diff options
author | Jason Gross <jgross@mit.edu> | 2016-11-17 14:27:31 -0500 |
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committer | Jason Gross <jgross@mit.edu> | 2016-11-17 14:27:31 -0500 |
commit | 7e1d623977f53d304c17358fa7c2083648efded8 (patch) | |
tree | f0a6007598bea6dc55d1b21ae2e866503c302a1b /src/SpecificGen | |
parent | 4970d6e012d390e94ccbc70bc792c96df4344910 (diff) |
Move ExtendedAddCoordinates to new file, SpecGen
Diffstat (limited to 'src/SpecificGen')
-rw-r--r-- | src/SpecificGen/GF2213_32ExtendedAddCoordinates.v | 83 | ||||
-rw-r--r-- | src/SpecificGen/GF2519_32ExtendedAddCoordinates.v | 83 | ||||
-rw-r--r-- | src/SpecificGen/GF25519_32ExtendedAddCoordinates.v | 83 | ||||
-rw-r--r-- | src/SpecificGen/GF25519_64ExtendedAddCoordinates.v | 83 | ||||
-rw-r--r-- | src/SpecificGen/GF41417_32ExtendedAddCoordinates.v | 83 | ||||
-rw-r--r-- | src/SpecificGen/GF5211_32ExtendedAddCoordinates.v | 83 |
6 files changed, 498 insertions, 0 deletions
diff --git a/src/SpecificGen/GF2213_32ExtendedAddCoordinates.v b/src/SpecificGen/GF2213_32ExtendedAddCoordinates.v new file mode 100644 index 000000000..3ab6d9ada --- /dev/null +++ b/src/SpecificGen/GF2213_32ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF2213_32. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field2213_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F2213_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F2213_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F2213_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field2213_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F2213_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F2213_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F2213_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. diff --git a/src/SpecificGen/GF2519_32ExtendedAddCoordinates.v b/src/SpecificGen/GF2519_32ExtendedAddCoordinates.v new file mode 100644 index 000000000..32ac4258f --- /dev/null +++ b/src/SpecificGen/GF2519_32ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF2519_32. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field2519_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F2519_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F2519_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F2519_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field2519_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F2519_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F2519_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F2519_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. diff --git a/src/SpecificGen/GF25519_32ExtendedAddCoordinates.v b/src/SpecificGen/GF25519_32ExtendedAddCoordinates.v new file mode 100644 index 000000000..0fdab1b24 --- /dev/null +++ b/src/SpecificGen/GF25519_32ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF25519_32. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field25519_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F25519_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F25519_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F25519_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field25519_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F25519_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F25519_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F25519_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. diff --git a/src/SpecificGen/GF25519_64ExtendedAddCoordinates.v b/src/SpecificGen/GF25519_64ExtendedAddCoordinates.v new file mode 100644 index 000000000..3c6f47518 --- /dev/null +++ b/src/SpecificGen/GF25519_64ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF25519_64. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field25519_64. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F25519_64_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F25519_64_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F25519_64_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field25519_64. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F25519_64_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F25519_64_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F25519_64_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. diff --git a/src/SpecificGen/GF41417_32ExtendedAddCoordinates.v b/src/SpecificGen/GF41417_32ExtendedAddCoordinates.v new file mode 100644 index 000000000..f75f179e8 --- /dev/null +++ b/src/SpecificGen/GF41417_32ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF41417_32. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field41417_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F41417_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F41417_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F41417_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field41417_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F41417_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F41417_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F41417_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. diff --git a/src/SpecificGen/GF5211_32ExtendedAddCoordinates.v b/src/SpecificGen/GF5211_32ExtendedAddCoordinates.v new file mode 100644 index 000000000..f1dcad937 --- /dev/null +++ b/src/SpecificGen/GF5211_32ExtendedAddCoordinates.v @@ -0,0 +1,83 @@ +Require Import Crypto.BaseSystem. +Require Import Crypto.ModularArithmetic.PrimeFieldTheorems. +Require Import Crypto.ModularArithmetic.ModularBaseSystem. +Require Import Crypto.Algebra. +Require Import Crypto.Util.Relations. +Require Import Crypto.Util.LetIn. +Require Import Crypto.Util.Tactics. + +Require Import Crypto.SpecificGen.GF5211_32. +Require Import Crypto.CompleteEdwardsCurve.ExtendedCoordinates. + +Definition edwards_extended_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + add sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). +Definition edwards_extended_carry_add_coordinates td P Q := +Eval cbv iota beta delta [ + Extended.add_coordinates + carry_add carry_sub mul + ] in + (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). +Print edwards_extended_add_coordinates. + +Create HintDb edwards_extended_add_coordinates_correct discriminated. +Section noncarry. + Local Existing Instance field5211_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_F5211_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_F5211_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_F5211_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ add sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End noncarry. +Section carry. + Local Existing Instance carry_field5211_32. + Hint Rewrite + (Ring.homomorphism_mul(is_homomorphism:=homomorphism_carry_F5211_32_decode)) + (Ring.homomorphism_add(H1 :=homomorphism_carry_F5211_32_decode)) + (Ring.homomorphism_sub(H1 :=homomorphism_carry_F5211_32_decode)) + : edwards_extended_add_coordinates_correct. + Lemma edwards_extended_carry_add_coordinates_correct td P Q : + Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q) + = (@ExtendedCoordinates.Extended.add_coordinates _ F.add F.sub F.mul (decode td) (Tuple.map (n:=4) decode P) (Tuple.map (n:=4) decode Q)). + Proof. + change (edwards_extended_carry_add_coordinates td P Q) + with (@ExtendedCoordinates.Extended.add_coordinates _ carry_add carry_sub mul td P Q). + destruct_head' prod. + simpl. + rewrite_strat topdown hints edwards_extended_add_coordinates_correct. + reflexivity. + Qed. +End carry. + +Lemma fieldwise_eq_edwards_extended_add_coordinates_carry_nocarry td P Q : + Tuple.fieldwise + (n:=4) eq + (edwards_extended_carry_add_coordinates td P Q) + (edwards_extended_add_coordinates td P Q). +Proof. + pose proof (edwards_extended_carry_add_coordinates_correct td P Q) as H0. + pose proof (edwards_extended_add_coordinates_correct td P Q) as H1. + rewrite <- H0 in H1; clear H0. + assert (Tuple.fieldwise + (fun x y => x = y) + (Tuple.map (n:=4) decode (edwards_extended_carry_add_coordinates td P Q)) + (Tuple.map (n:=4) decode (edwards_extended_add_coordinates td P Q))) + by (rewrite H1; reflexivity). + clear H1. + destruct (edwards_extended_carry_add_coordinates td P Q), (edwards_extended_add_coordinates td P Q). + destruct_head' prod; simpl; unfold eq; trivial. +Qed. |