From 91de9cfeb1b971475d77657d252f081315d1b53a Mon Sep 17 00:00:00 2001
From: RiceChuan <lc582041246@gmail.com>
Date: Mon, 16 Dec 2024 21:52:11 +0800
Subject: [PATCH 1/2] chore: use errors.New to replace fmt.Errorf with no
 parameters

Signed-off-by: RiceChuan <lc582041246@gmail.com>
---
 ecc/bls12-377/fr/gkr/gkr.go       | 9 +++++----
 ecc/bn254/fr/gkr/gkr.go           | 9 +++++----
 ecc/bn254/fr/sumcheck/sumcheck.go | 4 ++--
 3 files changed, 12 insertions(+), 10 deletions(-)

diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index fb3629fc0..c55db62a4 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index e52de1fc3..696f2e095 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bn254/fr/sumcheck/sumcheck.go b/ecc/bn254/fr/sumcheck/sumcheck.go
index 633d7c01c..a44078c49 100644
--- a/ecc/bn254/fr/sumcheck/sumcheck.go
+++ b/ecc/bn254/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
 	"github.com/consensys/gnark-crypto/ecc/bn254/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)

From f37e71095a397b36d4da01783948016da33998f0 Mon Sep 17 00:00:00 2001
From: Ivo Kubjas <ivo.kubjas@consensys.net>
Date: Thu, 19 Dec 2024 13:38:26 +0000
Subject: [PATCH 2/2] chore: go generate

---
 ecc/bls12-377/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls12-381/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls12-381/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls24-315/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls24-315/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bls24-317/fr/gkr/gkr.go                              | 9 +++++----
 ecc/bls24-317/fr/sumcheck/sumcheck.go                    | 4 ++--
 ecc/bw6-633/fr/gkr/gkr.go                                | 9 +++++----
 ecc/bw6-633/fr/sumcheck/sumcheck.go                      | 4 ++--
 ecc/bw6-761/fr/gkr/gkr.go                                | 9 +++++----
 ecc/bw6-761/fr/sumcheck/sumcheck.go                      | 4 ++--
 internal/generator/gkr/template/gkr.go.tmpl              | 9 +++++----
 internal/generator/sumcheck/template/sumcheck.go.tmpl    | 4 ++--
 .../test_vector_utils/small_rational/gkr/gkr.go          | 9 +++++----
 .../small_rational/sumcheck/sumcheck.go                  | 4 ++--
 15 files changed, 51 insertions(+), 44 deletions(-)

diff --git a/ecc/bls12-377/fr/sumcheck/sumcheck.go b/ecc/bls12-377/fr/sumcheck/sumcheck.go
index 71033d0df..f47584955 100644
--- a/ecc/bls12-377/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-377/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index 64398b3e2..bdae61d49 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls12-381/fr/sumcheck/sumcheck.go b/ecc/bls12-381/fr/sumcheck/sumcheck.go
index ee6e6d80d..269f2fa8b 100644
--- a/ecc/bls12-381/fr/sumcheck/sumcheck.go
+++ b/ecc/bls12-381/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls12-381/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index abeeb3c24..c88da7da8 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls24-315/fr/sumcheck/sumcheck.go b/ecc/bls24-315/fr/sumcheck/sumcheck.go
index 6cf52ba6c..63523203a 100644
--- a/ecc/bls24-315/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-315/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-315/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index f0e865f87..c0b0bd472 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bls24-317/fr/sumcheck/sumcheck.go b/ecc/bls24-317/fr/sumcheck/sumcheck.go
index 0ba7de052..d6c8c5fd1 100644
--- a/ecc/bls24-317/fr/sumcheck/sumcheck.go
+++ b/ecc/bls24-317/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr"
 	"github.com/consensys/gnark-crypto/ecc/bls24-317/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 2f2b91b5e..722950136 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bw6-633/fr/sumcheck/sumcheck.go b/ecc/bw6-633/fr/sumcheck/sumcheck.go
index 902757717..4c063b247 100644
--- a/ecc/bw6-633/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-633/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-633/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index eddfb771d..3c58a7ae9 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/polynomial"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []fr.Element, comb
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/ecc/bw6-761/fr/sumcheck/sumcheck.go b/ecc/bw6-761/fr/sumcheck/sumcheck.go
index ad97e1425..511c685a4 100644
--- a/ecc/bw6-761/fr/sumcheck/sumcheck.go
+++ b/ecc/bw6-761/fr/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr"
 	"github.com/consensys/gnark-crypto/ecc/bw6-761/fr/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/internal/generator/gkr/template/gkr.go.tmpl b/internal/generator/gkr/template/gkr.go.tmpl
index e346ae932..76ddf3bb2 100644
--- a/internal/generator/gkr/template/gkr.go.tmpl
+++ b/internal/generator/gkr/template/gkr.go.tmpl
@@ -1,4 +1,5 @@
 import (
+	"errors"
 	"fmt"
 	"{{.FieldPackagePath}}"
 	"{{.FieldPackagePath}}/polynomial"
@@ -131,7 +132,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []{{.ElementType}}
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -457,7 +458,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -657,14 +658,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/internal/generator/sumcheck/template/sumcheck.go.tmpl b/internal/generator/sumcheck/template/sumcheck.go.tmpl
index a4e17da82..2ca7ec497 100644
--- a/internal/generator/sumcheck/template/sumcheck.go.tmpl
+++ b/internal/generator/sumcheck/template/sumcheck.go.tmpl
@@ -1,5 +1,5 @@
 import (
-	"fmt"
+	"errors"
 	"{{.FieldPackagePath}}"
 	"{{.FieldPackagePath}}/polynomial"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
@@ -144,7 +144,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)
diff --git a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
index 52e301df6..73bb280a5 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -6,6 +6,7 @@
 package gkr
 
