From 887665793a64f3db2c0a3ec8074c406dc072dba5 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 22 Jan 2025 13:47:36 -0600
Subject: [PATCH 1/4] perf: parallelize subgroup check

---
 ecc/bls12-377/kzg/mpcsetup.go | 25 +++++++++++++++++++++----
 1 file changed, 21 insertions(+), 4 deletions(-)

diff --git a/ecc/bls12-377/kzg/mpcsetup.go b/ecc/bls12-377/kzg/mpcsetup.go
index 1d9da00586..46d3f6f219 100644
--- a/ecc/bls12-377/kzg/mpcsetup.go
+++ b/ecc/bls12-377/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bls12-377"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{

From 48efc4edf454bf45b7d5fc6cfc1bac67d7848e74 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 22 Jan 2025 13:51:14 -0600
Subject: [PATCH 2/4] build: generify changes

---
 ecc/bls12-381/kzg/mpcsetup.go                 | 25 ++++++++++++++++---
 ecc/bls24-315/kzg/mpcsetup.go                 | 25 ++++++++++++++++---
 ecc/bls24-317/kzg/mpcsetup.go                 | 25 ++++++++++++++++---
 ecc/bn254/kzg/mpcsetup.go                     | 25 ++++++++++++++++---
 ecc/bw6-633/kzg/mpcsetup.go                   | 25 ++++++++++++++++---
 ecc/bw6-761/kzg/mpcsetup.go                   | 25 ++++++++++++++++---
 .../generator/kzg/template/mpcsetup.go.tmpl   | 25 ++++++++++++++++---
 7 files changed, 147 insertions(+), 28 deletions(-)

diff --git a/ecc/bls12-381/kzg/mpcsetup.go b/ecc/bls12-381/kzg/mpcsetup.go
index d7fd7e8ec3..d9a454bc2b 100644
--- a/ecc/bls12-381/kzg/mpcsetup.go
+++ b/ecc/bls12-381/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bls12-381"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bls24-315/kzg/mpcsetup.go b/ecc/bls24-315/kzg/mpcsetup.go
index 2afb830462..66db498c7e 100644
--- a/ecc/bls24-315/kzg/mpcsetup.go
+++ b/ecc/bls24-315/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bls24-315"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bls24-317/kzg/mpcsetup.go b/ecc/bls24-317/kzg/mpcsetup.go
index 37c3e50dc7..18d0994857 100644
--- a/ecc/bls24-317/kzg/mpcsetup.go
+++ b/ecc/bls24-317/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bls24-317"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bn254/kzg/mpcsetup.go b/ecc/bn254/kzg/mpcsetup.go
index 39d6e10f9c..99acfd182e 100644
--- a/ecc/bn254/kzg/mpcsetup.go
+++ b/ecc/bn254/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bn254"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bw6-633/kzg/mpcsetup.go b/ecc/bw6-633/kzg/mpcsetup.go
index d2bf845925..1c1d64a506 100644
--- a/ecc/bw6-633/kzg/mpcsetup.go
+++ b/ecc/bw6-633/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bw6-633"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bw6-761/kzg/mpcsetup.go b/ecc/bw6-761/kzg/mpcsetup.go
index 77f2e1599d..2c9331c323 100644
--- a/ecc/bw6-761/kzg/mpcsetup.go
+++ b/ecc/bw6-761/kzg/mpcsetup.go
@@ -10,11 +10,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/bw6-761"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -120,12 +123,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/internal/generator/kzg/template/mpcsetup.go.tmpl b/internal/generator/kzg/template/mpcsetup.go.tmpl
index 973d23652c..75bb95fe6f 100644
--- a/internal/generator/kzg/template/mpcsetup.go.tmpl
+++ b/internal/generator/kzg/template/mpcsetup.go.tmpl
@@ -3,11 +3,14 @@ import (
 	"crypto/sha256"
 	"encoding/binary"
 	"errors"
+	"fmt"
 	curve "github.com/consensys/gnark-crypto/ecc/{{.Name}}"
 	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/fr"
 	"github.com/consensys/gnark-crypto/ecc/{{.Name}}/mpcsetup"
+	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
+	"runtime"
 )
 
 type MpcSetup struct {
@@ -113,12 +116,26 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 	}
 
 	if !next.srs.Vk.G2[1].IsInSubGroup() {
-		return errors.New("𝔾₂ representation not in subgroup")
+		return errors.New("[x]₂ representation not in subgroup")
 	}
-	for i := 1; i < len(next.srs.Pk.G1); i++ {
-		if !next.srs.Pk.G1[i].IsInSubGroup() {
-			return errors.New("𝔾₁ representation not in subgroup")
+
+	// TODO @Tabaie replace with batch subgroup check
+	n := len(next.srs.Pk.G1) - 1
+	fail := -1
+	wp := utils.NewWorkerPool()
+	defer wp.Stop()
+
+	wp.Submit(n, func(start, end int) {
+		for i := start; i < end; i++ {
+			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
+				fail = i + 1
+				break
+			}
 		}
+	}, n/runtime.NumCPU()+1).Wait()
+
+	if fail != -1 {
+		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{

