diff --git a/src/bellperson/mod.rs b/src/bellperson/mod.rs
index 6686fa2..0e0d8c8 100644
--- a/src/bellperson/mod.rs
+++ b/src/bellperson/mod.rs
@@ -8,10 +8,13 @@ pub mod solver;
 
 #[cfg(test)]
 mod tests {
-  use crate::bellperson::{
-    r1cs::{NovaShape, NovaWitness},
-    shape_cs::ShapeCS,
-    solver::SatisfyingAssignment,
+  use crate::{
+    bellperson::{
+      r1cs::{NovaShape, NovaWitness},
+      shape_cs::ShapeCS,
+      solver::SatisfyingAssignment,
+    },
+    traits::Group,
   };
   use bellperson::{gadgets::num::AllocatedNum, ConstraintSystem, SynthesisError};
   use ff::PrimeField;
@@ -39,10 +42,10 @@ mod tests {
     Ok(())
   }
 
-  #[test]
-  fn test_alloc_bit() {
-    type G = pasta_curves::pallas::Point;
-
+  fn test_alloc_bit_with<G>()
+  where
+    G: Group,
+  {
     // First create the shape
     let mut cs: ShapeCS<G> = ShapeCS::new();
     let _ = synthesize_alloc_bit(&mut cs);
@@ -56,4 +59,10 @@ mod tests {
     // Make sure that this is satisfiable
     assert!(shape.is_sat(&ck, &inst, &witness).is_ok());
   }
+
+  #[test]
+  fn test_alloc_bit() {
+    type G = pasta_curves::pallas::Point;
+    test_alloc_bit_with::<G>();
+  }
 }
diff --git a/src/circuit.rs b/src/circuit.rs
index 614e61c..d9ef590 100644
--- a/src/circuit.rs
+++ b/src/circuit.rs
@@ -372,8 +372,8 @@ impl<G: Group, SC: StepCircuit<G::Base>> Circuit<<G as Group>::Base>
 mod tests {
   use super::*;
   use crate::bellperson::{shape_cs::ShapeCS, solver::SatisfyingAssignment};
-  type G1 = pasta_curves::pallas::Point;
-  type G2 = pasta_curves::vesta::Point;
+  type PastaG1 = pasta_curves::pallas::Point;
+  type PastaG2 = pasta_curves::vesta::Point;
 
   use crate::constants::{BN_LIMB_WIDTH, BN_N_LIMBS};
   use crate::{
@@ -383,18 +383,22 @@ mod tests {
     traits::{circuit::TrivialTestCircuit, ROConstantsTrait},
   };
 
-  #[test]
-  fn test_recursive_circuit() {
-    // In the following we use 1 to refer to the primary, and 2 to refer to the secondary circuit
-    let params1 = NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, true);
-    let params2 = NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, false);
-    let ro_consts1: ROConstantsCircuit<G2> = PoseidonConstantsCircuit::new();
-    let ro_consts2: ROConstantsCircuit<G1> = PoseidonConstantsCircuit::new();
-
+  // In the following we use 1 to refer to the primary, and 2 to refer to the secondary circuit
+  fn test_recursive_circuit_with<G1, G2>(
+    primary_params: NovaAugmentedCircuitParams,
+    secondary_params: NovaAugmentedCircuitParams,
+    ro_consts1: ROConstantsCircuit<G2>,
+    ro_consts2: ROConstantsCircuit<G1>,
+    num_constraints_primary: usize,
+    num_constraints_secondary: usize,
+  ) where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+  {
     // Initialize the shape and ck for the primary
     let circuit1: NovaAugmentedCircuit<G2, TrivialTestCircuit<<G2 as Group>::Base>> =
       NovaAugmentedCircuit::new(
-        params1.clone(),
+        primary_params.clone(),
         None,
         TrivialTestCircuit::default(),
         ro_consts1.clone(),
@@ -402,12 +406,12 @@ mod tests {
     let mut cs: ShapeCS<G1> = ShapeCS::new();
     let _ = circuit1.synthesize(&mut cs);
     let (shape1, ck1) = cs.r1cs_shape();
-    assert_eq!(cs.num_constraints(), 9815);
+    assert_eq!(cs.num_constraints(), num_constraints_primary);
 
