chore: small cleanup in pairings (#1621)

Author: ivokub

std/algebra/emulated/sw_bls12381/pairing.go

@@ -86,7 +86,7 @@ func NewPairing(api frontend.API) (*Pairing, error) {
 //
 // This function checks that the Qᵢ are in the correct subgroup, but does not
 // check Pᵢ. See AssertIsOnG1.
-func (pr Pairing) Pair(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
+func (pr *Pairing) Pair(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
 	res, err := pr.MillerLoop(P, Q)
 	if err != nil {
 		return nil, fmt.Errorf("miller loop: %w", err)
@@ -99,7 +99,7 @@ func (pr Pairing) Pair(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
 // ∏ᵢ e(Pᵢ, Qᵢ) =? 1
 //
 // This function doesn't check that the inputs are in the correct subgroups.
-func (pr Pairing) PairingCheck(P []*G1Affine, Q []*G2Affine) error {
+func (pr *Pairing) PairingCheck(P []*G1Affine, Q []*G2Affine) error {
 	// check input size match
 	nP := len(P)
 	nQ := len(Q)
@@ -181,15 +181,15 @@ func (pr Pairing) PairingCheck(P []*G1Affine, Q []*G2Affine) error {
 	return nil
 }
 
-func (pr Pairing) IsEqual(x, y *GTEl) frontend.Variable {
+func (pr *Pairing) IsEqual(x, y *GTEl) frontend.Variable {
 	return pr.Ext12.IsEqual(x, y)
 }
 
-func (pr Pairing) AssertIsEqual(x, y *GTEl) {
+func (pr *Pairing) AssertIsEqual(x, y *GTEl) {
 	pr.Ext12.AssertIsEqual(x, y)
 }
 
-func (pr Pairing) MuxG2(sel frontend.Variable, inputs ...*G2Affine) *G2Affine {
+func (pr *Pairing) MuxG2(sel frontend.Variable, inputs ...*G2Affine) *G2Affine {
 	if len(inputs) == 0 {
 		return nil
 	}
@@ -253,7 +253,7 @@ func (pr Pairing) MuxG2(sel frontend.Variable, inputs ...*G2Affine) *G2Affine {
 	return &ret
 }
 
-func (pr Pairing) MuxGt(sel frontend.Variable, inputs ...*GTEl) *GTEl {
+func (pr *Pairing) MuxGt(sel frontend.Variable, inputs ...*GTEl) *GTEl {
 	if len(inputs) == 0 {
 		return nil
 	}
@@ -304,19 +304,19 @@ func (pr Pairing) MuxGt(sel frontend.Variable, inputs ...*GTEl) *GTEl {
 }
 
 // IsOnCurve returns a boolean indicating if the G1 point is in the curve.
-func (pr Pairing) IsOnCurve(P *G1Affine) frontend.Variable {
+func (pr *Pairing) IsOnCurve(P *G1Affine) frontend.Variable {
 	left, right := pr.g1.computeCurveEquation(P)
 	diff := pr.curveF.Sub(left, right)
 	return pr.curveF.IsZero(diff)
 }
 
-func (pr Pairing) AssertIsOnG1(P *G1Affine) {
+func (pr *Pairing) AssertIsOnG1(P *G1Affine) {
 	pr.g1.AssertIsOnG1(P)
 }
 
 // IsOnG1 returns a boolean indicating if the G1 point is on the curve and in
 // the prime subgroup.
-func (pr Pairing) IsOnG1(P *G1Affine) frontend.Variable {
+func (pr *Pairing) IsOnG1(P *G1Affine) frontend.Variable {
 	// To check that a point P is on G1, we need to check it is of prime order r.
 	// This means that we need to check:
 	//   [r]P == 0
@@ -338,24 +338,24 @@ func (pr Pairing) IsOnG1(P *G1Affine) frontend.Variable {
 	return pr.api.And(isOnCurve, isInSubgroup)
 }
 
-func (pr Pairing) AssertIsOnTwist(Q *G2Affine) {
+func (pr *Pairing) AssertIsOnTwist(Q *G2Affine) {
 	pr.g2.AssertIsOnTwist(Q)
 }
 
