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-rw-r--r-- | _CoqProject | 1 | ||||
-rw-r--r-- | src/Spec/Encoding.v | 60 |
2 files changed, 61 insertions, 0 deletions
diff --git a/_CoqProject b/_CoqProject index fab90e35e..0b8aaa6bf 100644 --- a/_CoqProject +++ b/_CoqProject @@ -25,6 +25,7 @@ src/Rep/GaloisRep.v src/Spec/CompleteEdwardsCurve.v src/Spec/EdDSA.v src/Spec/EdDSA25519.v +src/Spec/Encoding.v src/Spec/ModularArithmetic.v src/Specific/EdDSA25519.v src/Specific/GF25519.v diff --git a/src/Spec/Encoding.v b/src/Spec/Encoding.v new file mode 100644 index 000000000..95ac85c97 --- /dev/null +++ b/src/Spec/Encoding.v @@ -0,0 +1,60 @@ +Require Import ZArith.ZArith Zpower ZArith. +Require Import NPeano. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems Crypto.ModularArithmetic.ModularArithmeticTheorems. +Require Import Bedrock.Word. +Require Import VerdiTactics. +Require Import Crypto.Util.NatUtil. + +Class Encoding (T B:Type) := { + enc : T -> B ; + dec : B -> option T ; + encoding_valid : forall x, dec (enc x) = Some x +}. +Notation "'encoding' 'of' T 'as' B" := (Encoding T B) (at level 50). + +Local Open Scope nat_scope. + +Section ModularWordEncoding. + Context {m : Z} {sz : nat} {m_pos : (0 < m)%Z} {bound_check : Z.to_nat m < 2 ^ sz}. + + Definition Fm_enc (x : F m) : word sz := natToWord sz (Z.to_nat (FieldToZ x)). + + Definition Fm_dec (x_ : word sz) : option (F m) := + let z := Z.of_nat (wordToNat (x_)) in + if Z_lt_dec z m + then Some (ZToField z) + else None + . + + Lemma bound_check_N : forall x : F m, (N.of_nat (Z.to_nat x) < Npow2 sz)%N. + Proof. + intro. + pose proof (FieldToZ_range x m_pos) as x_range. + rewrite <- Nnat.N2Nat.id. + rewrite Npow2_nat. + apply (Nat2N_inj_lt (Z.to_nat x) (pow2 sz)). + rewrite ZUtil.Zpow_pow2. + destruct x_range as [x_low x_high]. + apply Z2Nat.inj_lt in x_high; try omega. + rewrite <- ZUtil.pow_Z2N_Zpow by omega. + replace (Z.to_nat 2) with 2%nat by auto. + omega. + Qed. + + Lemma Fm_encoding_valid : forall x, Fm_dec (Fm_enc x) = Some x. + Proof. + unfold Fm_dec, Fm_enc; intros. + pose proof (FieldToZ_range x m_pos). + rewrite wordToNat_natToWord_idempotent by apply bound_check_N. + rewrite Z2Nat.id by omega. + rewrite ZToField_idempotent. + break_if; auto; omega. + Qed. + + Instance modular_word_encoding : encoding of F m as word sz := { + enc := Fm_enc; + dec := Fm_dec; + encoding_valid := Fm_encoding_valid + }. + +End ModularWordEncoding. |