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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.ModularBaseSystemInterface.
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.
Require Import Crypto.Util.Notations.
Local Open Scope Z.
(* BEGIN PseudoMersenneBaseParams instance construction. *)
Definition modulus : Z := 2^255 - 19.
Lemma prime_modulus : prime modulus. Admitted.
Definition int_width := 32%Z.
Instance params25519 : PseudoMersenneBaseParams modulus.
construct_params prime_modulus 10%nat 255.
Defined.
Definition mul2modulus := Eval compute in (construct_mul2modulus params25519).
Instance subCoeff : SubtractionCoefficient modulus params25519.
apply Build_SubtractionCoefficient with (coeff := mul2modulus).
cbv; auto.
cbv [ModularBaseSystem.decode].
apply ZToField_eqmod.
cbv; reflexivity.
Defined.
Definition freezePreconditions25519 : freezePreconditions params25519 int_width.
Proof.
constructor; compute_preconditions.
Defined.
(* END PseudoMersenneBaseParams instance construction. *)
(* Precompute k and c *)
Definition k_ := Eval compute in k.
Definition c_ := Eval compute in c.
Definition k_subst : k = k_ := eq_refl k_.
Definition c_subst : c = c_ := eq_refl c_.
Definition fe25519 : Type := Eval cbv in fe.
Local Opaque Z.shiftr Z.shiftl Z.land Z.mul Z.add Z.sub Let_In.
Definition add (f g:fe25519) : { fg | phi fg = @ModularArithmetic.add modulus (phi f) (phi g) }.
Proof.
cbv [fe25519] in *.
repeat match goal with [p : (_*Z)%type |- _ ] => destruct p end.
eexists.
rewrite <-add_phi.
apply f_equal.
cbv.
reflexivity.
Qed.
Definition mul (f g:fe25519) : { fg | phi fg = @ModularArithmetic.mul modulus (phi f) (phi g) }.
Proof.
cbv [fe25519] in *.
repeat match goal with [p : (_*Z)%type |- _ ] => destruct p end.
eexists.
rewrite <-(mul_phi (c_ := c_) (k_ := k_)) by auto using k_subst,c_subst.
apply f_equal.
cbv.
autorewrite with zsimplify.
reflexivity.
Qed.
(*
Local Transparent Let_In.
Eval cbv iota beta delta [proj1_sig mul Let_In] in (fun f0 f1 f2 f3 f4 g0 g1 g2 g3 g4 => proj1_sig (mul (f4,f3,f2,f1,f0) (g4,g3,g2,g1,g0))).
*)
(* TODO: This file should eventually contain the following operations:
toBytes
fromBytes
inv
opp
sub
zero
one
eq
*)
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