 import (
+	"errors"
 	"fmt"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational"
@@ -136,7 +137,7 @@ func (e *eqTimesGateEvalSumcheckLazyClaims) VerifyFinalEval(r []small_rational.S
 	if evaluation.Equal(&purportedValue) {
 		return nil
 	}
-	return fmt.Errorf("incompatible evaluations")
+	return errors.New("incompatible evaluations")
 }
 
 type eqTimesGateEvalSumcheckClaims struct {
@@ -461,7 +462,7 @@ func setup(c Circuit, assignment WireAssignment, transcriptSettings fiatshamir.S
 	o.nbVars = assignment.NumVars()
 	nbInstances := assignment.NumInstances()
 	if 1<<o.nbVars != nbInstances {
-		return o, fmt.Errorf("number of instances must be power of 2")
+		return o, errors.New("number of instances must be power of 2")
 	}
 
 	if o.pool == nil {
@@ -661,14 +662,14 @@ func Verify(c Circuit, assignment WireAssignment, proof Proof, transcriptSetting
 		if wire.noProof() { // input wires with one claim only
 			// make sure the proof is empty
 			if len(finalEvalProof) != 0 || len(proofW.PartialSumPolys) != 0 {
-				return fmt.Errorf("no proof allowed for input wire with a single claim")
+				return errors.New("no proof allowed for input wire with a single claim")
 			}
 
 			if wire.NbClaims() == 1 { // input wire
 				// simply evaluate and see if it matches
 				evaluation := assignment[wire].Evaluate(claim.evaluationPoints[0], claims.memPool)
 				if !claim.claimedEvaluations[0].Equal(&evaluation) {
-					return fmt.Errorf("incorrect input wire claim")
+					return errors.New("incorrect input wire claim")
 				}
 			}
 		} else if err = sumcheck.Verify(
diff --git a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
index d5cd387d8..e711cbcf2 100644
--- a/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
+++ b/internal/generator/test_vector_utils/small_rational/sumcheck/sumcheck.go
@@ -6,7 +6,7 @@
 package sumcheck
 
 import (
-	"fmt"
+	"errors"
 	fiatshamir "github.com/consensys/gnark-crypto/fiat-shamir"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational"
 	"github.com/consensys/gnark-crypto/internal/generator/test_vector_utils/small_rational/polynomial"
@@ -151,7 +151,7 @@ func Verify(claims LazyClaims, proof Proof, transcriptSettings fiatshamir.Settin
 
 	for j := 0; j < claims.VarsNum(); j++ {
 		if len(proof.PartialSumPolys[j]) != claims.Degree(j) {
-			return fmt.Errorf("malformed proof")
+			return errors.New("malformed proof")
 		}
 		copy(gJ[1:], proof.PartialSumPolys[j])
 		gJ[0].Sub(&gJR, &proof.PartialSumPolys[j][0]) // Requirement that gⱼ(0) + gⱼ(1) = gⱼ₋₁(r)