From cf8bbfbd057a747d4aeafc30b1fd9717031500c4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lucas=20Men=C3=A9ndez?= <hi@lucasmenendez.me>
Date: Wed, 15 Jan 2025 09:08:41 +0100
Subject: [PATCH] inverse function to U8ToVar (VarToU8) and tests

---
 utils/utils.go      | 46 +++++++++++++++++++++++++++++++++++++--------
 utils/utils_test.go | 28 +++++++++++++++++++++++++++
 2 files changed, 66 insertions(+), 8 deletions(-)

diff --git a/utils/utils.go b/utils/utils.go
index 300a58a..72249f9 100644
--- a/utils/utils.go
+++ b/utils/utils.go
@@ -41,14 +41,7 @@ func UnpackVarToScalar[S emulated.FieldParams](api frontend.API, v frontend.Vari
 	var fr S
 	nBits := int(fr.BitsPerLimb())
 	nLimbs := int(fr.NbLimbs())
-	limbs := make([]frontend.Variable, nLimbs)
-	// get binary representation of the variable
-	vBin := bits.ToBinary(api, v, bits.WithNbDigits(nBits*nLimbs))
-	// group bits into limbs of nbBits until fill all limbs or all bits
-	for i := 0; i < nLimbs; i++ {
-		g := vBin[i*nBits : (i+1)*nBits]
-		limbs[i] = bits.FromBinary(api, g)
-	}
+	limbs := varToLimbsOfBits(api, v, nLimbs, nBits)
 	// convert limbs to emulated element of the field
 	field, err := emulated.NewField[S](api)
 	if err != nil {
@@ -89,6 +82,27 @@ func U8ToVar(api frontend.API, u8 []uints.U8) (frontend.Variable, error) {
 	return res, nil
 }
 
+// VarToU8 converts a variable to a slice of uint8. First, the variable is
+// converted to a slice of uint64, then each uint64 is converted to a slice
+// of uint8 and concatenated. Finally, the endianness is swapped to match the
+// expected endianness of the slice of uint8.
+func VarToU8(api frontend.API, v frontend.Variable) ([]uints.U8, error) {
+	limbs := varToLimbsOfBits(api, v, 4, 64)
+	// convert each limb to []uint8
+	bf, err := uints.New[uints.U64](api)
+	if err != nil {
+		return nil, err
+	}
+	var u8 []uints.U8
+	for _, limb := range limbs {
+		bLimb := bf.ValueOf(limb)
+		for _, b := range bLimb {
+			u8 = append(u8, b)
+		}
+	}
+	return SwapEndianness(u8), nil
+}
+
 // SwapEndianness swaps the endianness of a slice of uint8 by reversing it.
 func SwapEndianness(u8 []uints.U8) []uints.U8 {
 	var swap []uints.U8
@@ -105,3 +119,19 @@ func SwapEndianness(u8 []uints.U8) []uints.U8 {
 func StrictCmp(api frontend.API, a, b frontend.Variable) frontend.Variable {
 	return api.Select(api.IsZero(api.Sub(a, b)), 0, 1)
 }
+
+// varToLimbsOfBits function converts a variable to a slice of variables, each
+// representing a limb of nbBits. The variable is first converted to a binary
+// representation, then the bits are grouped into limbs of nbBits until all
+// limbs are filled or all bits are used.
+func varToLimbsOfBits(api frontend.API, v frontend.Variable, nLimbs, nBits int) []frontend.Variable {
+	limbs := make([]frontend.Variable, nLimbs)
+	// get binary representation of the variable
+	vBin := bits.ToBinary(api, v, bits.WithNbDigits(nBits*nLimbs))
+	// group bits into limbs of nbBits until fill all limbs or all bits
+	for i := 0; i < nLimbs; i++ {
+		g := vBin[i*nBits : (i+1)*nBits]
+		limbs[i] = bits.FromBinary(api, g)
+	}
+	return limbs
+}
diff --git a/utils/utils_test.go b/utils/utils_test.go
index b2042fe..4ea20e7 100644
--- a/utils/utils_test.go
+++ b/utils/utils_test.go
@@ -45,3 +45,31 @@ func TestUnpackPackVar(t *testing.T) {
 		test.WithCurves(ecc.BW6_761), test.WithBackends(backend.GROTH16),
 		test.WithProverOpts(groth16.GetNativeProverOptions(ecc.BN254.ScalarField(), ecc.BW6_761.ScalarField())))
 }
+
+type testVarToU8Circuit struct {
+	Input frontend.Variable
+}
+
+func (c *testVarToU8Circuit) Define(api frontend.API) error {
+	u8s, err := VarToU8(api, c.Input)
+	if err != nil {
+		return err
+	}
+	v, err := U8ToVar(api, u8s)
+	if err != nil {
+		return err
+	}
+	api.AssertIsEqual(c.Input, v)
+	return nil
+}
+
+func TestVarToU8(t *testing.T) {
+	assert := test.NewAssert(t)
+	// generate a random big number
+	r, err := rand.Int(rand.Reader, ecc.BLS12_377.ScalarField())
+	assert.NoError(err)
+
+	assert.SolvingSucceeded(&testVarToU8Circuit{}, &testVarToU8Circuit{Input: r},
+		test.WithCurves(ecc.BW6_761), test.WithBackends(backend.GROTH16),
+		test.WithProverOpts(groth16.GetNativeProverOptions(ecc.BN254.ScalarField(), ecc.BW6_761.ScalarField())))
+}