diff --git a/snark-verifier/Cargo.toml b/snark-verifier/Cargo.toml
index 5ce80f0d..46d4b419 100644
--- a/snark-verifier/Cargo.toml
+++ b/snark-verifier/Cargo.toml
@@ -11,13 +11,13 @@ num-integer = "0.1.45"
 num-traits = "0.2.15"
 rand = "0.8"
 hex = "0.4"
-halo2_curves = { git = "https://github.com/privacy-scaling-explorations/halo2curves", tag = "0.3.1", package = "halo2curves" }
+halo2_curves = { git = "https://github.com/privacy-scaling-explorations/halo2curves", tag = "0.3.2", package = "halo2curves" }
 
 # parallel
 rayon = { version = "1.5.3", optional = true }
 
 # system_halo2
-halo2_proofs = { git = "https://github.com/privacy-scaling-explorations/halo2", tag = "v2023_02_02", optional = true }
+halo2_proofs = { git = "https://github.com/privacy-scaling-explorations/halo2", tag = "v2023_04_20", optional = true }
 
 # loader_evm
 sha3 = { version = "0.10", optional = true }
@@ -27,15 +27,15 @@ rlp = { version = "0.5.2", default-features = false, features = ["std"], optiona
 revm = { version = "= 2.3.1", optional = true }
 
 # loader_halo2
-halo2_wrong_ecc = { git = "https://github.com/privacy-scaling-explorations/halo2wrong", tag = "v2023_02_02", package = "ecc", optional = true }
-poseidon = { git = "https://github.com/privacy-scaling-explorations/poseidon", tag = "v2022_10_22", optional = true }
+halo2_wrong_ecc = { git = "https://github.com/privacy-scaling-explorations/halo2wrong", tag = "v2023_04_20", package = "ecc", optional = true }
+poseidon = { git = "https://github.com/privacy-scaling-explorations/poseidon", tag = "v2023_04_20", optional = true }
 
 [dev-dependencies]
 rand_chacha = "0.3.1"
 paste = "1.0.7"
 
 # system_halo2
-halo2_wrong_ecc = { git = "https://github.com/privacy-scaling-explorations/halo2wrong", tag = "v2023_02_02", package = "ecc" }
+halo2_wrong_ecc = { git = "https://github.com/privacy-scaling-explorations/halo2wrong", tag = "v2023_04_20", package = "ecc" }
 
 # loader_evm
 crossterm = { version = "0.25" }
@@ -46,11 +46,16 @@ default = ["loader_evm", "loader_halo2", "system_halo2"]
 
 parallel = ["dep:rayon"]
 
+# loaders
 loader_evm = ["dep:bytes", "dep:sha3", "dep:primitive-types", "dep:rlp", "dep:revm"]
 loader_halo2 = ["dep:halo2_proofs", "dep:halo2_wrong_ecc", "dep:poseidon"]
 
+# systems
 system_halo2 = ["dep:halo2_proofs"]
 
+# features of halo2
+halo2_circuit_params = ["halo2_proofs?/circuit-params", "halo2_wrong_ecc?/circuit-params"]
+
 [[example]]
 name = "evm-verifier"
 required-features = ["loader_evm", "system_halo2"]
diff --git a/snark-verifier/examples/evm-verifier-with-accumulator.rs b/snark-verifier/examples/evm-verifier-with-accumulator.rs
index ba23e352..369600e3 100644
--- a/snark-verifier/examples/evm-verifier-with-accumulator.rs
+++ b/snark-verifier/examples/evm-verifier-with-accumulator.rs
@@ -34,7 +34,7 @@ type PlonkSuccinctVerifier = verifier::plonk::PlonkSuccinctVerifier<As, LimbsEnc
 type PlonkVerifier = verifier::plonk::PlonkVerifier<As, LimbsEncoding<LIMBS, BITS>>;
 
 mod application {
-    use halo2_curves::bn256::Fr;
+    use halo2_curves::{bn256::Fr, ff::Field};
     use halo2_proofs::{
         circuit::{Layouter, SimpleFloorPlanner, Value},
         plonk::{Advice, Circuit, Column, ConstraintSystem, Error, Fixed, Instance},
@@ -117,6 +117,8 @@ mod application {
     impl Circuit<Fr> for StandardPlonk {
         type Config = StandardPlonkConfig;
         type FloorPlanner = SimpleFloorPlanner;
+        #[cfg(feature = "halo2_circuit_params")]
+        type Params = ();
 
         fn without_witnesses(&self) -> Self {
             Self::default()
@@ -136,7 +138,7 @@ mod application {
                 || "",
                 |mut region| {
                     region.assign_advice(|| "", config.a, 0, || Value::known(self.0))?;
-                    region.assign_fixed(|| "", config.q_a, 0, || Value::known(-Fr::one()))?;
+                    region.assign_fixed(|| "", config.q_a, 0, || Value::known(-Fr::ONE))?;
 
                     region.assign_advice(|| "", config.a, 1, || Value::known(-Fr::from(5)))?;
                     for (idx, column) in (1..).zip([
@@ -149,7 +151,7 @@ mod application {
                         region.assign_fixed(|| "", column, 1, || Value::known(Fr::from(idx)))?;
                     }
 
-                    let a = region.assign_advice(|| "", config.a, 2, || Value::known(Fr::one()))?;
+                    let a = region.assign_advice(|| "", config.a, 2, || Value::known(Fr::ONE))?;
                     a.copy_advice(|| "", &mut region, config.b, 3)?;
                     a.copy_advice(|| "", &mut region, config.c, 4)?;
 
@@ -185,7 +187,7 @@ mod aggregation {
             AccumulationScheme, AccumulationSchemeProver,
         },
         system,
-        util::arithmetic::{fe_to_limbs, FieldExt},
+        util::arithmetic::{fe_to_limbs, PrimeField},
         verifier::{plonk::PlonkProtocol, SnarkVerifier},
     };
     use std::rc::Rc;
@@ -309,7 +311,7 @@ mod aggregation {
     }
 
     impl AggregationConfig {
-        pub fn configure<F: FieldExt>(
+        pub fn configure<F: PrimeField>(
             meta: &mut ConstraintSystem<F>,
             composition_bits: Vec<usize>,
             overflow_bits: Vec<usize>,
@@ -410,6 +412,8 @@ mod aggregation {
     impl Circuit<Fr> for AggregationCircuit {
         type Config = AggregationConfig;
         type FloorPlanner = SimpleFloorPlanner;
+        #[cfg(feature = "halo2_circuit_params")]
+        type Params = ();
 
         fn without_witnesses(&self) -> Self {
             Self {
diff --git a/snark-verifier/examples/evm-verifier.rs b/snark-verifier/examples/evm-verifier.rs
index 58b08074..6e58d330 100644
--- a/snark-verifier/examples/evm-verifier.rs
+++ b/snark-verifier/examples/evm-verifier.rs
@@ -1,4 +1,7 @@
-use halo2_curves::bn256::{Bn256, Fq, Fr, G1Affine};
+use halo2_curves::{
+    bn256::{Bn256, Fq, Fr, G1Affine},
+    ff::Field,
+};
 use halo2_proofs::{
     circuit::{Layouter, SimpleFloorPlanner, Value},
     dev::MockProver,
@@ -103,6 +106,8 @@ impl StandardPlonk {
 impl Circuit<Fr> for StandardPlonk {
     type Config = StandardPlonkConfig;
     type FloorPlanner = SimpleFloorPlanner;
+    #[cfg(feature = "halo2_circuit_params")]
+    type Params = ();
 
     fn without_witnesses(&self) -> Self {
         Self::default()
@@ -122,7 +127,7 @@ impl Circuit<Fr> for StandardPlonk {
             || "",
             |mut region| {
                 region.assign_advice(|| "", config.a, 0, || Value::known(self.0))?;
-                region.assign_fixed(|| "", config.q_a, 0, || Value::known(-Fr::one()))?;
+                region.assign_fixed(|| "", config.q_a, 0, || Value::known(-Fr::ONE))?;
 
                 region.assign_advice(|| "", config.a, 1, || Value::known(-Fr::from(5)))?;
                 for (idx, column) in (1..).zip([
@@ -135,7 +140,7 @@ impl Circuit<Fr> for StandardPlonk {
                     region.assign_fixed(|| "", column, 1, || Value::known(Fr::from(idx)))?;
                 }
 
