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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -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 | ||
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| import ( | ||
| "math/big" | ||
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| "github.com/consensys/gnark-crypto/ecc/bn254/fr" | ||
| ) | ||
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| var scalingFactor, _ = new(big.Int).SetString("6360561867910373094066688120553762416144456282423235903351243436111059670888", 10) | ||
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| type Point struct { | ||
| X, Y *big.Int | ||
| } | ||
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| // 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 | ||
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| // Step 2: Compute negF = -f mod p | ||
| var negF fr.Element | ||
| negF.Neg(&f) // negF = -f mod p | ||
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| // Step 3: Compute the inverse of negF in the field | ||
| var negFInv fr.Element | ||
| negFInv.Inverse(&negF) // negFInv = (-f)^{-1} mod p | ||
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| 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 | ||
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| // 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 | ||
| } | ||
| } | ||
|
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| // 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 | ||
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| // Step 2: Compute negF = -f mod p | ||
| var negF fr.Element | ||
| negF.Neg(&f) // negF = -f mod p | ||
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| // 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 | ||
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| // 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' | ||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,22 @@ | ||
| package twistededwards | ||
|
|
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| import ( | ||
| "math/big" | ||
| "testing" | ||
| ) | ||
|
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| func TestXxx(t *testing.T) { | ||
| p := new(Point) | ||
| p.X, _ = new(big.Int).SetString("20284931487578954787250358776722960153090567235942462656834196519767860852891", 10) | ||
| p.Y, _ = new(big.Int).SetString("21185575020764391300398134415668786804224896114060668011215204645513129497221", 10) | ||
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| 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) | ||
| } | ||
| } |