From a7ee2ec2a9f65b58693c1440717bb3f685781e43 Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 22 Jan 2025 15:16:52 -0600
Subject: [PATCH 3/4] fix: error channel

---
 ecc/bls12-377/kzg/mpcsetup.go                    | 14 ++++++++------
 ecc/bls12-381/kzg/mpcsetup.go                    | 14 ++++++++------
 ecc/bls24-315/kzg/mpcsetup.go                    | 14 ++++++++------
 ecc/bls24-317/kzg/mpcsetup.go                    | 14 ++++++++------
 ecc/bn254/kzg/mpcsetup.go                        | 14 ++++++++------
 ecc/bw6-633/kzg/mpcsetup.go                      | 14 ++++++++------
 ecc/bw6-761/kzg/mpcsetup.go                      | 14 ++++++++------
 internal/generator/kzg/template/mpcsetup.go.tmpl | 14 ++++++++------
 utils/parallel.go                                |  4 ++++
 9 files changed, 68 insertions(+), 48 deletions(-)

diff --git a/ecc/bls12-377/kzg/mpcsetup.go b/ecc/bls12-377/kzg/mpcsetup.go
index 46d3f6f219..84d156a737 100644
--- a/ecc/bls12-377/kzg/mpcsetup.go
+++ b/ecc/bls12-377/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bls12-381/kzg/mpcsetup.go b/ecc/bls12-381/kzg/mpcsetup.go
index d9a454bc2b..5934f73cb7 100644
--- a/ecc/bls12-381/kzg/mpcsetup.go
+++ b/ecc/bls12-381/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bls24-315/kzg/mpcsetup.go b/ecc/bls24-315/kzg/mpcsetup.go
index 66db498c7e..41a720c175 100644
--- a/ecc/bls24-315/kzg/mpcsetup.go
+++ b/ecc/bls24-315/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bls24-317/kzg/mpcsetup.go b/ecc/bls24-317/kzg/mpcsetup.go
index 18d0994857..b3f6e2a00a 100644
--- a/ecc/bls24-317/kzg/mpcsetup.go
+++ b/ecc/bls24-317/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bn254/kzg/mpcsetup.go b/ecc/bn254/kzg/mpcsetup.go
index 99acfd182e..bbb55b0dae 100644
--- a/ecc/bn254/kzg/mpcsetup.go
+++ b/ecc/bn254/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bw6-633/kzg/mpcsetup.go b/ecc/bw6-633/kzg/mpcsetup.go
index 1c1d64a506..505ee8cf85 100644
--- a/ecc/bw6-633/kzg/mpcsetup.go
+++ b/ecc/bw6-633/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/ecc/bw6-761/kzg/mpcsetup.go b/ecc/bw6-761/kzg/mpcsetup.go
index 2c9331c323..aacdd0c113 100644
--- a/ecc/bw6-761/kzg/mpcsetup.go
+++ b/ecc/bw6-761/kzg/mpcsetup.go
@@ -128,21 +128,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/internal/generator/kzg/template/mpcsetup.go.tmpl b/internal/generator/kzg/template/mpcsetup.go.tmpl
index 75bb95fe6f..8e9e4e187d 100644
--- a/internal/generator/kzg/template/mpcsetup.go.tmpl
+++ b/internal/generator/kzg/template/mpcsetup.go.tmpl
@@ -121,21 +121,23 @@ func (s *MpcSetup) Verify(next *MpcSetup) error {
 