     // Initialize the shape and ck for the secondary
     let circuit2: NovaAugmentedCircuit<G1, TrivialTestCircuit<<G1 as Group>::Base>> =
       NovaAugmentedCircuit::new(
-        params2.clone(),
+        secondary_params.clone(),
         None,
         TrivialTestCircuit::default(),
         ro_consts2.clone(),
@@ -415,7 +419,7 @@ mod tests {
     let mut cs: ShapeCS<G2> = ShapeCS::new();
     let _ = circuit2.synthesize(&mut cs);
     let (shape2, ck2) = cs.r1cs_shape();
-    assert_eq!(cs.num_constraints(), 10347);
+    assert_eq!(cs.num_constraints(), num_constraints_secondary);
 
     // Execute the base case for the primary
     let zero1 = <<G2 as Group>::Base as Field>::ZERO;
@@ -431,7 +435,7 @@ mod tests {
     );
     let circuit1: NovaAugmentedCircuit<G2, TrivialTestCircuit<<G2 as Group>::Base>> =
       NovaAugmentedCircuit::new(
-        params1,
+        primary_params,
         Some(inputs1),
         TrivialTestCircuit::default(),
         ro_consts1,
@@ -453,16 +457,28 @@ mod tests {
       Some(inst1),
       None,
     );
-    let circuit: NovaAugmentedCircuit<G1, TrivialTestCircuit<<G1 as Group>::Base>> =
+    let circuit2: NovaAugmentedCircuit<G1, TrivialTestCircuit<<G1 as Group>::Base>> =
       NovaAugmentedCircuit::new(
-        params2,
+        secondary_params,
         Some(inputs2),
         TrivialTestCircuit::default(),
         ro_consts2,
       );
-    let _ = circuit.synthesize(&mut cs2);
+    let _ = circuit2.synthesize(&mut cs2);
     let (inst2, witness2) = cs2.r1cs_instance_and_witness(&shape2, &ck2).unwrap();
     // Make sure that it is satisfiable
     assert!(shape2.is_sat(&ck2, &inst2, &witness2).is_ok());
   }
+
+  #[test]
+  fn test_recursive_circuit() {
+    let params1 = NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, true);
+    let params2 = NovaAugmentedCircuitParams::new(BN_LIMB_WIDTH, BN_N_LIMBS, false);
+    let ro_consts1: ROConstantsCircuit<PastaG2> = PoseidonConstantsCircuit::new();
+    let ro_consts2: ROConstantsCircuit<PastaG1> = PoseidonConstantsCircuit::new();
+
+    test_recursive_circuit_with::<PastaG1, PastaG2>(
+      params1, params2, ro_consts1, ro_consts2, 9815, 10347,
+    );
+  }
 }
diff --git a/src/gadgets/ecc.rs b/src/gadgets/ecc.rs
index 0947826..104a027 100644
--- a/src/gadgets/ecc.rs
+++ b/src/gadgets/ecc.rs
@@ -975,16 +975,14 @@ mod tests {
 
   #[test]
   fn test_ecc_circuit_ops() {
-    test_ecc_circuit_ops_with::<pallas::Base, pallas::Scalar, pallas::Point, vesta::Point>();
-    test_ecc_circuit_ops_with::<vesta::Base, vesta::Scalar, vesta::Point, pallas::Point>();
+    test_ecc_circuit_ops_with::<pallas::Point, vesta::Point>();
+    test_ecc_circuit_ops_with::<vesta::Point, pallas::Point>();
   }
 
-  fn test_ecc_circuit_ops_with<B, S, G1, G2>()
+  fn test_ecc_circuit_ops_with<G1, G2>()
   where
-    B: PrimeField,
-    S: PrimeField,
-    G1: Group<Base = B, Scalar = S>,
-    G2: Group<Base = S, Scalar = B>,
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
   {
     // First create the shape
     let mut cs: ShapeCS<G2> = ShapeCS::new();
@@ -1027,16 +1025,14 @@ mod tests {
 
   #[test]
   fn test_ecc_circuit_add_equal() {
-    test_ecc_circuit_add_equal_with::<pallas::Base, pallas::Scalar, pallas::Point, vesta::Point>();
-    test_ecc_circuit_add_equal_with::<vesta::Base, vesta::Scalar, vesta::Point, pallas::Point>();
+    test_ecc_circuit_add_equal_with::<pallas::Point, vesta::Point>();
+    test_ecc_circuit_add_equal_with::<vesta::Point, pallas::Point>();
   }
 
