From fc02e12f2e865c9f9b1d9b035c45527d63737b8d Mon Sep 17 00:00:00 2001
From: Kris Kwiatkowski <kris@cloudflare.com>
Date: Wed, 3 Oct 2018 11:29:31 +0100
Subject: [PATCH] makes p751 consistent with p503

formatting, moves constant values to consts.go, etc.
---
 p751/arith_generic.go |  2 +-
 p751/consts.go        | 44 ++++++++++++++++++++++++++++++++-----------
 p751/field_ops.go     | 24 +++--------------------
 3 files changed, 37 insertions(+), 33 deletions(-)

diff --git a/p751/arith_generic.go b/p751/arith_generic.go
index 89ceb87..17e2941 100644
--- a/p751/arith_generic.go
+++ b/p751/arith_generic.go
@@ -1,4 +1,4 @@
-// +build noasm arm64 arm
+// +build noasm !amd64
 
 package p751
 
diff --git a/p751/consts.go b/p751/consts.go
index bf539a8..e49918e 100644
--- a/p751/consts.go
+++ b/p751/consts.go
@@ -166,26 +166,48 @@ var P751_BobIsogenyStrategy = [strategySizeB]uint32{
 	0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,
 	0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01}
 
+// Used internally by this package. Not consts as Go doesn't allow arrays to be consts
+// -------------------------------
+
+// p751
+var p751 = FpElement{
+	0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff,
+	0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff,
+	0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
+	0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
+
+// 2*p751
+var p751x2 = FpElement{
+	0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,
+	0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,
+	0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED,
+	0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38}
+
+// p751 + 1
+var p751p1 = FpElement{
+	0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
+	0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000,
+	0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
+	0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
+
+// R^2 = (2^768)^2 mod p
+var p751R2 = FpElement{
+	2535603850726686808, 15780896088201250090, 6788776303855402382,
+	17585428585582356230, 5274503137951975249, 2266259624764636289,
+	11695651972693921304, 13072885652150159301, 4908312795585420432,
+	6229583484603254826, 488927695601805643, 72213483953973}
+
+// 1*R mod p
 var P751_OneFp2 = Fp2Element{
     A: FpElement{
     	0x249ad, 0x0, 0x0, 0x0, 0x0, 0x8310000000000000, 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x2d5b24bce5e2},
-    B: FpElement{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},
 }
 
+// 1/2 * R mod p
 var P751_HalfFp2 = Fp2Element{
     A: FpElement{
         0x00000000000124D6, 0x0000000000000000, 0x0000000000000000,
         0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000,
         0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52,
         0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F},
-    B: FpElement{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 }
-
-// (2^768)^2 mod p
-// This can't be a constant because Go doesn't allow array constants, so try
-// not to modify it.
-var montgomeryRsq = FpElement{
-	2535603850726686808, 15780896088201250090, 6788776303855402382,
-	17585428585582356230, 5274503137951975249, 2266259624764636289,
-	11695651972693921304, 13072885652150159301, 4908312795585420432,
-	6229583484603254826, 488927695601805643, 72213483953973}
diff --git a/p751/field_ops.go b/p751/field_ops.go
index 5bc24d1..12796c6 100644
--- a/p751/field_ops.go
+++ b/p751/field_ops.go
@@ -4,24 +4,6 @@ import . "github.com/cloudflare/p751sidh/internal/isogeny"
 
 // 2*p751
 var (
-	// p751
-	p751 = FpElement{
-		0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff,
-		0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff,
-		0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
-		0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
-	// p751 + 1
-	p751p1 = FpElement{
-		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
-		0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000,
-		0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
-		0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
-	// 2*p751
-	p751x2 = FpElement{
-		0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,
-		0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,
-		0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED,
-		0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38}
 )
 
 //------------------------------------------------------------------------------
@@ -166,9 +148,9 @@ func (fp751Ops) ToMontgomery(x *Fp2Element) {
 	var aRR FpElementX2
 
 	// convert to montgomery domain
-	fp751Mul(&aRR, &x.A, &montgomeryRsq)   // = a*R*R
-	fp751MontgomeryReduce(&x.A, &aRR)      // = a*R mod p
-	fp751Mul(&aRR, &x.B, &montgomeryRsq)
+	fp751Mul(&aRR, &x.A, &p751R2)		// = a*R*R
+	fp751MontgomeryReduce(&x.A, &aRR)   // = a*R mod p
+	fp751Mul(&aRR, &x.B, &p751R2)
 	fp751MontgomeryReduce(&x.B, &aRR)
 }