 	// TODO @Tabaie replace with batch subgroup check
 	n := len(next.srs.Pk.G1) - 1
-	fail := -1
 	wp := utils.NewWorkerPool()
 	defer wp.Stop()
+	fail := make(chan error, wp.NbWorkers())
 
 	wp.Submit(n, func(start, end int) {
 		for i := start; i < end; i++ {
 			if !next.srs.Pk.G1[i+1].IsInSubGroup() {
-				fail = i + 1
+				fail <- fmt.Errorf("[x^%d]₁ representation not in subgroup", i+1)
 				break
 			}
 		}
-	}, n/runtime.NumCPU()+1).Wait()
-
-	if fail != -1 {
-		return fmt.Errorf("[x^%d]₁ representation not in subgroup", fail)
+	}, n/wp.NbWorkers()+1).Wait()
+	close(fail)
+	for err := range fail {
+		if err != nil {
+			return err
+		}
 	}
 
 	if err := next.proof.Verify(append([]byte("KZG Setup"), challenge...), 0, mpcsetup.ValueUpdate{
diff --git a/utils/parallel.go b/utils/parallel.go
index 0421fab507..1a67bc95b1 100644
--- a/utils/parallel.go
+++ b/utils/parallel.go
@@ -35,6 +35,10 @@ func NewWorkerPool() *WorkerPool {
 	return p
 }
 
+func (wp *WorkerPool) NbWorkers() int {
+	return wp.nbWorkers
+}
+
 // Stop (but does not wait) the pool. It frees the worker.
 func (wp *WorkerPool) Stop() {
 	close(wp.chJobs)

From fd00f4da8df4c392f5d3853fed281fbea910cece Mon Sep 17 00:00:00 2001
From: Arya Tabaie <15056835+Tabaie@users.noreply.github.com>
Date: Wed, 22 Jan 2025 15:18:45 -0600
Subject: [PATCH 4/4] fix: remove unused import

---
 ecc/bls12-377/kzg/mpcsetup.go                    | 1 -
 ecc/bls12-381/kzg/mpcsetup.go                    | 1 -
 ecc/bls24-315/kzg/mpcsetup.go                    | 1 -
 ecc/bls24-317/kzg/mpcsetup.go                    | 1 -
 ecc/bn254/kzg/mpcsetup.go                        | 1 -
 ecc/bw6-633/kzg/mpcsetup.go                      | 1 -
 ecc/bw6-761/kzg/mpcsetup.go                      | 1 -
 internal/generator/kzg/template/mpcsetup.go.tmpl | 1 -
 8 files changed, 8 deletions(-)

diff --git a/ecc/bls12-377/kzg/mpcsetup.go b/ecc/bls12-377/kzg/mpcsetup.go
index 84d156a737..c8243506f6 100644
--- a/ecc/bls12-377/kzg/mpcsetup.go
+++ b/ecc/bls12-377/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bls12-381/kzg/mpcsetup.go b/ecc/bls12-381/kzg/mpcsetup.go
index 5934f73cb7..f448261352 100644
--- a/ecc/bls12-381/kzg/mpcsetup.go
+++ b/ecc/bls12-381/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bls24-315/kzg/mpcsetup.go b/ecc/bls24-315/kzg/mpcsetup.go
index 41a720c175..7d41f3d74f 100644
--- a/ecc/bls24-315/kzg/mpcsetup.go
+++ b/ecc/bls24-315/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bls24-317/kzg/mpcsetup.go b/ecc/bls24-317/kzg/mpcsetup.go
index b3f6e2a00a..a460fe934e 100644
--- a/ecc/bls24-317/kzg/mpcsetup.go
+++ b/ecc/bls24-317/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bn254/kzg/mpcsetup.go b/ecc/bn254/kzg/mpcsetup.go
index bbb55b0dae..c5bc0a9542 100644
--- a/ecc/bn254/kzg/mpcsetup.go
+++ b/ecc/bn254/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bw6-633/kzg/mpcsetup.go b/ecc/bw6-633/kzg/mpcsetup.go
index 505ee8cf85..2fdc655579 100644
--- a/ecc/bw6-633/kzg/mpcsetup.go
+++ b/ecc/bw6-633/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/ecc/bw6-761/kzg/mpcsetup.go b/ecc/bw6-761/kzg/mpcsetup.go
index aacdd0c113..f85644f4cc 100644
--- a/ecc/bw6-761/kzg/mpcsetup.go
+++ b/ecc/bw6-761/kzg/mpcsetup.go
@@ -17,7 +17,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {
diff --git a/internal/generator/kzg/template/mpcsetup.go.tmpl b/internal/generator/kzg/template/mpcsetup.go.tmpl
index 8e9e4e187d..913cccca66 100644
--- a/internal/generator/kzg/template/mpcsetup.go.tmpl
+++ b/internal/generator/kzg/template/mpcsetup.go.tmpl
@@ -10,7 +10,6 @@ import (
 	"github.com/consensys/gnark-crypto/utils"
 	"io"
 	"math/big"
-	"runtime"
 )
 
 type MpcSetup struct {