-                let a = region.assign_advice(|| "", config.a, 2, || Value::known(Fr::one()))?;
+                let a = region.assign_advice(|| "", config.a, 2, || Value::known(Fr::ONE))?;
                 a.copy_advice(|| "", &mut region, config.b, 3)?;
                 a.copy_advice(|| "", &mut region, config.c, 4)?;
 
diff --git a/snark-verifier/src/loader.rs b/snark-verifier/src/loader.rs
index 897890b1..1481fd64 100644
--- a/snark-verifier/src/loader.rs
+++ b/snark-verifier/src/loader.rs
@@ -122,12 +122,12 @@ pub trait ScalarLoader<F: PrimeField> {
 
     /// Load `zero` as constant.
     fn load_zero(&self) -> Self::LoadedScalar {
-        self.load_const(&F::zero())
+        self.load_const(&F::ZERO)
     }
 
     /// Load `one` as constant.
     fn load_one(&self) -> Self::LoadedScalar {
-        self.load_const(&F::one())
+        self.load_const(&F::ONE)
     }
 
     /// Assert lhs and rhs field elements are equal.
@@ -150,13 +150,13 @@ pub trait ScalarLoader<F: PrimeField> {
 
         let loader = values.first().unwrap().1.loader();
         iter::empty()
-            .chain(if constant == F::zero() {
+            .chain(if constant == F::ZERO {
                 None
             } else {
                 Some(Cow::Owned(loader.load_const(&constant)))
             })
             .chain(values.iter().map(|&(coeff, value)| {
-                if coeff == F::one() {
+                if coeff == F::ONE {
                     Cow::Borrowed(value)
                 } else {
                     Cow::Owned(loader.load_const(&coeff) * value)
@@ -179,13 +179,13 @@ pub trait ScalarLoader<F: PrimeField> {
 
         let loader = values.first().unwrap().1.loader();
         iter::empty()
-            .chain(if constant == F::zero() {
+            .chain(if constant == F::ZERO {
                 None
             } else {
                 Some(loader.load_const(&constant))
             })
             .chain(values.iter().map(|&(coeff, lhs, rhs)| {
-                if coeff == F::one() {
+                if coeff == F::ONE {
                     lhs.clone() * rhs
                 } else {
                     loader.load_const(&coeff) * lhs * rhs
@@ -197,20 +197,20 @@ pub trait ScalarLoader<F: PrimeField> {
 
     /// Sum field elements with coefficients.
     fn sum_with_coeff(&self, values: &[(F, &Self::LoadedScalar)]) -> Self::LoadedScalar {
-        self.sum_with_coeff_and_const(values, F::zero())
+        self.sum_with_coeff_and_const(values, F::ZERO)
     }
 
     /// Sum field elements and constant.
     fn sum_with_const(&self, values: &[&Self::LoadedScalar], constant: F) -> Self::LoadedScalar {
         self.sum_with_coeff_and_const(
-            &values.iter().map(|&value| (F::one(), value)).collect_vec(),
+            &values.iter().map(|&value| (F::ONE, value)).collect_vec(),
             constant,
         )
     }
 
     /// Sum field elements.
     fn sum(&self, values: &[&Self::LoadedScalar]) -> Self::LoadedScalar {
-        self.sum_with_const(values, F::zero())
+        self.sum_with_const(values, F::ZERO)
     }
 
     /// Sum product of field elements with coefficients.
@@ -218,7 +218,7 @@ pub trait ScalarLoader<F: PrimeField> {
         &self,
         values: &[(F, &Self::LoadedScalar, &Self::LoadedScalar)],
     ) -> Self::LoadedScalar {
-        self.sum_products_with_coeff_and_const(values, F::zero())
+        self.sum_products_with_coeff_and_const(values, F::ZERO)
     }
 
     /// Sum product of field elements and constant.
@@ -230,7 +230,7 @@ pub trait ScalarLoader<F: PrimeField> {
         self.sum_products_with_coeff_and_const(
             &values
                 .iter()
-                .map(|&(lhs, rhs)| (F::one(), lhs, rhs))
+                .map(|&(lhs, rhs)| (F::ONE, lhs, rhs))
                 .collect_vec(),
             constant,
         )
@@ -241,7 +241,7 @@ pub trait ScalarLoader<F: PrimeField> {
         &self,
         values: &[(&Self::LoadedScalar, &Self::LoadedScalar)],
     ) -> Self::LoadedScalar {
-        self.sum_products_with_const(values, F::zero())
+        self.sum_products_with_const(values, F::ZERO)
     }
 
     /// Product of field elements.
diff --git a/snark-verifier/src/loader/evm/loader.rs b/snark-verifier/src/loader/evm/loader.rs
index 911625b6..6a756ced 100644
--- a/snark-verifier/src/loader/evm/loader.rs
+++ b/snark-verifier/src/loader/evm/loader.rs
@@ -721,8 +721,8 @@ impl<F: PrimeField<Repr = [u8; 0x20]>> ScalarLoader<F> for Rc<EvmLoader> {
         }
 
         let push_addend = |(coeff, value): &(F, &Scalar)| {
-            assert_ne!(*coeff, F::zero());
-            match (*coeff == F::one(), &value.value) {
+            assert_ne!(*coeff, F::ZERO);
+            match (*coeff == F::ONE, &value.value) {
                 (true, _) => self.push(value),
                 (false, Value::Constant(value)) => self.push(&self.scalar(Value::Constant(
                     fe_to_u256(*coeff * u256_to_fe::<F>(*value)),
@@ -736,7 +736,7 @@ impl<F: PrimeField<Repr = [u8; 0x20]>> ScalarLoader<F> for Rc<EvmLoader> {
         };
 
         let mut values = values.iter();
-        let initial_value = if constant == F::zero() {
+        let initial_value = if constant == F::ZERO {
             push_addend(values.next().unwrap())
         } else {
             self.push(&self.scalar(Value::Constant(fe_to_u256(constant))))
@@ -770,8 +770,8 @@ impl<F: PrimeField<Repr = [u8; 0x20]>> ScalarLoader<F> for Rc<EvmLoader> {
         }
 
         let push_addend = |(coeff, lhs, rhs): &(F, &Scalar, &Scalar)| {
-            assert_ne!(*coeff, F::zero());
-            match (*coeff == F::one(), &lhs.value, &rhs.value) {
+            assert_ne!(*coeff, F::ZERO);
+            match (*coeff == F::ONE, &lhs.value, &rhs.value) {
                 (_, Value::Constant(lhs), Value::Constant(rhs)) => {
                     self.push(&self.scalar(Value::Constant(fe_to_u256(
                         *coeff * u256_to_fe::<F>(*lhs) * u256_to_fe::<F>(*rhs),
@@ -800,7 +800,7 @@ impl<F: PrimeField<Repr = [u8; 0x20]>> ScalarLoader<F> for Rc<EvmLoader> {
         };
 
         let mut values = values.iter();
-        let initial_value = if constant == F::zero() {
+        let initial_value = if constant == F::ZERO {
             push_addend(values.next().unwrap())
         } else {
             self.push(&self.scalar(Value::Constant(fe_to_u256(constant))))
diff --git a/snark-verifier/src/loader/evm/util.rs b/snark-verifier/src/loader/evm/util.rs
index 62792ee8..689518da 100644
--- a/snark-verifier/src/loader/evm/util.rs
+++ b/snark-verifier/src/loader/evm/util.rs
@@ -74,7 +74,7 @@ pub fn modulus<F>() -> U256
 where
     F: PrimeField<Repr = [u8; 32]>,
 {
-    U256::from_little_endian((-F::one()).to_repr().as_ref()) + 1
+    U256::from_little_endian((-F::ONE).to_repr().as_ref()) + 1
 }
 