 // IsOnTwist returns a boolean indicating if the G2 point is in the twist.
-func (pr Pairing) IsOnTwist(Q *G2Affine) frontend.Variable {
+func (pr *Pairing) IsOnTwist(Q *G2Affine) frontend.Variable {
 	left, right := pr.g2.computeTwistEquation(Q)
 	diff := pr.Ext2.Sub(left, right)
 	return pr.Ext2.IsZero(diff)
 }
 
-func (pr Pairing) AssertIsOnG2(Q *G2Affine) {
+func (pr *Pairing) AssertIsOnG2(Q *G2Affine) {
 	pr.g2.AssertIsOnG2(Q)
 }
 
 // IsOnG2 returns a boolean indicating if the G2 point is on the curve and in
 // the prime subgroup.
-func (pr Pairing) IsOnG2(Q *G2Affine) frontend.Variable {
+func (pr *Pairing) IsOnG2(Q *G2Affine) frontend.Variable {
 	// 1 - is Q on curve
 	isOnCurve := pr.IsOnTwist(Q)
 	// 2 - is Q in the subgroup
@@ -383,7 +383,7 @@ var loopCounter = [64]int8{
 //
 // This function checks that the Qᵢ are in the correct subgroup, but does not
 // check Pᵢ. See AssertIsOnG1.
-func (pr Pairing) MillerLoop(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
+func (pr *Pairing) MillerLoop(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
 
 	// check input size match
 	n := len(P)
@@ -403,7 +403,7 @@ func (pr Pairing) MillerLoop(P []*G1Affine, Q []*G2Affine) (*GTEl, error) {
 }
 
 // millerLoopLines computes the multi-Miller loop from points in G1 and precomputed lines in G2
-func (pr Pairing) millerLoopLines(P []*G1Affine, lines []lineEvaluations, init *GTEl, first bool) (*GTEl, error) {
+func (pr *Pairing) millerLoopLines(P []*G1Affine, lines []lineEvaluations, init *GTEl, first bool) (*GTEl, error) {
 
 	// check input size match
 	n := len(P)
@@ -489,7 +489,7 @@ func (pr Pairing) millerLoopLines(P []*G1Affine, lines []lineEvaluations, init *
 // where d = (p¹²-1)/r = (p¹²-1)/Φ₁₂(p) ⋅ Φ₁₂(p)/r = (p⁶-1)(p²+1)(p⁴ - p² +1)/r
 // we use instead d=s ⋅ (p⁶-1)(p²+1)(p⁴ - p² +1)/r
 // where s is the cofactor 3 (Hayashida et al.)
-func (pr Pairing) FinalExponentiation(e *GTEl) *GTEl {
+func (pr *Pairing) FinalExponentiation(e *GTEl) *GTEl {
 	z := pr.Copy(e)
 
 	// Easy part
@@ -531,7 +531,7 @@ func (pr Pairing) FinalExponentiation(e *GTEl) *GTEl {
 // L. Eagen, and is based on a personal communication with A. Novakovic.
 //
 // [On Proving Pairings]: https://eprint.iacr.org/2024/640.pdf
-func (pr Pairing) AssertFinalExponentiationIsOne(x *GTEl) {
+func (pr *Pairing) AssertFinalExponentiationIsOne(x *GTEl) {
 	tower := pr.ToTower(x)
 
 	res, err := pr.curveF.NewHint(finalExpHint, 18, tower[0], tower[1], tower[2], tower[3], tower[4], tower[5], tower[6], tower[7], tower[8], tower[9], tower[10], tower[11])
@@ -587,7 +587,7 @@ func (pr Pairing) AssertFinalExponentiationIsOne(x *GTEl) {
 // doubleAndAddStep doubles p1 and adds p2 to the result in affine coordinates.
 // Then evaluates the lines going through p1 and p2 or -p2 (line1) and p1 and p1+p2 (line2).
 // https://eprint.iacr.org/2022/1162 (Section 6.1)
-func (pr Pairing) doubleAndAddStep(p1, p2 *g2AffP) (*g2AffP, *lineEvaluation, *lineEvaluation) {
+func (pr *Pairing) doubleAndAddStep(p1, p2 *g2AffP) (*g2AffP, *lineEvaluation, *lineEvaluation) {
 
 	var line1, line2 lineEvaluation
 	var p g2AffP
@@ -641,7 +641,7 @@ func (pr Pairing) doubleAndAddStep(p1, p2 *g2AffP) (*g2AffP, *lineEvaluation, *l
 
