diff --git a/std/recursion/plonk/verifier.go b/std/recursion/plonk/verifier.go
index d360868d05..8c5533f07b 100644
--- a/std/recursion/plonk/verifier.go
+++ b/std/recursion/plonk/verifier.go
@@ -2,6 +2,8 @@ package plonk
 
 import (
 	"fmt"
+	"math/big"
+	"strconv"
 
 	fr_bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 	fr_bls12381 "github.com/consensys/gnark-crypto/ecc/bls12-381/fr"
@@ -20,6 +22,7 @@ import (
 	"github.com/consensys/gnark/std/commitments/kzg"
 	fiatshamir "github.com/consensys/gnark/std/fiat-shamir"
 	"github.com/consensys/gnark/std/hash"
+	"github.com/consensys/gnark/std/math/bits"
 	"github.com/consensys/gnark/std/math/emulated"
 	"github.com/consensys/gnark/std/recursion"
 )
@@ -253,30 +256,34 @@ func PlaceholderWitness[FR emulated.FieldParams](ccs constraint.ConstraintSystem
 
 type Verifier[FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra.G2ElementT, GtEl algebra.GtElementT] struct {
 	api     frontend.API
+	scalars *emulated.Field[FR]
 	curve   algebra.Curve[FR, G1El]
 	pairing algebra.Pairing[G1El, G2El, GtEl]
 	kzgHash hash.FieldHasher
-	fsHash  hash.FieldHasher
 	htfHash hash.FieldHasher
 }
 
-func NewVerifier[
-	FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra.G2ElementT, GtEl algebra.GtElementT](
+func NewVerifier[FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra.G2ElementT, GtEl algebra.GtElementT](
 	api frontend.API, curve algebra.Curve[FR, G1El], pairing algebra.Pairing[G1El, G2El, GtEl],
-	fsHash hash.FieldHasher) *Verifier[FR, G1El, G2El, GtEl] {
+) (*Verifier[FR, G1El, G2El, GtEl], error) {
+	f, err := emulated.NewField[FR](api)
+	if err != nil {
+		return nil, fmt.Errorf("new scalars: %w", err)
+	}
 	return &Verifier[FR, G1El, G2El, GtEl]{
 		api:     api,
+		scalars: f,
 		curve:   curve,
 		pairing: pairing,
-		fsHash:  fsHash,
-	}
+	}, nil
 }
 
 func (v *Verifier[FR, G1El, G2El, GtEl]) AssertProof(vk VerifyingKey[FR, G1El, G2El], proof Proof[FR, G1El, G2El], witness Witness[FR]) error {
+	var fr FR
 	if len(proof.Bsb22Commitments) != len(vk.Qcp) {
 		return fmt.Errorf("BSB22 commitment number mismatch")
 	}
-	fs, err := recursion.NewTranscript(v.api, nil, []string{"gamma", "beta", "alpha", "zeta"})
+	fs, err := recursion.NewTranscript(v.api, fr.Modulus(), []string{"gamma", "beta", "alpha", "zeta"})
 	if err != nil {
 		return fmt.Errorf("init new transcript: %w", err)
 	}
@@ -563,17 +570,16 @@ func (v *Verifier[FR, G1El, G2El, GtEl]) bindPublicData(fs *fiatshamir.Transcrip
 	return nil
 }
 
-func (v *Verifier[FR, G1El, G2El, GtEl]) deriveRandomness(fs *fiatshamir.Transcript, challenge string, points ...G1El) (emulated.Element[FR], error) {
-	var ret emulated.Element[FR]
+func (v *Verifier[FR, G1El, G2El, GtEl]) deriveRandomness(fs *fiatshamir.Transcript, challenge string, points ...G1El) (*emulated.Element[FR], error) {
 	for i := range points {
 		if err := fs.Bind(challenge, v.curve.MarshalG1(points[i])); err != nil {
-			return ret, fmt.Errorf("bind challenge %d: %w", i, err)
+			return nil, fmt.Errorf("bind challenge %d: %w", i, err)
 		}
 	}
 	b, err := fs.ComputeChallenge(challenge)
 	if err != nil {
-		return ret, fmt.Errorf("compute challenge: %w", err)
+		return nil, fmt.Errorf("compute challenge: %w", err)
 	}
-	_ = b
+	ret := v.scalars.FromBits(bits.ToBinary(v.api, b))
 	return ret, nil
 }
diff --git a/std/recursion/plonk/verifier_test.go b/std/recursion/plonk/verifier_test.go
index 4d394d0692..cc9c1452b9 100644
--- a/std/recursion/plonk/verifier_test.go
+++ b/std/recursion/plonk/verifier_test.go
@@ -63,12 +63,11 @@ type OuterCircuit[FR emulated.FieldParams, G1El algebra.G1ElementT, G2El algebra
 	Proof        Proof[FR, G1El, G2El]
 	VerifyingKey VerifyingKey[FR, G1El, G2El]
 	InnerWitness Witness[FR]
-
-	target *big.Int // TODO: remove later
 }
 
-func (c *OuterCircuit[S, G1El, G2El, GtEl]) Define(api frontend.API) error {
-	curve, err := algebra.GetCurve[S, G1El](api)
+func (c *OuterCircuit[FR, G1El, G2El, GtEl]) Define(api frontend.API) error {
+	var fr FR
+	curve, err := algebra.GetCurve[FR, G1El](api)
 	if err != nil {
 		return fmt.Errorf("new curve: %w", err)
 	}
@@ -76,12 +75,14 @@ func (c *OuterCircuit[S, G1El, G2El, GtEl]) Define(api frontend.API) error {
 	if err != nil {
 		return fmt.Errorf("get pairing: %w", err)
 	}
-	// TODO: should do automatically but we need modulus. Hopefully Arithmetization returns it.
-	fsHhash, err := recursion.NewHash(api, c.target, true)
+	fsHhash, err := recursion.NewHash(api, fr.Modulus(), true)
 	if err != nil {
 		return fmt.Errorf("get hash: %w", err)
 	}
-	verifier := NewVerifier(api, curve, pairing, fsHhash)
+	verifier, err := NewVerifier(api, curve, pairing, fsHhash)
+	if err != nil {
+		return fmt.Errorf("new verifier: %w", err)
+	}
 	err = verifier.AssertProof(c.VerifyingKey, c.Proof, c.InnerWitness)
 	return err
 }
@@ -102,13 +103,11 @@ func TestBLS12InBW6(t *testing.T) {
 		InnerWitness: PlaceholderWitness[sw_bls12377.ScalarField](innerCcs),
 		Proof:        PlaceholderProof[sw_bls12377.ScalarField, sw_bls12377.G1Affine, sw_bls12377.G2Affine](innerCcs),
 		VerifyingKey: PlaceholderVerifyingKey[sw_bls12377.ScalarField, sw_bls12377.G1Affine, sw_bls12377.G2Affine](innerCcs),
-		target:       ecc.BLS12_377.ScalarField(),
 	}
 	outerAssignment := &OuterCircuit[sw_bls12377.ScalarField, sw_bls12377.G1Affine, sw_bls12377.G2Affine, sw_bls12377.GT]{
 		InnerWitness: circuitWitness,
 		Proof:        circuitProof,
 		VerifyingKey: circuitVk,
-		target:       ecc.BLS12_377.ScalarField(),
 	}
 	assert.CheckCircuit(outerCircuit, test.WithValidAssignment(outerAssignment), test.WithCurves(ecc.BW6_761),
 		test.NoFuzzing(), test.NoSerializationChecks(), test.NoSolidityChecks())