 /// Encode instances and proof into calldata.
diff --git a/snark-verifier/src/loader/halo2/loader.rs b/snark-verifier/src/loader/halo2/loader.rs
index 17a51183..fb27ee49 100644
--- a/snark-verifier/src/loader/halo2/loader.rs
+++ b/snark-verifier/src/loader/halo2/loader.rs
@@ -159,7 +159,7 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .scalar_chip()
                 .sum_with_coeff_and_const(
                     &mut self.ctx_mut(),
-                    &[(C::Scalar::one(), assigned)],
+                    &[(C::Scalar::ONE, assigned)],
                     *constant,
                 )
                 .map(Value::Assigned)
@@ -168,8 +168,8 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .scalar_chip()
                 .sum_with_coeff_and_const(
                     &mut self.ctx_mut(),
-                    &[(C::Scalar::one(), lhs), (C::Scalar::one(), rhs)],
-                    C::Scalar::zero(),
+                    &[(C::Scalar::ONE, lhs), (C::Scalar::ONE, rhs)],
+                    C::Scalar::ZERO,
                 )
                 .map(Value::Assigned)
                 .unwrap(),
@@ -188,7 +188,7 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .scalar_chip()
                 .sum_with_coeff_and_const(
                     &mut self.ctx_mut(),
-                    &[(-C::Scalar::one(), assigned)],
+                    &[(-C::Scalar::ONE, assigned)],
                     *constant,
                 )
                 .map(Value::Assigned)
@@ -197,7 +197,7 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .scalar_chip()
                 .sum_with_coeff_and_const(
                     &mut self.ctx_mut(),
-                    &[(C::Scalar::one(), assigned)],
+                    &[(C::Scalar::ONE, assigned)],
                     -*constant,
                 )
                 .map(Value::Assigned)
@@ -224,7 +224,7 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .sum_with_coeff_and_const(
                     &mut self.ctx_mut(),
                     &[(*constant, assigned)],
-                    C::Scalar::zero(),
+                    C::Scalar::ZERO,
                 )
                 .map(Value::Assigned)
                 .unwrap(),
@@ -232,8 +232,8 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> Halo2Loader<'a, C, Ecc
                 .scalar_chip()
                 .sum_products_with_coeff_and_const(
                     &mut self.ctx_mut(),
-                    &[(C::Scalar::one(), lhs, rhs)],
-                    C::Scalar::zero(),
+                    &[(C::Scalar::ONE, lhs, rhs)],
+                    C::Scalar::ZERO,
                 )
                 .map(Value::Assigned)
                 .unwrap(),
@@ -651,7 +651,7 @@ impl<'a, C: CurveAffine, EccChip: EccInstructions<'a, C>> EcPointLoader<C>
                             fixed_base.push((scalar, *base))
                         }
                         (Value::Constant(scalar), Value::Assigned(_))
-                            if scalar.eq(&C::Scalar::one()) =>
+                            if scalar.eq(&C::Scalar::ONE) =>
                         {
                             variable_base_non_scaled.push(base);
                         }
diff --git a/snark-verifier/src/loader/halo2/shim.rs b/snark-verifier/src/loader/halo2/shim.rs
index 7ae65496..7a41f30a 100644
--- a/snark-verifier/src/loader/halo2/shim.rs
+++ b/snark-verifier/src/loader/halo2/shim.rs
@@ -1,4 +1,4 @@
-use crate::util::arithmetic::{CurveAffine, FieldExt};
+use crate::util::arithmetic::{CurveAffine, PrimeField};
 use halo2_proofs::{
     circuit::{Cell, Value},
     plonk::Error,
@@ -15,7 +15,7 @@ pub trait Context: Debug {
 }
 
 /// Instructions to handle field element operations.
-pub trait IntegerInstructions<'a, F: FieldExt>: Clone + Debug {
+pub trait IntegerInstructions<'a, F: PrimeField>: Clone + Debug {
     /// Context.
     type Context: Context;
     /// Assigned cell.
@@ -41,8 +41,8 @@ pub trait IntegerInstructions<'a, F: FieldExt>: Clone + Debug {
     fn sum_with_coeff_and_const(
         &self,
         ctx: &mut Self::Context,
-        values: &[(F::Scalar, impl Deref<Target = Self::AssignedInteger>)],
-        constant: F::Scalar,
+        values: &[(F, impl Deref<Target = Self::AssignedInteger>)],
+        constant: F,
     ) -> Result<Self::AssignedInteger, Error>;
 
     /// Sum product of integers with coefficients and constant.
@@ -50,11 +50,11 @@ pub trait IntegerInstructions<'a, F: FieldExt>: Clone + Debug {
         &self,
         ctx: &mut Self::Context,
         values: &[(
-            F::Scalar,
+            F,
             impl Deref<Target = Self::AssignedInteger>,
             impl Deref<Target = Self::AssignedInteger>,
         )],
-        constant: F::Scalar,
+        constant: F,
     ) -> Result<Self::AssignedInteger, Error>;
 
     /// Returns `lhs - rhs`.
@@ -162,7 +162,7 @@ mod halo2_wrong {
     use crate::{
         loader::halo2::{Context, EccInstructions, IntegerInstructions},
         util::{
-            arithmetic::{CurveAffine, FieldExt, Group},
+            arithmetic::{CurveAffine, Group, PrimeField},
             Itertools,
         },
     };
@@ -181,7 +181,7 @@ mod halo2_wrong {
     use rand::rngs::OsRng;
     use std::{iter, ops::Deref};
 
-    impl<'a, F: FieldExt> Context for RegionCtx<'a, F> {
+    impl<'a, F: PrimeField> Context for RegionCtx<'a, F> {
         fn constrain_equal(&mut self, lhs: Cell, rhs: Cell) -> Result<(), Error> {
             self.constrain_equal(lhs, rhs)
         }
@@ -191,7 +191,7 @@ mod halo2_wrong {
         }
     }
 
-    impl<'a, F: FieldExt> IntegerInstructions<'a, F> for MainGate<F> {
+    impl<'a, F: PrimeField> IntegerInstructions<'a, F> for MainGate<F> {
         type Context = RegionCtx<'a, F>;
         type AssignedCell = AssignedCell<F, F>;
         type AssignedInteger = AssignedCell<F, F>;
@@ -268,7 +268,7 @@ mod halo2_wrong {
                         ctx,
                         [Term::assigned_to_mul(lhs), Term::assigned_to_mul(rhs)],
                         constant,
-                        CombinationOptionCommon::CombineToNextScaleMul(-F::one(), *scalar).into(),
+                        CombinationOptionCommon::CombineToNextScaleMul(-F::ONE, *scalar).into(),
                     )?;
                     let acc =
                         Value::known(*scalar) * lhs.value() * rhs.value() + Value::known(constant);
@@ -283,11 +283,11 @@ mod halo2_wrong {
                                         Term::assigned_to_mul(rhs),
                                         Term::Zero,
                                         Term::Zero,
-                                        Term::Unassigned(acc, F::one()),
+                                        Term::Unassigned(acc, F::ONE),
                                     ],
-                                    F::zero(),
+                                    F::ZERO,
                                     CombinationOptionCommon::CombineToNextScaleMul(
-                                        -F::one(),
+                                        -F::ONE,
                                         *scalar,
                                     )
                                     .into(),
@@ -303,9 +303,9 @@ mod halo2_wrong {
                             Term::Zero,
                             Term::Zero,
                             Term::Zero,
-                            Term::Unassigned(output, F::zero()),
+                            Term::Unassigned(output, F::ZERO),
                         ],
-                        F::zero(),
+                        F::ZERO,
                         CombinationOptionCommon::OneLinerAdd.into(),
                     )
                     .map(|mut outputs| outputs.swap_remove(4))
@@ -327,7 +327,7 @@ mod halo2_wrong {
             ctx: &mut Self::Context,
             value: &Self::AssignedInteger,
         ) -> Result<Self::AssignedInteger, Error> {
-            MainGateInstructions::neg_with_constant(self, ctx, value, F::zero())
+            MainGateInstructions::neg_with_constant(self, ctx, value, F::ZERO)
         }
 
         fn invert(
diff --git a/snark-verifier/src/pcs/ipa.rs b/snark-verifier/src/pcs/ipa.rs
index c782c65f..191d9410 100644
--- a/snark-verifier/src/pcs/ipa.rs
+++ b/snark-verifier/src/pcs/ipa.rs
@@ -401,7 +401,7 @@ fn h_eval<F: PrimeField, T: LoadedScalar<F>>(xi: &[T], z: &T) -> T {
 fn h_coeffs<F: Field>(xi: &[F], scalar: F) -> Vec<F> {
     assert!(!xi.is_empty());
 