 // doubleStep doubles p1 in affine coordinates, and evaluates the tangent line to p1.
 // https://eprint.iacr.org/2022/1162 (Section 6.1)
-func (pr Pairing) doubleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation) {
+func (pr *Pairing) doubleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation) {
 
 	var p g2AffP
 	var line lineEvaluation
@@ -676,7 +676,7 @@ func (pr Pairing) doubleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation) {
 }
 
 // tripleStep triples p1 in affine coordinates, and evaluates the line in Miller loop
-func (pr Pairing) tripleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation, *lineEvaluation) {
+func (pr *Pairing) tripleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation, *lineEvaluation) {
 
 	var line1, line2 lineEvaluation
 	var res g2AffP
@@ -731,7 +731,7 @@ func (pr Pairing) tripleStep(p1 *g2AffP) (*g2AffP, *lineEvaluation, *lineEvaluat
 // and multiplies it in 𝔽p¹² by previous.
 //
 // This method is needed for evmprecompiles/ecpair.
-func (pr Pairing) MillerLoopAndMul(P *G1Affine, Q *G2Affine, previous *GTEl) (*GTEl, error) {
+func (pr *Pairing) MillerLoopAndMul(P *G1Affine, Q *G2Affine, previous *GTEl) (*GTEl, error) {
 	res, err := pr.MillerLoop([]*G1Affine{P}, []*G2Affine{Q})
 	if err != nil {
 		return nil, fmt.Errorf("miller loop: %w", err)
@@ -750,14 +750,14 @@ func (pr Pairing) MillerLoopAndMul(P *G1Affine, Q *G2Affine, previous *GTEl) (*G
 // This method is needed for evmprecompiles/ecpair.
 //
 // [On Proving Pairings]: https://eprint.iacr.org/2024/640.pdf
-func (pr Pairing) AssertMillerLoopAndFinalExpIsOne(P *G1Affine, Q *G2Affine, previous *GTEl) {
+func (pr *Pairing) AssertMillerLoopAndFinalExpIsOne(P *G1Affine, Q *G2Affine, previous *GTEl) {
 	t2 := pr.millerLoopAndFinalExpResult(P, Q, previous)
 	pr.AssertIsEqual(t2, pr.Ext12.One())
 }
 
 // millerLoopAndFinalExpResult computes the Miller loop between P and Q,
 // multiplies it in 𝔽p¹² by previous and returns the result.
-func (pr Pairing) millerLoopAndFinalExpResult(P *G1Affine, Q *G2Affine, previous *GTEl) *GTEl {
+func (pr *Pairing) millerLoopAndFinalExpResult(P *G1Affine, Q *G2Affine, previous *GTEl) *GTEl {
 	tower := pr.ToTower(previous)
 
 	// hint the non-residue witness
@@ -840,7 +840,7 @@ func (pr Pairing) millerLoopAndFinalExpResult(P *G1Affine, Q *G2Affine, previous
 // This method is needed for evmprecompiles/ecpair.
 //
 // [On Proving Pairings]: https://eprint.iacr.org/2024/640.pdf
-func (pr Pairing) IsMillerLoopAndFinalExpOne(P *G1Affine, Q *G2Affine, previous *GTEl) frontend.Variable {
+func (pr *Pairing) IsMillerLoopAndFinalExpOne(P *G1Affine, Q *G2Affine, previous *GTEl) frontend.Variable {
 	t2 := pr.millerLoopAndFinalExpResult(P, Q, previous)
 
 	res := pr.IsEqual(t2, pr.Ext12.One())