From 38281cb0a624b40b4c7249ce6218cdab2c51f110 Mon Sep 17 00:00:00 2001
From: Lucas Menendez <hi@lucasmenendez.me>
Date: Mon, 11 Nov 2024 09:40:53 +0100
Subject: [PATCH] twistedEdwards helpers

---
 go.mod                                        |  1 +
 go.sum                                        |  2 +
 internal/twistededwards/twistededwards.go     | 77 +++++++++++++++++++
 .../twistededwards/twistededwards_test.go     | 22 ++++++
 4 files changed, 102 insertions(+)
 create mode 100644 internal/twistededwards/twistededwards.go
 create mode 100644 internal/twistededwards/twistededwards_test.go

diff --git a/go.mod b/go.mod
index e278700..777f8c4 100644
--- a/go.mod
+++ b/go.mod
@@ -26,6 +26,7 @@ require (
 	github.com/cockroachdb/tokenbucket v0.0.0-20230807174530-cc333fc44b06 // indirect
 	github.com/consensys/bavard v0.1.22 // indirect
 	github.com/davecgh/go-spew v1.1.2-0.20180830191138-d8f796af33cc // indirect
+	github.com/dchest/blake512 v1.0.0 // indirect
 	github.com/fxamacker/cbor/v2 v2.7.0 // indirect
 	github.com/getsentry/sentry-go v0.27.0 // indirect
 	github.com/glendc/go-external-ip v0.1.0 // indirect
diff --git a/go.sum b/go.sum
index 4688c6a..d627896 100644
--- a/go.sum
+++ b/go.sum
@@ -34,6 +34,8 @@ github.com/coreos/go-systemd/v22 v22.5.0/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSV
 github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E=
 github.com/davecgh/go-spew v1.1.2-0.20180830191138-d8f796af33cc h1:U9qPSI2PIWSS1VwoXQT9A3Wy9MM3WgvqSxFWenqJduM=
 github.com/davecgh/go-spew v1.1.2-0.20180830191138-d8f796af33cc/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
+github.com/dchest/blake512 v1.0.0 h1:oDFEQFIqFSeuA34xLtXZ/rWxCXdSjirjzPhey5EUvmA=
+github.com/dchest/blake512 v1.0.0/go.mod h1:FV1x7xPPLWukZlpDpWQ88rF/SFwZ5qbskrzhLMB92JI=
 github.com/frankban/quicktest v1.14.6 h1:7Xjx+VpznH+oBnejlPUj8oUpdxnVs4f8XU8WnHkI4W8=
 github.com/frankban/quicktest v1.14.6/go.mod h1:4ptaffx2x8+WTWXmUCuVU6aPUX1/Mz7zb5vbUoiM6w0=
 github.com/fxamacker/cbor/v2 v2.7.0 h1:iM5WgngdRBanHcxugY4JySA0nk1wZorNOpTgCMedv5E=
diff --git a/internal/twistededwards/twistededwards.go b/internal/twistededwards/twistededwards.go
new file mode 100644
index 0000000..c50b08b
--- /dev/null
+++ b/internal/twistededwards/twistededwards.go
@@ -0,0 +1,77 @@
+// twistededwards package provides helper functions to transform points (x, y)
+// from TwistedEdwards to Reduced TwistedEdwards and vice versa. These functions
+// are required because Gnark uses the Reduced TwistedEdwards formula while
+// Iden3 uses the standard TwistedEdwards formula.
+// See https://github.com/bellesmarta/baby_jubjub for more information.
+package twistededwards
+
+import (
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
+)
+
+var scalingFactor, _ = new(big.Int).SetString("6360561867910373094066688120553762416144456282423235903351243436111059670888", 10)
+
+type Point struct {
+	X, Y *big.Int
+}
+
+// Convert Reduced TwistedEdwards x' to TwistedEdwards:
+//
+//	x = x'/(-f)
+//	y' = y
+func (p *Point) FromRTEtoTE() *Point {
+	// Step 1: Convert scalingFactor to fr.Element (mod p)
+	var f fr.Element
+	f.SetBigInt(scalingFactor) // f = scalingFactor mod p
+
+	// Step 2: Compute negF = -f mod p
+	var negF fr.Element
+	negF.Neg(&f) // negF = -f mod p
+
+	// Step 3: Compute the inverse of negF in the field
+	var negFInv fr.Element
+	negFInv.Inverse(&negF) // negFInv = (-f)^{-1} mod p
+
+	xTE := new(fr.Element)
+	xTE.SetBigInt(p.X)
+	// Step 4: Multiply g.inner.X by negFInv to get xTE
+	xRTE := new(fr.Element)
+	xRTE.Mul(xTE, &negFInv) // xTE = g.inner.X * negFInv mod p
+
+	// Step 5: Convert xTE and g.inner.Y to *big.Int
+	xRTEBigInt := new(big.Int)
+	xRTE.BigInt(xRTEBigInt)
+	return &Point{
+		X: xRTEBigInt, // x = x' / (-f)
+		Y: p.Y,        // y' = y
+	}
+}
+
+// Convert TwistedEdwards to Reduced TwistedEdwards:
+//
+//	x' = x*(-f)
+//	y = y'
+func (p *Point) FromTEtoRTE() *Point {
+	// Step 1: Convert scalingFactor to fr.Element (mod p)
+	var f fr.Element
+	f.SetBigInt(scalingFactor) // f = scalingFactor mod p
+
+	// Step 2: Compute negF = -f mod p
+	var negF fr.Element
+	negF.Neg(&f) // negF = -f mod p
+
+	// Step 4: Multiply g.inner.X by negF to get xTE
+	xRTE := new(fr.Element).SetBigInt(p.X)
+	xTE := new(fr.Element)
+	xTE.Mul(xRTE, &negF) // xTE = g.inner.X * -f mod p
+
+	// Step 5: Convert xTE and g.inner.Y to *big.Int
+	xTEBigInt := new(big.Int)
+	xTE.BigInt(xTEBigInt)
+	return &Point{
+		X: xTEBigInt, // x' = x * (-f)
+		Y: p.Y,       // y = y'
+	}
+}
diff --git a/internal/twistededwards/twistededwards_test.go b/internal/twistededwards/twistededwards_test.go
new file mode 100644
index 0000000..e2c2af7
--- /dev/null
+++ b/internal/twistededwards/twistededwards_test.go
@@ -0,0 +1,22 @@
+package twistededwards
+
+import (
+	"math/big"
+	"testing"
+)
+
+func TestXxx(t *testing.T) {
+	p := new(Point)
+	p.X, _ = new(big.Int).SetString("20284931487578954787250358776722960153090567235942462656834196519767860852891", 10)
+	p.Y, _ = new(big.Int).SetString("21185575020764391300398134415668786804224896114060668011215204645513129497221", 10)
+
+	expectedRTE, _ := new(big.Int).SetString("5730906301301611931737915251485454905492689746504994962065413628158661689313", 10)
+	pPrime := p.FromTEtoRTE()
+	if pPrime.X.Cmp(expectedRTE) != 0 {
+		t.Errorf("Expected %v, got %v", expectedRTE, pPrime.X)
+	}
+	pPrimePrime := pPrime.FromRTEtoTE()
+	if pPrimePrime.X.Cmp(p.X) != 0 || pPrimePrime.Y.Cmp(p.Y) != 0 {
+		t.Errorf("Expected %v, got %v", p, pPrimePrime)
+	}
+}