-    let mut coeffs = vec![F::zero(); 1 << xi.len()];
+    let mut coeffs = vec![F::ZERO; 1 << xi.len()];
     coeffs[0] = scalar;
 
     for (len, xi) in xi.iter().rev().enumerate().map(|(i, xi)| (1 << i, xi)) {
diff --git a/snark-verifier/src/pcs/ipa/accumulation.rs b/snark-verifier/src/pcs/ipa/accumulation.rs
index 7da4197a..feaeaae9 100644
--- a/snark-verifier/src/pcs/ipa/accumulation.rs
+++ b/snark-verifier/src/pcs/ipa/accumulation.rs
@@ -197,13 +197,13 @@ where
 
         let (u, h) = instances
             .iter()
-            .map(|IpaAccumulator { u, xi }| (*u, h_coeffs(xi, C::Scalar::one())))
+            .map(|IpaAccumulator { u, xi }| (*u, h_coeffs(xi, C::Scalar::ONE)))
             .chain(a_b_u.map(|(a, b, u)| {
                 (
                     u,
                     iter::empty()
                         .chain([b, a])
-                        .chain(iter::repeat_with(C::Scalar::zero).take(pk.domain.n - 2))
+                        .chain(iter::repeat(C::Scalar::ZERO).take(pk.domain.n - 2))
                         .collect(),
                 )
             }))
diff --git a/snark-verifier/src/pcs/ipa/decider.rs b/snark-verifier/src/pcs/ipa/decider.rs
index 933480f3..7ea6cfd0 100644
--- a/snark-verifier/src/pcs/ipa/decider.rs
+++ b/snark-verifier/src/pcs/ipa/decider.rs
@@ -48,7 +48,7 @@ mod native {
             dk: &Self::DecidingKey,
             IpaAccumulator { u, xi }: IpaAccumulator<C, NativeLoader>,
         ) -> Result<(), Error> {
-            let h = h_coeffs(&xi, C::Scalar::one());
+            let h = h_coeffs(&xi, C::Scalar::ONE);
             (u == multi_scalar_multiplication(&h, &dk.g).to_affine())
                 .then_some(())
                 .ok_or_else(|| Error::AssertionFailure("U == commit(G, h)".to_string()))
diff --git a/snark-verifier/src/pcs/ipa/multiopen/bgh19.rs b/snark-verifier/src/pcs/ipa/multiopen/bgh19.rs
index a852267a..ee423d19 100644
--- a/snark-verifier/src/pcs/ipa/multiopen/bgh19.rs
+++ b/snark-verifier/src/pcs/ipa/multiopen/bgh19.rs
@@ -5,7 +5,7 @@ use crate::{
         PolynomialCommitmentScheme, Query,
     },
     util::{
-        arithmetic::{CurveAffine, FieldExt, Fraction},
+        arithmetic::{CurveAffine, Fraction, PrimeField},
         msm::Msm,
         transcript::TranscriptRead,
         Itertools,
@@ -160,7 +160,7 @@ where
 
 fn query_sets<F, T>(queries: &[Query<F, T>]) -> Vec<QuerySet<F, T>>
 where
-    F: FieldExt,
+    F: PrimeField + Ord,
     T: Clone,
 {
     let poly_shifts = queries.iter().fold(
@@ -216,7 +216,7 @@ where
 
 fn query_set_coeffs<F, T>(sets: &[QuerySet<F, T>], x: &T, x_3: &T) -> Vec<QuerySetCoeff<F, T>>
 where
-    F: FieldExt,
+    F: PrimeField + Ord,
     T: LoadedScalar<F>,
 {
     let loader = x.loader();
@@ -258,7 +258,7 @@ struct QuerySet<'a, F, T> {
 
 impl<'a, F, T> QuerySet<'a, F, T>
 where
-    F: FieldExt,
+    F: PrimeField,
     T: LoadedScalar<F>,
 {
     fn msm<C: CurveAffine, L: Loader<C, LoadedScalar = T>>(
@@ -310,7 +310,7 @@ struct QuerySetCoeff<F, T> {
 
 impl<F, T> QuerySetCoeff<F, T>
 where
-    F: FieldExt,
+    F: PrimeField + Ord,
     T: LoadedScalar<F>,
 {
     fn new(shifts: &[F], powers_of_x: &[T], x_3: &T, x_3_minus_x_shift_i: &BTreeMap<F, T>) -> Self {
@@ -325,7 +325,7 @@ where
                     .filter(|&(i, _)| i != j)
                     .map(|(_, shift_i)| (*shift_j - shift_i))
                     .reduce(|acc, value| acc * value)
-                    .unwrap_or_else(|| F::one())
+                    .unwrap_or(F::ONE)
             })
             .collect_vec();
 
diff --git a/snark-verifier/src/pcs/kzg/accumulation.rs b/snark-verifier/src/pcs/kzg/accumulation.rs
index 1f901568..5139d49e 100644
--- a/snark-verifier/src/pcs/kzg/accumulation.rs
+++ b/snark-verifier/src/pcs/kzg/accumulation.rs
@@ -2,7 +2,7 @@ use crate::{
     loader::{native::NativeLoader, LoadedScalar, Loader},
     pcs::{kzg::KzgAccumulator, AccumulationScheme, AccumulationSchemeProver},
     util::{
-        arithmetic::{Curve, CurveAffine, Field, MultiMillerLoop},
+        arithmetic::{Curve, CurveAffine, Field, MultiMillerLoop, PrimeField},
         msm::Msm,
         transcript::{TranscriptRead, TranscriptWrite},
     },
@@ -19,6 +19,7 @@ pub struct KzgAs<M, MOS>(PhantomData<(M, MOS)>);
 impl<M, L, MOS> AccumulationScheme<M::G1Affine, L> for KzgAs<M, MOS>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField,
     L: Loader<M::G1Affine>,
     MOS: Clone + Debug,
 {
@@ -139,6 +140,7 @@ where
 impl<M, MOS> AccumulationSchemeProver<M::G1Affine> for KzgAs<M, MOS>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField,
     MOS: Clone + Debug,
 {
     type ProvingKey = KzgAsProvingKey<M::G1Affine>;
diff --git a/snark-verifier/src/pcs/kzg/decider.rs b/snark-verifier/src/pcs/kzg/decider.rs
index 417a39dc..7258d771 100644
--- a/snark-verifier/src/pcs/kzg/decider.rs
+++ b/snark-verifier/src/pcs/kzg/decider.rs
@@ -48,7 +48,7 @@ mod native {
             AccumulationDecider,
         },
         util::{
-            arithmetic::{Group, MillerLoopResult, MultiMillerLoop},
+            arithmetic::{Group, MillerLoopResult, MultiMillerLoop, PrimeField},
             Itertools,
         },
         Error,
@@ -58,6 +58,7 @@ mod native {
     impl<M, MOS> AccumulationDecider<M::G1Affine, NativeLoader> for KzgAs<M, MOS>
     where
         M: MultiMillerLoop,
+        M::Scalar: PrimeField,
         MOS: Clone + Debug,
     {
         type DecidingKey = KzgDecidingKey<M>;
diff --git a/snark-verifier/src/pcs/kzg/multiopen/bdfg21.rs b/snark-verifier/src/pcs/kzg/multiopen/bdfg21.rs
index 3a448056..3f1934e3 100644
--- a/snark-verifier/src/pcs/kzg/multiopen/bdfg21.rs
+++ b/snark-verifier/src/pcs/kzg/multiopen/bdfg21.rs
@@ -6,7 +6,7 @@ use crate::{
         PolynomialCommitmentScheme, Query,
     },
     util::{
-        arithmetic::{CurveAffine, FieldExt, Fraction, MultiMillerLoop},
+        arithmetic::{CurveAffine, Fraction, MultiMillerLoop, PrimeField},
         msm::Msm,
         transcript::TranscriptRead,
         Itertools,
@@ -27,6 +27,7 @@ pub struct Bdfg21;
 impl<M, L> PolynomialCommitmentScheme<M::G1Affine, L> for KzgAs<M, Bdfg21>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField + Ord,
     L: Loader<M::G1Affine>,
 {
     type VerifyingKey = KzgSuccinctVerifyingKey<M::G1Affine>;
@@ -114,7 +115,7 @@ where
     }
 }
 
-fn query_sets<F: FieldExt, T: Clone>(queries: &[Query<F, T>]) -> Vec<QuerySet<F, T>> {
+fn query_sets<F: PrimeField + Ord, T: Clone>(queries: &[Query<F, T>]) -> Vec<QuerySet<F, T>> {
     let poly_shifts = queries.iter().fold(
         Vec::<(usize, Vec<F>, Vec<&T>)>::new(),
         |mut poly_shifts, query| {
@@ -166,7 +167,7 @@ fn query_sets<F: FieldExt, T: Clone>(queries: &[Query<F, T>]) -> Vec<QuerySet<F,
     )
 }
 
-fn query_set_coeffs<'a, F: FieldExt, T: LoadedScalar<F>>(
+fn query_set_coeffs<'a, F: PrimeField + Ord, T: LoadedScalar<F>>(
     sets: &[QuerySet<'a, F, T>],
     z: &T,
     z_prime: &T,
@@ -225,7 +226,7 @@ struct QuerySet<'a, F, T> {
     evals: Vec<Vec<&'a T>>,
 }
 
-impl<'a, F: FieldExt, T: LoadedScalar<F>> QuerySet<'a, F, T> {
+impl<'a, F: PrimeField, T: LoadedScalar<F>> QuerySet<'a, F, T> {
     fn msm<C: CurveAffine, L: Loader<C, LoadedScalar = T>>(
         &self,
         coeff: &QuerySetCoeff<F, T>,
@@ -270,7 +271,7 @@ struct QuerySetCoeff<F, T> {
 
 impl<F, T> QuerySetCoeff<F, T>
 where
-    F: FieldExt,
+    F: PrimeField + Ord,
     T: LoadedScalar<F>,
 {
     fn new(
@@ -292,7 +293,7 @@ where
                     .filter(|&(i, _)| i != j)
                     .map(|(_, shift_i)| (*shift_j - shift_i))
                     .reduce(|acc, value| acc * value)
-                    .unwrap_or_else(|| F::one())
+                    .unwrap_or(F::ONE)
             })
             .collect_vec();
 
