fix: register gates in GKR Poseidon

std/permutation/poseidon2/gkr-poseidon2/gkr-poseidon2.go

@@ -3,6 +3,7 @@ package gkr_poseidon2
 import (
 	"errors"
 	"fmt"
+	"sync"
 
 	"github.com/consensys/gnark/constraint/solver/gkrgates"
 	"github.com/consensys/gnark/internal/kvstore"
@@ -103,14 +104,6 @@ func intGate2(api gkr.GateAPI, x ...frontend.Variable) frontend.Variable {
 	return api.Add(api.Mul(x[1], 3), x[0])
 }
 
-// extGate applies the first row of the external matrix
-func extGate(api gkr.GateAPI, x ...frontend.Variable) frontend.Variable {
-	if len(x) != 2 {
-		panic("expected 2 inputs")
-	}
-	return api.Add(api.Mul(x[0], 2), x[1])
-}
-
 // extAddGate applies the first row of the external matrix to the first two elements and adds the third
 func extAddGate(api gkr.GateAPI, x ...frontend.Variable) frontend.Variable {
 	if len(x) != 3 {
@@ -184,6 +177,7 @@ func defineCircuit(api frontend.API) (gkrCircuit *gkrapi.Circuit, in1, in2, out
 	}
 	gateNamer := newRoundGateNamer(&p, curve)
 
+	registerStaticGates()
 	if err = registerGates(&p, curve); err != nil {
 		return
 	}
@@ -294,6 +288,7 @@ func RegisterGates(curves ...ecc.ID) error {
 	if len(curves) == 0 {
 		return errors.New("expected at least one curve")
 	}
+	registerStaticGates()
 	for _, curve := range curves {
 		p, err := poseidon2.GetDefaultParameters(curve)
 		if err != nil {
@@ -306,6 +301,37 @@ func RegisterGates(curves ...ecc.ID) error {
 	return nil
 }
 
+var staticGatesOnce sync.Once
+
+func registerStaticGates() {
+	staticGatesOnce.Do(func() {
+		if err := gkrgates.Register(pow4Gate, 1, gkrgates.WithUnverifiedDegree(4)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(pow4TimesGate, 2, gkrgates.WithUnverifiedDegree(5)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(pow3Gate, 1, gkrgates.WithUnverifiedDegree(3)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(pow2Gate, 1, gkrgates.WithUnverifiedDegree(2)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(pow2TimesGate, 2, gkrgates.WithUnverifiedDegree(3)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(extGate2, 2, gkrgates.WithUnverifiedDegree(1)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(intGate2, 2, gkrgates.WithUnverifiedDegree(1)); err != nil {
+			panic(err)
+		}
+		if err := gkrgates.Register(extAddGate, 3, gkrgates.WithUnverifiedDegree(1)); err != nil {
+			panic(err)
+		}
+	})
+}
+
 func registerGates(p *poseidon2.Parameters, curve ecc.ID) error {
 	const (
 		x = iota
@@ -379,9 +405,4 @@ func (n roundGateNamer) linear(varIndex, round int) gkr.GateName {
 	return gkr.GateName(fmt.Sprintf("x%d-l-op-round=%d;%s", varIndex, round, n))
 }
 
-// integrated is the name of a gate where a polynomial of total degree 1 is applied to the input, followed by an S-box
-func (n roundGateNamer) integrated(varIndex, round int) gkr.GateName {
-	return gkr.GateName(fmt.Sprintf("x%d-i-op-round=%d;%s", varIndex, round, n))
-}
-
 type gkrPoseidon2Key struct{}