diff --git a/ecc/bls12-377/fr/gkr/gkr.go b/ecc/bls12-377/fr/gkr/gkr.go
index 19f4e9bb2..5eb0e2c61 100644
--- a/ecc/bls12-377/fr/gkr/gkr.go
+++ b/ecc/bls12-377/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bls12-377/fr/gkr/gkr_test.go b/ecc/bls12-377/fr/gkr/gkr_test.go
index 15ff485d9..d80d1e39f 100644
--- a/ecc/bls12-377/fr/gkr/gkr_test.go
+++ b/ecc/bls12-377/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bls12-378/fr/gkr/gkr.go b/ecc/bls12-378/fr/gkr/gkr.go
index c576d7aca..ceada9579 100644
--- a/ecc/bls12-378/fr/gkr/gkr.go
+++ b/ecc/bls12-378/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bls12-378/fr/gkr/gkr_test.go b/ecc/bls12-378/fr/gkr/gkr_test.go
index 462ee5fdd..aef3b7b07 100644
--- a/ecc/bls12-378/fr/gkr/gkr_test.go
+++ b/ecc/bls12-378/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bls12-381/fr/gkr/gkr.go b/ecc/bls12-381/fr/gkr/gkr.go
index 64b48da06..b4d322ad1 100644
--- a/ecc/bls12-381/fr/gkr/gkr.go
+++ b/ecc/bls12-381/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bls12-381/fr/gkr/gkr_test.go b/ecc/bls12-381/fr/gkr/gkr_test.go
index bf6877cb5..1c3ee3d23 100644
--- a/ecc/bls12-381/fr/gkr/gkr_test.go
+++ b/ecc/bls12-381/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bls24-315/fr/gkr/gkr.go b/ecc/bls24-315/fr/gkr/gkr.go
index ca1f4c833..49d6a0554 100644
--- a/ecc/bls24-315/fr/gkr/gkr.go
+++ b/ecc/bls24-315/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bls24-315/fr/gkr/gkr_test.go b/ecc/bls24-315/fr/gkr/gkr_test.go
index 7fd419d28..fd14819be 100644
--- a/ecc/bls24-315/fr/gkr/gkr_test.go
+++ b/ecc/bls24-315/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bls24-317/fr/gkr/gkr.go b/ecc/bls24-317/fr/gkr/gkr.go
index 0dc5b4883..fde5babfd 100644
--- a/ecc/bls24-317/fr/gkr/gkr.go
+++ b/ecc/bls24-317/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bls24-317/fr/gkr/gkr_test.go b/ecc/bls24-317/fr/gkr/gkr_test.go
index 35288f1d0..2d6134f87 100644
--- a/ecc/bls24-317/fr/gkr/gkr_test.go
+++ b/ecc/bls24-317/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bn254/fr/gkr/gkr.go b/ecc/bn254/fr/gkr/gkr.go
index df189b19d..94a2735b9 100644
--- a/ecc/bn254/fr/gkr/gkr.go
+++ b/ecc/bn254/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bn254/fr/gkr/gkr_test.go b/ecc/bn254/fr/gkr/gkr_test.go
index 429998b12..422ddb997 100644
--- a/ecc/bn254/fr/gkr/gkr_test.go
+++ b/ecc/bn254/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bw6-633/fr/gkr/gkr.go b/ecc/bw6-633/fr/gkr/gkr.go
index 888c2c3c5..899729723 100644
--- a/ecc/bw6-633/fr/gkr/gkr.go
+++ b/ecc/bw6-633/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bw6-633/fr/gkr/gkr_test.go b/ecc/bw6-633/fr/gkr/gkr_test.go
index 5a683825f..7b2abc9dc 100644
--- a/ecc/bw6-633/fr/gkr/gkr_test.go
+++ b/ecc/bw6-633/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bw6-756/fr/gkr/gkr.go b/ecc/bw6-756/fr/gkr/gkr.go
index 5fe30d6d2..ae9a3ecfa 100644
--- a/ecc/bw6-756/fr/gkr/gkr.go
+++ b/ecc/bw6-756/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bw6-756/fr/gkr/gkr_test.go b/ecc/bw6-756/fr/gkr/gkr_test.go
index 2632d06f1..7f24681ed 100644
--- a/ecc/bw6-756/fr/gkr/gkr_test.go
+++ b/ecc/bw6-756/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/ecc/bw6-761/fr/gkr/gkr.go b/ecc/bw6-761/fr/gkr/gkr.go
index c98a8ab05..fda102869 100644
--- a/ecc/bw6-761/fr/gkr/gkr.go
+++ b/ecc/bw6-761/fr/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...fr.Element) (res fr.Element) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/ecc/bw6-761/fr/gkr/gkr_test.go b/ecc/bw6-761/fr/gkr/gkr_test.go
index 4120b3aff..976fb661d 100644
--- a/ecc/bw6-761/fr/gkr/gkr_test.go
+++ b/ecc/bw6-761/fr/gkr/gkr_test.go
@@ -45,6 +45,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []fr.Element{four, three}, []fr.Element{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []fr.Element{four, three}, []fr.Element{two, three})
 }
@@ -203,6 +211,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]fr.Element) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]fr.Element) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate:   Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]fr.Element) {
 