@@ -369,6 +370,7 @@ where
 impl<M> CostEstimation<M::G1Affine> for KzgAs<M, Bdfg21>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField,
 {
     type Input = Vec<Query<M::Scalar>>;
 
diff --git a/snark-verifier/src/pcs/kzg/multiopen/gwc19.rs b/snark-verifier/src/pcs/kzg/multiopen/gwc19.rs
index e5741163..b664d536 100644
--- a/snark-verifier/src/pcs/kzg/multiopen/gwc19.rs
+++ b/snark-verifier/src/pcs/kzg/multiopen/gwc19.rs
@@ -23,6 +23,7 @@ pub struct Gwc19;
 impl<M, L> PolynomialCommitmentScheme<M::G1Affine, L> for KzgAs<M, Gwc19>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField,
     L: Loader<M::G1Affine>,
 {
     type VerifyingKey = KzgSuccinctVerifyingKey<M::G1Affine>;
@@ -160,6 +161,7 @@ where
 impl<M> CostEstimation<M::G1Affine> for KzgAs<M, Gwc19>
 where
     M: MultiMillerLoop,
+    M::Scalar: PrimeField,
 {
     type Input = Vec<Query<M::Scalar>>;
 
diff --git a/snark-verifier/src/system/halo2.rs b/snark-verifier/src/system/halo2.rs
index c3f0e7ef..90c72a49 100644
--- a/snark-verifier/src/system/halo2.rs
+++ b/snark-verifier/src/system/halo2.rs
@@ -2,7 +2,7 @@
 
 use crate::{
     util::{
-        arithmetic::{root_of_unity, CurveAffine, Domain, FieldExt, Rotation},
+        arithmetic::{root_of_unity, CurveAffine, Domain, FromUniformBytes, PrimeField, Rotation},
         Itertools,
     },
     verifier::plonk::protocol::{
@@ -96,7 +96,10 @@ pub fn compile<'a, C: CurveAffine, P: Params<'a, C>>(
     params: &P,
     vk: &VerifyingKey<C>,
     config: Config,
-) -> PlonkProtocol<C> {
+) -> PlonkProtocol<C>
+where
+    C::Scalar: FromUniformBytes<64>,
+{
     assert_eq!(vk.get_domain().k(), params.k());
 
     let cs = vk.cs();
@@ -184,7 +187,7 @@ impl From<poly::Rotation> for Rotation {
     }
 }
 
-struct Polynomials<'a, F: FieldExt> {
+struct Polynomials<'a, F: PrimeField> {
     cs: &'a ConstraintSystem<F>,
     zk: bool,
     query_instance: bool,
@@ -203,7 +206,7 @@ struct Polynomials<'a, F: FieldExt> {
     num_lookup_z: usize,
 }
 
-impl<'a, F: FieldExt> Polynomials<'a, F> {
+impl<'a, F: PrimeField> Polynomials<'a, F> {
     fn new(
         cs: &'a ConstraintSystem<F>,
         zk: bool,
@@ -538,7 +541,7 @@ impl<'a, F: FieldExt> Polynomials<'a, F> {
     }
 
     fn l_active(&self) -> Expression<F> {
-        Expression::Constant(F::one()) - self.l_last() - self.l_blind()
+        Expression::Constant(F::ONE) - self.l_last() - self.l_blind()
     }
 
     fn system_challenge_offset(&self) -> usize {
@@ -563,7 +566,7 @@ impl<'a, F: FieldExt> Polynomials<'a, F> {
     }
 
     fn permutation_constraints(&'a self, t: usize) -> impl IntoIterator<Item = Expression<F>> + 'a {
-        let one = &Expression::Constant(F::one());
+        let one = &Expression::Constant(F::ONE);
         let l_0 = &Expression::<F>::CommonPolynomial(CommonPolynomial::Lagrange(0));
         let l_last = &self.l_last();
         let l_active = &self.l_active();
@@ -658,7 +661,7 @@ impl<'a, F: FieldExt> Polynomials<'a, F> {
     }
 
     fn lookup_constraints(&'a self, t: usize) -> impl IntoIterator<Item = Expression<F>> + 'a {
-        let one = &Expression::Constant(F::one());
+        let one = &Expression::Constant(F::ONE);
         let l_0 = &Expression::<F>::CommonPolynomial(CommonPolynomial::Lagrange(0));
         let l_last = &self.l_last();
         let l_active = &self.l_active();
@@ -772,7 +775,7 @@ impl<C: CurveAffine> EncodedChallenge<C> for MockChallenge {
 }
 
 #[derive(Default)]
-struct MockTranscript<F: FieldExt>(F);
+struct MockTranscript<F: PrimeField>(F);
 
 impl<C: CurveAffine> Transcript<C, MockChallenge> for MockTranscript<C::Scalar> {
     fn squeeze_challenge(&mut self) -> MockChallenge {
@@ -789,7 +792,10 @@ impl<C: CurveAffine> Transcript<C, MockChallenge> for MockTranscript<C::Scalar>
     }
 }
 
-fn transcript_initial_state<C: CurveAffine>(vk: &VerifyingKey<C>) -> C::Scalar {
+fn transcript_initial_state<C: CurveAffine>(vk: &VerifyingKey<C>) -> C::Scalar
+where
+    C::Scalar: FromUniformBytes<64>,
+{
     let mut transcript = MockTranscript::default();
     vk.hash_into(&mut transcript).unwrap();
     transcript.0
diff --git a/snark-verifier/src/system/halo2/test.rs b/snark-verifier/src/system/halo2/test.rs
index 03e5503a..6c328dce 100644
--- a/snark-verifier/src/system/halo2/test.rs
+++ b/snark-verifier/src/system/halo2/test.rs
@@ -1,4 +1,4 @@
-use crate::util::arithmetic::CurveAffine;
+use crate::util::arithmetic::{CurveAffine, FromUniformBytes, WithSmallOrderMulGroup};
 use halo2_proofs::{
     dev::MockProver,
     plonk::{create_proof, verify_proof, Circuit, ProvingKey},
@@ -47,6 +47,7 @@ pub fn create_proof_checked<'a, S, C, P, V, VS, TW, TR, EC, R>(
 ) -> Vec<u8>
 where
     S: CommitmentScheme,
+    S::Scalar: WithSmallOrderMulGroup<3> + FromUniformBytes<64> + Ord,
     S::ParamsVerifier: 'a,
     C: Circuit<S::Scalar>,
     P: Prover<'a, S>,
diff --git a/snark-verifier/src/system/halo2/test/circuit/maingate.rs b/snark-verifier/src/system/halo2/test/circuit/maingate.rs
index 82d63b5e..d6eb9ea9 100644
--- a/snark-verifier/src/system/halo2/test/circuit/maingate.rs
+++ b/snark-verifier/src/system/halo2/test/circuit/maingate.rs
@@ -1,4 +1,4 @@
-use crate::util::arithmetic::{CurveAffine, FieldExt};
+use crate::util::arithmetic::{CurveAffine, PrimeField};
 use halo2_proofs::{
     circuit::{floor_planner::V1, Layouter, Value},
     plonk::{Circuit, ConstraintSystem, Error},
@@ -19,7 +19,7 @@ pub struct MainGateWithRangeConfig {
 }
 
 impl MainGateWithRangeConfig {
-    pub fn configure<F: FieldExt>(
+    pub fn configure<F: PrimeField>(
         meta: &mut ConstraintSystem<F>,
         composition_bits: Vec<usize>,
         overflow_bits: Vec<usize>,
@@ -33,11 +33,11 @@ impl MainGateWithRangeConfig {
         }
     }
 
-    pub fn main_gate<F: FieldExt>(&self) -> MainGate<F> {
+    pub fn main_gate<F: PrimeField>(&self) -> MainGate<F> {
         MainGate::new(self.main_gate_config.clone())
     }
 
-    pub fn range_chip<F: FieldExt>(&self) -> RangeChip<F> {
+    pub fn range_chip<F: PrimeField>(&self) -> RangeChip<F> {
         RangeChip::new(self.range_config.clone())
     }
 
@@ -54,7 +54,7 @@ impl MainGateWithRangeConfig {
 #[derive(Clone, Default)]
 pub struct MainGateWithRange<F>(Vec<F>);
 
