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Require Import Crypto.ModularArithmetic.ModularBaseSystem.
Require Import Crypto.ModularArithmetic.ModularBaseSystemOpt.
Require Import Crypto.ModularArithmetic.PseudoMersenneBaseParams.
Require Import Crypto.ModularArithmetic.PseudoMersenneBaseParamProofs.
Require Import Crypto.ModularArithmetic.PseudoMersenneBaseRep.
Require Import Coq.Lists.List Crypto.Util.ListUtil.
Require Import Crypto.ModularArithmetic.PrimeFieldTheorems.
Require Import Crypto.Tactics.VerdiTactics.
Require Import Crypto.BaseSystem.
Import ListNotations.
Require Import Coq.ZArith.ZArith Coq.ZArith.Zpower Coq.ZArith.ZArith Coq.ZArith.Znumtheory.
Local Open Scope Z.
(* BEGIN PseudoMersenneBaseParams instance construction. *)
Definition modulus : Z := 2^130 - 5.
Lemma prime_modulus : prime modulus. Admitted.
Instance params1305 : PseudoMersenneBaseParams modulus.
construct_params prime_modulus 5%nat 130.
Defined.
Definition mul2modulus := Eval compute in (construct_mul2modulus params1305).
Instance subCoeff : SubtractionCoefficient modulus params1305.
apply Build_SubtractionCoefficient with (coeff := mul2modulus); cbv; auto.
Defined.
(* END PseudoMersenneBaseParams instance construction. *)
(* Precompute k and c *)
Definition k_ := Eval compute in k.
Definition c_ := Eval compute in c.
(* Makes Qed not take forever *)
Opaque Z.shiftr Pos.iter Z.div2 Pos.div2 Pos.div2_up Pos.succ Z.land
Z.of_N Pos.land N.ldiff Pos.pred_N Pos.pred_double Z.opp Z.mul Pos.mul
Let_In digits Z.add Pos.add Z.pos_sub.
Local Open Scope nat_scope.
Lemma GF1305Base26_mul_reduce_formula :
forall f0 f1 f2 f3 f4 g0 g1 g2 g3 g4,
{ls | forall f g, rep [f0;f1;f2;f3;f4] f
-> rep [g0;g1;g2;g3;g4] g
-> rep ls (f*g)%F}.
Proof.
eexists; intros ? ? Hf Hg.
pose proof (carry_mul_opt_correct k_ c_ (eq_refl k) (eq_refl c_) [0;4;3;2;1;0]_ _ _ _ Hf Hg) as Hfg.
compute_formula.
Defined.
Lemma GF1305Base26_add_formula :
forall f0 f1 f2 f3 f4 g0 g1 g2 g3 g4,
{ls | forall f g, rep [f0;f1;f2;f3;f4] f
-> rep [g0;g1;g2;g3;g4] g
-> rep ls (f + g)%F}.
Proof.
eexists; intros ? ? Hf Hg.
pose proof (add_opt_rep _ _ _ _ Hf Hg) as Hfg.
compute_formula.
Defined.
Lemma GF25519Base25Point5_sub_formula :
forall f0 f1 f2 f3 f4 f5 f6 f7 f8 f9
g0 g1 g2 g3 g4 g5 g6 g7 g8 g9,
{ls | forall f g, rep [f0;f1;f2;f3;f4;f5;f6;f7;f8;f9] f
-> rep [g0;g1;g2;g3;g4;g5;g6;g7;g8;g9] g
-> rep ls (f - g)%F}.
Proof.
eexists.
intros f g Hf Hg.
pose proof (sub_opt_rep _ _ _ _ Hf Hg) as Hfg.
compute_formula.
Defined.
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