 	c := make(Circuit, 3)
diff --git a/internal/generator/gkr/template/gkr.go.tmpl b/internal/generator/gkr/template/gkr.go.tmpl
index 049702508..e346ae932 100644
--- a/internal/generator/gkr/template/gkr.go.tmpl
+++ b/internal/generator/gkr/template/gkr.go.tmpl
@@ -869,10 +869,10 @@ func (g AddGate) Evaluate(x ...{{.ElementType}}) (res {{.ElementType}}) {
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -894,7 +894,7 @@ func (g MulGate) Evaluate(x ...{{.ElementType}}) (res {{.ElementType}}) {
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return
diff --git a/internal/generator/gkr/template/gkr.test.go.tmpl b/internal/generator/gkr/template/gkr.test.go.tmpl
index 525abd6c9..b553c2366 100644
--- a/internal/generator/gkr/template/gkr.test.go.tmpl
+++ b/internal/generator/gkr/template/gkr.test.go.tmpl
@@ -31,6 +31,14 @@ func TestNoGate(t *testing.T) {
 	testManyInstances(t, 1, testNoGate)
 }
 
+func TestSingleAddGateTwoInstances(t *testing.T) {
+	testSingleAddGate(t, []{{.ElementType}}{four, three}, []{{.ElementType}}{two, three})
+}
+
+func TestSingleAddGate(t *testing.T) {
+	testManyInstances(t, 2, testSingleAddGate)
+}
+
 func TestSingleMulGateTwoInstances(t *testing.T) {
 	testSingleMulGate(t, []{{.ElementType}}{four, three}, []{{.ElementType}}{two, three})
 }
@@ -193,6 +201,25 @@ func testNoGate(t *testing.T, inputAssignments ...[]{{.ElementType}}) {
 	assert.NoError(t, err, "proof rejected")
 }
 
+func testSingleAddGate(t *testing.T, inputAssignments ...[]{{.ElementType}}) {
+	c := make(Circuit, 3)
+	c[2] = Wire{
+		Gate: Gates["add"],
+		Inputs: []*Wire{&c[0], &c[1]},
+	}
+
+	assignment := WireAssignment{&c[0]: inputAssignments[0], &c[1]: inputAssignments[1]}.Complete(c)
+
+	proof, err := Prove(c, assignment, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t,err)
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(1, 1)))
+	assert.NoError(t, err, "proof rejected")
+
+	err = Verify(c, assignment, proof, fiatshamir.WithHash(test_vector_utils.NewMessageCounter(0, 1)))
+	assert.NotNil(t, err, "bad proof accepted")
+}
+
 func testSingleMulGate(t *testing.T, inputAssignments ...[]{{.ElementType}}) {
 
 	c := make(Circuit, 3)
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 a2bef7d1e..d0dae64a6 100644
--- a/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
+++ b/internal/generator/test_vector_utils/small_rational/gkr/gkr.go
@@ -884,10 +884,10 @@ func (g AddGate) Evaluate(x ...small_rational.SmallRational) (res small_rational
 	// set zero
 	case 1:
 		res.Set(&x[0])
-	case 2:
+	default:
 		res.Add(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Add(&res, &x[2])
+			res.Add(&res, &x[i])
 		}
 	}
 	return
@@ -909,7 +909,7 @@ func (g MulGate) Evaluate(x ...small_rational.SmallRational) (res small_rational
 	default:
 		res.Mul(&x[0], &x[1])
 		for i := 2; i < len(x); i++ {
-			res.Mul(&res, &x[2])
+			res.Mul(&res, &x[i])
 		}
 	}
 	return