-impl<F: FieldExt> MainGateWithRange<F> {
+impl<F: PrimeField> MainGateWithRange<F> {
     pub fn new(inner: Vec<F>) -> Self {
         Self(inner)
     }
@@ -68,12 +68,14 @@ impl<F: FieldExt> MainGateWithRange<F> {
     }
 }
 
-impl<F: FieldExt> Circuit<F> for MainGateWithRange<F> {
+impl<F: PrimeField> Circuit<F> for MainGateWithRange<F> {
     type Config = MainGateWithRangeConfig;
     type FloorPlanner = V1;
+    #[cfg(feature = "halo2_circuit_params")]
+    type Params = ();
 
     fn without_witnesses(&self) -> Self {
-        Self(vec![F::zero()])
+        Self(vec![F::ZERO])
     }
 
     fn configure(meta: &mut ConstraintSystem<F>) -> Self::Config {
@@ -97,7 +99,7 @@ impl<F: FieldExt> Circuit<F> for MainGateWithRange<F> {
                 range_chip.decompose(&mut ctx, Value::known(F::from(u32::MAX as u64)), 8, 39)?;
                 let a = range_chip.assign(&mut ctx, Value::known(self.0[0]), 8, 68)?;
                 let b = main_gate.sub_sub_with_constant(&mut ctx, &a, &a, &a, F::from(2))?;
-                let cond = main_gate.assign_bit(&mut ctx, Value::known(F::one()))?;
+                let cond = main_gate.assign_bit(&mut ctx, Value::known(F::ONE))?;
                 main_gate.select(&mut ctx, &a, &b, &cond)?;
 
                 Ok(a)
diff --git a/snark-verifier/src/system/halo2/test/circuit/standard.rs b/snark-verifier/src/system/halo2/test/circuit/standard.rs
index 90f30f2b..51e3baf6 100644
--- a/snark-verifier/src/system/halo2/test/circuit/standard.rs
+++ b/snark-verifier/src/system/halo2/test/circuit/standard.rs
@@ -1,4 +1,4 @@
-use crate::util::arithmetic::FieldExt;
+use crate::util::arithmetic::PrimeField;
 use halo2_proofs::{
     circuit::{floor_planner::V1, Layouter, Value},
     plonk::{Advice, Circuit, Column, ConstraintSystem, Error, Fixed, Instance},
@@ -21,7 +21,7 @@ pub struct StandardPlonkConfig {
 }
 
 impl StandardPlonkConfig {
-    pub fn configure<F: FieldExt>(meta: &mut ConstraintSystem<F>) -> Self {
+    pub fn configure<F: PrimeField>(meta: &mut ConstraintSystem<F>) -> Self {
         let [a, b, c] = [(); 3].map(|_| meta.advice_column());
         let [q_a, q_b, q_c, q_ab, constant] = [(); 5].map(|_| meta.fixed_column());
         let instance = meta.instance_column();
@@ -63,7 +63,7 @@ impl StandardPlonkConfig {
 #[derive(Clone, Default)]
 pub struct StandardPlonk<F>(F);
 
-impl<F: FieldExt> StandardPlonk<F> {
+impl<F: PrimeField> StandardPlonk<F> {
     pub fn rand<R: RngCore>(mut rng: R) -> Self {
         Self(F::from(rng.next_u32() as u64))
     }
@@ -73,9 +73,11 @@ impl<F: FieldExt> StandardPlonk<F> {
     }
 }
 
-impl<F: FieldExt> Circuit<F> for StandardPlonk<F> {
+impl<F: PrimeField> Circuit<F> for StandardPlonk<F> {
     type Config = StandardPlonkConfig;
     type FloorPlanner = V1;
+    #[cfg(feature = "halo2_circuit_params")]
+    type Params = ();
 
     fn without_witnesses(&self) -> Self {
         Self::default()
@@ -95,7 +97,7 @@ impl<F: FieldExt> Circuit<F> for StandardPlonk<F> {
             || "",
             |mut region| {
                 region.assign_advice(|| "", config.a, 0, || Value::known(self.0))?;
-                region.assign_fixed(|| "", config.q_a, 0, || Value::known(-F::one()))?;
+                region.assign_fixed(|| "", config.q_a, 0, || Value::known(-F::ONE))?;
 
                 region.assign_advice(|| "", config.a, 1, || Value::known(-F::from(5)))?;
                 for (column, idx) in [
@@ -111,7 +113,7 @@ impl<F: FieldExt> Circuit<F> for StandardPlonk<F> {
                     region.assign_fixed(|| "", *column, 1, || Value::known(F::from(idx)))?;
                 }
 
-                let a = region.assign_advice(|| "", config.a, 2, || Value::known(F::one()))?;
+                let a = region.assign_advice(|| "", config.a, 2, || Value::known(F::ONE))?;
                 a.copy_advice(|| "", &mut region, config.b, 3)?;
                 a.copy_advice(|| "", &mut region, config.c, 4)?;
 
diff --git a/snark-verifier/src/system/halo2/test/kzg.rs b/snark-verifier/src/system/halo2/test/kzg.rs
index c8b4fc77..107af76e 100644
--- a/snark-verifier/src/system/halo2/test/kzg.rs
+++ b/snark-verifier/src/system/halo2/test/kzg.rs
@@ -1,6 +1,6 @@
 use crate::{
     system::halo2::test::{read_or_create_srs, MainGateWithRange},
-    util::arithmetic::{fe_to_limbs, CurveAffine, MultiMillerLoop},
+    util::arithmetic::{fe_to_limbs, CurveAffine, MultiMillerLoop, PrimeField},
 };
 use halo2_curves::serde::SerdeObject;
 use halo2_proofs::poly::{commitment::ParamsProver, kzg::commitment::ParamsKZG};
@@ -19,13 +19,17 @@ pub const TESTDATA_DIR: &str = "./src/system/halo2/test/kzg/testdata";
 pub const LIMBS: usize = 4;
 pub const BITS: usize = 68;
 
-pub fn setup<M: MultiMillerLoop>(k: u32) -> ParamsKZG<M> {
+pub fn setup<M: MultiMillerLoop>(k: u32) -> ParamsKZG<M>
+where
+    M::Scalar: PrimeField,
+{
     ParamsKZG::<M>::setup(k, ChaCha20Rng::from_seed(Default::default()))
 }
 
 pub fn main_gate_with_range_with_mock_kzg_accumulator<M: MultiMillerLoop>(
 ) -> MainGateWithRange<M::Scalar>
 where
+    M::Scalar: PrimeField,
     M::G1Affine: SerdeObject,
     M::G2Affine: SerdeObject,
 {
diff --git a/snark-verifier/src/system/halo2/test/kzg/halo2.rs b/snark-verifier/src/system/halo2/test/kzg/halo2.rs
index 1fd461da..df297811 100644
--- a/snark-verifier/src/system/halo2/test/kzg/halo2.rs
+++ b/snark-verifier/src/system/halo2/test/kzg/halo2.rs
@@ -254,6 +254,8 @@ impl Accumulation {
 impl Circuit<Fr> for Accumulation {
     type Config = MainGateWithRangeConfig;
     type FloorPlanner = V1;
+    #[cfg(feature = "halo2_circuit_params")]
+    type Params = ();
 
     fn without_witnesses(&self) -> Self {
         Self {
diff --git a/snark-verifier/src/system/halo2/transcript.rs b/snark-verifier/src/system/halo2/transcript.rs
index 6de1b739..09896029 100644
--- a/snark-verifier/src/system/halo2/transcript.rs
+++ b/snark-verifier/src/system/halo2/transcript.rs
@@ -3,7 +3,7 @@
 use crate::{
     loader::native::{self, NativeLoader},
     util::{
-        arithmetic::CurveAffine,
+        arithmetic::{CurveAffine, FromUniformBytes},
         transcript::{Transcript, TranscriptRead, TranscriptWrite},
     },
     Error,
@@ -17,7 +17,10 @@ pub mod evm;
 #[cfg(feature = "loader_halo2")]
 pub mod halo2;
 
-impl<C: CurveAffine, R: Read> Transcript<C, NativeLoader> for Blake2bRead<R, C, Challenge255<C>> {
+impl<C: CurveAffine, R: Read> Transcript<C, NativeLoader> for Blake2bRead<R, C, Challenge255<C>>
+where
+    C::Scalar: FromUniformBytes<64>,
+{
     fn loader(&self) -> &NativeLoader {
         &native::LOADER
     }
@@ -37,8 +40,9 @@ impl<C: CurveAffine, R: Read> Transcript<C, NativeLoader> for Blake2bRead<R, C,
     }
 }
 
