_valid;
encoding_canonical := point_encoding_canonical
}.
End PointEncoding.
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