From 7eeb48adc07d6ef14a2147c43218246c314514ae Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 18 Dec 2024 18:32:29 -0600
Subject: [PATCH] refactor linearCombCoeffs -> randomMonomials

---
 backend/groth16/bn254/mpcsetup/phase1.go |  2 +-
 backend/groth16/bn254/mpcsetup/phase2.go |  2 +-
 backend/groth16/bn254/mpcsetup/utils.go  | 15 ++++++++-------
 3 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/backend/groth16/bn254/mpcsetup/phase1.go b/backend/groth16/bn254/mpcsetup/phase1.go
index 381749980..571043051 100644
--- a/backend/groth16/bn254/mpcsetup/phase1.go
+++ b/backend/groth16/bn254/mpcsetup/phase1.go
@@ -244,7 +244,7 @@ func multiValueUpdateCheck(a []curve.G1Affine, b []curve.G2Affine, c, d []curve.
 	g1s = append(g1s, d...)
 
 	g1Num, g1Denom := linearCombinationsG1(g1s, bivariateRandomMonomials(ends...), ends)
-	g2Num, g2Denom := linearCombinationsG2(b, linearCombCoeffs(len(b)))
+	g2Num, g2Denom := linearCombinationsG2(b, randomMonomials(len(b)))
 
 	if !sameRatio(g1Num, g1Denom, g2Num, g2Denom) {
 		return errors.New("multi-value update check failed")
diff --git a/backend/groth16/bn254/mpcsetup/phase2.go b/backend/groth16/bn254/mpcsetup/phase2.go
index 3d50ef818..b5007e073 100644
--- a/backend/groth16/bn254/mpcsetup/phase2.go
+++ b/backend/groth16/bn254/mpcsetup/phase2.go
@@ -72,7 +72,7 @@ func (p *Phase2) Verify(next *Phase2) error {
 		return errors.New("contribution size mismatch")
 	}
 
-	r := linearCombCoeffs(len(next.Parameters.G1.Z) + len(next.Parameters.G1.PKK) + 1)
+	r := randomMonomials(len(next.Parameters.G1.Z) + len(next.Parameters.G1.PKK) + 1)
 
 	verifyContribution := func(update *valueUpdate, g1Denominator, g1Numerator []curve.G1Affine, g2Denominator, g2Numerator *curve.G2Affine, dst byte) error {
 		g1Num := linearCombination(g1Numerator, r)
diff --git a/backend/groth16/bn254/mpcsetup/utils.go b/backend/groth16/bn254/mpcsetup/utils.go
index 05bb3cf89..14384c7bf 100644
--- a/backend/groth16/bn254/mpcsetup/utils.go
+++ b/backend/groth16/bn254/mpcsetup/utils.go
@@ -29,21 +29,22 @@ func bitReverse[T any](a []T) {
 	}
 }
 
-func linearCombCoeffs(n int) []fr.Element {
-	return bivariateRandomMonomials(n)
+// Returns [1, a, a², ..., aᴺ⁻¹ ] for random a
+func randomMonomials(N int) []fr.Element {
+	return bivariateRandomMonomials(N)
 }
 
 // Returns [1, a, a², ..., aᴺ⁻¹ ]
-func powers(a *fr.Element, n int) []fr.Element {
+func powers(a *fr.Element, N int) []fr.Element {
 
-	result := make([]fr.Element, n)
-	if n >= 1 {
+	result := make([]fr.Element, N)
+	if N >= 1 {
 		result[0].SetOne()
 	}
-	if n >= 2 {
+	if N >= 2 {
 		result[1].Set(a)
 	}
-	for i := 2; i < n; i++ {
+	for i := 2; i < N; i++ {
 		result[i].Mul(&result[i-1], a)
 	}
 	return result