-impl<C: CurveAffine, R: Read> TranscriptRead<C, NativeLoader>
-    for Blake2bRead<R, C, Challenge255<C>>
+impl<C: CurveAffine, R: Read> TranscriptRead<C, NativeLoader> for Blake2bRead<R, C, Challenge255<C>>
+where
+    C::Scalar: FromUniformBytes<64>,
 {
     fn read_scalar(&mut self) -> Result<C::Scalar, Error> {
         halo2_proofs::transcript::TranscriptRead::read_scalar(self)
@@ -51,7 +55,10 @@ impl<C: CurveAffine, R: Read> TranscriptRead<C, NativeLoader>
     }
 }
 
-impl<C: CurveAffine, W: Write> Transcript<C, NativeLoader> for Blake2bWrite<W, C, Challenge255<C>> {
+impl<C: CurveAffine, W: Write> Transcript<C, NativeLoader> for Blake2bWrite<W, C, Challenge255<C>>
+where
+    C::Scalar: FromUniformBytes<64>,
+{
     fn loader(&self) -> &NativeLoader {
         &native::LOADER
     }
@@ -71,13 +78,19 @@ impl<C: CurveAffine, W: Write> Transcript<C, NativeLoader> for Blake2bWrite<W, C
     }
 }
 
-impl<C: CurveAffine> TranscriptWrite<C> for Blake2bWrite<Vec<u8>, C, Challenge255<C>> {
+impl<C: CurveAffine> TranscriptWrite<C> for Blake2bWrite<Vec<u8>, C, Challenge255<C>>
+where
+    C::Scalar: FromUniformBytes<64>,
+{
     fn write_scalar(&mut self, scalar: C::Scalar) -> Result<(), Error> {
         halo2_proofs::transcript::TranscriptWrite::write_scalar(self, scalar)
             .map_err(|err| Error::Transcript(err.kind(), err.to_string()))
     }
 
-    fn write_ec_point(&mut self, ec_point: C) -> Result<(), Error> {
+    fn write_ec_point(&mut self, ec_point: C) -> Result<(), Error>
+    where
+        C::Scalar: FromUniformBytes<64>,
+    {
         halo2_proofs::transcript::TranscriptWrite::write_point(self, ec_point)
             .map_err(|err| Error::Transcript(err.kind(), err.to_string()))
     }
diff --git a/snark-verifier/src/system/halo2/transcript/halo2.rs b/snark-verifier/src/system/halo2/transcript/halo2.rs
index 8519a8ca..c05cace9 100644
--- a/snark-verifier/src/system/halo2/transcript/halo2.rs
+++ b/snark-verifier/src/system/halo2/transcript/halo2.rs
@@ -7,7 +7,7 @@ use crate::{
         Loader, ScalarLoader,
     },
     util::{
-        arithmetic::{fe_to_fe, CurveAffine, PrimeField},
+        arithmetic::{fe_to_fe, CurveAffine, FromUniformBytes, PrimeField},
         hash::Poseidon,
         transcript::{Transcript, TranscriptRead, TranscriptWrite},
         Itertools,
@@ -58,6 +58,7 @@ impl<'a, C, R, EccChip, const T: usize, const RATE: usize, const R_F: usize, con
     PoseidonTranscript<C, Rc<Halo2Loader<'a, C, EccChip>>, Value<R>, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
     EccChip: NativeEncoding<'a, C>,
 {
@@ -77,6 +78,7 @@ impl<'a, C, R, EccChip, const T: usize, const RATE: usize, const R_F: usize, con
     for PoseidonTranscript<C, Rc<Halo2Loader<'a, C, EccChip>>, Value<R>, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
     EccChip: NativeEncoding<'a, C>,
 {
@@ -120,6 +122,7 @@ impl<'a, C, R, EccChip, const T: usize, const RATE: usize, const R_F: usize, con
     for PoseidonTranscript<C, Rc<Halo2Loader<'a, C, EccChip>>, Value<R>, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
     EccChip: NativeEncoding<'a, C>,
 {
@@ -156,6 +159,8 @@ where
 
 impl<C: CurveAffine, S, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize>
     PoseidonTranscript<C, NativeLoader, S, T, RATE, R_F, R_P>
+where
+    C::Scalar: FromUniformBytes<64>,
 {
     /// Initialize [`PoseidonTranscript`] given readable or writeable stream for
     /// verifying or proving with [`NativeLoader`].
@@ -170,6 +175,8 @@ impl<C: CurveAffine, S, const T: usize, const RATE: usize, const R_F: usize, con
 
 impl<C: CurveAffine, S, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize>
     Transcript<C, NativeLoader> for PoseidonTranscript<C, NativeLoader, S, T, RATE, R_F, R_P>
+where
+    C::Scalar: FromUniformBytes<64>,
 {
     fn loader(&self) -> &NativeLoader {
         &native::LOADER
@@ -207,6 +214,7 @@ impl<C, R, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     TranscriptRead<C, NativeLoader> for PoseidonTranscript<C, NativeLoader, R, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
 {
     fn read_scalar(&mut self) -> Result<C::Scalar, Error> {
@@ -261,6 +269,7 @@ impl<C, W, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     for PoseidonTranscript<C, NativeLoader, W, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     W: Write,
 {
     fn write_scalar(&mut self, scalar: C::Scalar) -> Result<(), Error> {
@@ -307,6 +316,8 @@ impl<C: CurveAffine> EncodedChallenge<C> for ChallengeScalar<C> {
 impl<C: CurveAffine, S, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize>
     halo2_proofs::transcript::Transcript<C, ChallengeScalar<C>>
     for PoseidonTranscript<C, NativeLoader, S, T, RATE, R_F, R_P>
+where
+    C::Scalar: FromUniformBytes<64>,
 {
     fn squeeze_challenge(&mut self) -> ChallengeScalar<C> {
         ChallengeScalar::new(&Transcript::squeeze_challenge(self))
@@ -334,6 +345,7 @@ impl<C, R, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     for PoseidonTranscript<C, NativeLoader, R, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
 {
     fn read_point(&mut self) -> io::Result<C> {
@@ -358,6 +370,7 @@ impl<C, R, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     for PoseidonTranscript<C, NativeLoader, R, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     R: Read,
 {
     fn init(reader: R) -> Self {
@@ -370,6 +383,7 @@ impl<C, W, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     for PoseidonTranscript<C, NativeLoader, W, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     W: Write,
 {
     fn write_point(&mut self, ec_point: C) -> io::Result<()> {
@@ -392,6 +406,7 @@ impl<C, W, const T: usize, const RATE: usize, const R_F: usize, const R_P: usize
     for PoseidonTranscript<C, NativeLoader, W, T, RATE, R_F, R_P>
 where
     C: CurveAffine,
+    C::Scalar: FromUniformBytes<64>,
     W: Write,
 {
     fn init(writer: W) -> Self {
diff --git a/snark-verifier/src/util/arithmetic.rs b/snark-verifier/src/util/arithmetic.rs
index af32ded0..22924e00 100644
--- a/snark-verifier/src/util/arithmetic.rs
+++ b/snark-verifier/src/util/arithmetic.rs
@@ -11,13 +11,10 @@ use std::{
 };
 
 pub use halo2_curves::{
-    group::{
-        ff::{BatchInvert, Field, PrimeField},
-        prime::PrimeCurveAffine,
-        Curve, Group, GroupEncoding,
-    },
+    ff::{BatchInvert, Field, FromUniformBytes, PrimeField, WithSmallOrderMulGroup},
+    group::{prime::PrimeCurveAffine, Curve, Group, GroupEncoding},
     pairing::MillerLoopResult,
-    Coordinates, CurveAffine, CurveExt, FieldExt,
+    Coordinates, CurveAffine, CurveExt,
 };
 
 /// [`halo2_curves::pairing::MultiMillerLoop`] with [`std::fmt::Debug`].
@@ -51,7 +48,7 @@ pub fn batch_invert_and_mul<F: PrimeField>(values: &mut [F], coeff: &F) {
     let products = values
         .iter()
         .filter(|value| !value.is_zero_vartime())
-        .scan(F::one(), |acc, value| {
+        .scan(F::ONE, |acc, value| {
             *acc *= value;
             Some(*acc)
         })
@@ -63,7 +60,7 @@ pub fn batch_invert_and_mul<F: PrimeField>(values: &mut [F], coeff: &F) {
         .iter_mut()
         .rev()
         .filter(|value| !value.is_zero_vartime())
-        .zip(products.into_iter().rev().skip(1).chain(Some(F::one())))
+        .zip(products.into_iter().rev().skip(1).chain(Some(F::ONE)))
     {
         let mut inv = all_product_inv * product;
         mem::swap(value, &mut inv);
@@ -73,7 +70,7 @@ pub fn batch_invert_and_mul<F: PrimeField>(values: &mut [F], coeff: &F) {
 
 /// Batch invert [`PrimeField`] elements.
 pub fn batch_invert<F: PrimeField>(values: &mut [F]) {
-    batch_invert_and_mul(values, &F::one())
+    batch_invert_and_mul(values, &F::ONE)
 }
 
 /// Root of unity of 2^k-sized multiplicative subgroup of [`PrimeField`] by
@@ -86,7 +83,7 @@ pub fn batch_invert<F: PrimeField>(values: &mut [F]) {
 pub fn root_of_unity<F: PrimeField>(k: usize) -> F {
     assert!(k <= F::S as usize);
 
-    iter::successors(Some(F::root_of_unity()), |acc| Some(acc.square()))
+    iter::successors(Some(F::ROOT_OF_UNITY), |acc| Some(acc.square()))
         .take(F::S as usize - k + 1)
         .last()
         .unwrap()
@@ -244,7 +241,7 @@ impl<T: FieldOps + Clone> Fraction<T> {
 
 /// Modulus of a [`PrimeField`]
 pub fn modulus<F: PrimeField>() -> BigUint {
-    fe_to_big(-F::one()) + 1usize
+    fe_to_big(-F::ONE) + 1usize
 }
 
 /// Convert a [`BigUint`] into a [`PrimeField`] .
@@ -300,7 +297,7 @@ pub fn fe_to_limbs<F1: PrimeField, F2: PrimeField, const LIMBS: usize, const BIT
 
 /// Returns iterator that yields scalar^0, scalar^1, scalar^2...
 pub fn powers<F: Field>(scalar: F) -> impl Iterator<Item = F> {
-    iter::successors(Some(F::one()), move |power| Some(scalar * power))
+    iter::successors(Some(F::ONE), move |power| Some(scalar * power))
 }
 
 /// Compute inner product of 2 slice of [`Field`].
diff --git a/snark-verifier/src/util/hash/poseidon.rs b/snark-verifier/src/util/hash/poseidon.rs
index 60d55d9f..99e2d6ac 100644
--- a/snark-verifier/src/util/hash/poseidon.rs
+++ b/snark-verifier/src/util/hash/poseidon.rs
@@ -1,17 +1,20 @@
 use crate::{
     loader::{LoadedScalar, ScalarLoader},
-    util::{arithmetic::FieldExt, Itertools},
+    util::{
+        arithmetic::{FromUniformBytes, PrimeField},
+        Itertools,
+    },
 };
 use poseidon::{self, SparseMDSMatrix, Spec};
 use std::{iter, marker::PhantomData, mem};
 
 #[derive(Debug)]
-struct State<F: FieldExt, L, const T: usize, const RATE: usize> {
+struct State<F: PrimeField, L, const T: usize, const RATE: usize> {
     inner: [L; T],
     _marker: PhantomData<F>,
 }
 
-impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> State<F, L, T, RATE> {
+impl<F: PrimeField, L: LoadedScalar<F>, const T: usize, const RATE: usize> State<F, L, T, RATE> {
     fn new(inner: [L; T]) -> Self {
         Self {
             inner,
@@ -62,7 +65,7 @@ impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> State<F
                 *state = state.loader().sum_with_const(
                     &[state],
                     if idx == 0 {
-                        F::one() + constant
+                        F::ONE + constant
                     } else {
                         *constant
                     },
@@ -98,7 +101,7 @@ impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> State<F
                 .zip(self.inner.iter().skip(1))
                 .map(|(coeff, state)| {
                     self.loader()
-                        .sum_with_coeff(&[(*coeff, &self.inner[0]), (F::one(), state)])
+                        .sum_with_coeff(&[(*coeff, &self.inner[0]), (F::ONE, state)])
                 }),
         )
         .collect_vec()
@@ -109,13 +112,15 @@ impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> State<F
 
 /// Poseidon hasher with configurable `RATE`.
 #[derive(Debug)]
-pub struct Poseidon<F: FieldExt, L, const T: usize, const RATE: usize> {
+pub struct Poseidon<F: PrimeField, L, const T: usize, const RATE: usize> {
     spec: Spec<F, T, RATE>,
     state: State<F, L, T, RATE>,
     buf: Vec<L>,
 }
 
-impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> Poseidon<F, L, T, RATE> {
+impl<F: FromUniformBytes<64>, L: LoadedScalar<F>, const T: usize, const RATE: usize>
+    Poseidon<F, L, T, RATE>
+{
     /// Initialize a poseidon hasher.
     pub fn new(loader: &L::Loader, r_f: usize, r_p: usize) -> Self {
         Self {
@@ -179,7 +184,7 @@ impl<F: FieldExt, L: LoadedScalar<F>, const T: usize, const RATE: usize> Poseido
             self.state.sbox_full(constants);
             self.state.apply_mds(&mds);
         }
-        self.state.sbox_full(&[F::zero(); T]);
+        self.state.sbox_full(&[F::ZERO; T]);
         self.state.apply_mds(&mds);
     }
 }
diff --git a/snark-verifier/src/util/poly.rs b/snark-verifier/src/util/poly.rs
index eef2f593..752b269d 100644
--- a/snark-verifier/src/util/poly.rs
+++ b/snark-verifier/src/util/poly.rs
@@ -57,7 +57,7 @@ impl<F: Field> Polynomial<F> {
             coeffs
                 .iter()
                 .rev()
-                .fold(F::zero(), |acc, coeff| acc * x + coeff)
+                .fold(F::ZERO, |acc, coeff| acc * x + coeff)
         };
 
         #[cfg(feature = "parallel")]
@@ -71,7 +71,7 @@ impl<F: Field> Polynomial<F> {
             }
 
             let chunk_size = Integer::div_ceil(&self.len(), &num_threads);
-            let mut results = vec![F::zero(); num_threads];
+            let mut results = vec![F::ZERO; num_threads];
             parallelize_iter(
                 results
                     .iter_mut()
@@ -79,7 +79,7 @@ impl<F: Field> Polynomial<F> {
                     .zip(powers(x.pow_vartime(&[chunk_size as u64, 0, 0, 0]))),
                 |((result, coeffs), scalar)| *result = evaluate_serial(coeffs) * scalar,
             );
-            results.iter().fold(F::zero(), |acc, result| acc + result)
+            results.iter().fold(F::ZERO, |acc, result| acc + result)
         }
         #[cfg(not(feature = "parallel"))]
         evaluate_serial(&self.0)
@@ -134,10 +134,10 @@ impl<F: Field> Mul<F> for Polynomial<F> {
     type Output = Polynomial<F>;
 
     fn mul(mut self, rhs: F) -> Polynomial<F> {
-        if rhs == F::zero() {
-            return Polynomial::new(vec![F::zero(); self.len()]);
+        if rhs == F::ZERO {
+            return Polynomial::new(vec![F::ZERO; self.len()]);
         }
-        if rhs == F::one() {
+        if rhs == F::ONE {
             return self;
         }
         parallelize(&mut self.0, |(lhs, _)| {
diff --git a/snark-verifier/src/verifier/plonk/proof.rs b/snark-verifier/src/verifier/plonk/proof.rs
index 962417ec..27123d87 100644
--- a/snark-verifier/src/verifier/plonk/proof.rs
+++ b/snark-verifier/src/verifier/plonk/proof.rs
@@ -175,7 +175,7 @@ where
             .map(|query| {
                 let shift = protocol
                     .domain
-                    .rotate_scalar(C::Scalar::one(), query.rotation);
+                    .rotate_scalar(C::Scalar::ONE, query.rotation);
                 pcs::Query::new(query.poly, shift)
             })
             .collect()
diff --git a/snark-verifier/src/verifier/plonk/protocol.rs b/snark-verifier/src/verifier/plonk/protocol.rs
index 3cf8e462..94d107ce 100644
--- a/snark-verifier/src/verifier/plonk/protocol.rs
+++ b/snark-verifier/src/verifier/plonk/protocol.rs
@@ -208,7 +208,7 @@ where
         let numer = zn_minus_one.clone() * &n_inv;
         let omegas = langranges
             .iter()
-            .map(|&i| loader.load_const(&domain.rotate_scalar(C::Scalar::one(), Rotation(i))))
+            .map(|&i| loader.load_const(&domain.rotate_scalar(C::Scalar::ONE, Rotation(i))))
             .collect_vec();
         let lagrange_evals = omegas
             .iter()
@@ -485,7 +485,7 @@ impl<F: Clone + Default> Sum for Expression<F> {
 
 impl<F: Field> One for Expression<F> {
     fn one() -> Self {
-        Expression::Constant(F::one())
+        Expression::Constant(F::ONE)
     }
 }