-  fn test_ecc_circuit_add_equal_with<B, S, G1, G2>()
+  fn test_ecc_circuit_add_equal_with<G1, G2>()
   where
-    B: PrimeField,
-    S: PrimeField,
-    G1: Group<Base = B, Scalar = S>,
-    G2: Group<Base = S, Scalar = B>,
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
   {
     // First create the shape
     let mut cs: ShapeCS<G2> = ShapeCS::new();
@@ -1083,17 +1079,14 @@ mod tests {
 
   #[test]
   fn test_ecc_circuit_add_negation() {
-    test_ecc_circuit_add_negation_with::<pallas::Base, pallas::Scalar, pallas::Point, vesta::Point>(
-    );
-    test_ecc_circuit_add_negation_with::<vesta::Base, vesta::Scalar, vesta::Point, pallas::Point>();
+    test_ecc_circuit_add_negation_with::<pallas::Point, vesta::Point>();
+    test_ecc_circuit_add_negation_with::<vesta::Point, pallas::Point>();
   }
 
-  fn test_ecc_circuit_add_negation_with<B, S, G1, G2>()
+  fn test_ecc_circuit_add_negation_with<G1, G2>()
   where
-    B: PrimeField,
-    S: PrimeField,
-    G1: Group<Base = B, Scalar = S>,
-    G2: Group<Base = S, Scalar = B>,
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
   {
     // First create the shape
     let mut cs: ShapeCS<G2> = ShapeCS::new();
diff --git a/src/lib.rs b/src/lib.rs
index 8ee6854..c416517 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -787,13 +787,16 @@ fn compute_digest<G: Group, T: Serialize>(o: &T) -> G::Scalar {
 
 #[cfg(test)]
 mod tests {
+  use crate::provider::pedersen::CommitmentKeyExtTrait;
+
   use super::*;
-  type G1 = pasta_curves::pallas::Point;
-  type G2 = pasta_curves::vesta::Point;
-  type EE1 = provider::ipa_pc::EvaluationEngine<G1>;
-  type EE2 = provider::ipa_pc::EvaluationEngine<G2>;
-  type S1 = spartan::RelaxedR1CSSNARK<G1, EE1>;
-  type S2 = spartan::RelaxedR1CSSNARK<G2, EE2>;
+  type EE1<G1> = provider::ipa_pc::EvaluationEngine<G1>;
+  type EE2<G2> = provider::ipa_pc::EvaluationEngine<G2>;
+  type S1<G1> = spartan::RelaxedR1CSSNARK<G1, EE1<G1>>;
+  type S2<G2> = spartan::RelaxedR1CSSNARK<G2, EE2<G2>>;
+  type S1Prime<G1> = spartan::pp::RelaxedR1CSSNARK<G1, EE1<G1>>;
+  type S2Prime<G2> = spartan::pp::RelaxedR1CSSNARK<G2, EE2<G2>>;
+
   use ::bellperson::{gadgets::num::AllocatedNum, ConstraintSystem, SynthesisError};
   use core::marker::PhantomData;
   use ff::PrimeField;
@@ -848,15 +851,21 @@ mod tests {
     }
   }
 
-  #[test]
-  fn test_ivc_trivial() {
+  fn test_ivc_trivial_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+  {
+    let test_circuit1 = TrivialTestCircuit::<<G1 as Group>::Scalar>::default();
+    let test_circuit2 = TrivialTestCircuit::<<G2 as Group>::Scalar>::default();
+
     // produce public parameters
     let pp = PublicParams::<
       G1,
       G2,
       TrivialTestCircuit<<G1 as Group>::Scalar>,
       TrivialTestCircuit<<G2 as Group>::Scalar>,
-    >::setup(TrivialTestCircuit::default(), TrivialTestCircuit::default());
+    >::setup(test_circuit1.clone(), test_circuit2.clone());
 
     let num_steps = 1;
 
@@ -864,8 +873,8 @@ mod tests {
     let res = RecursiveSNARK::prove_step(
       &pp,
       None,
-      TrivialTestCircuit::default(),
-      TrivialTestCircuit::default(),
+      test_circuit1,
+      test_circuit2,
       vec![<G1 as Group>::Scalar::ZERO],
       vec![<G2 as Group>::Scalar::ZERO],
     );
@@ -883,7 +892,17 @@ mod tests {
   }
 
   #[test]
-  fn test_ivc_nontrivial() {
+  fn test_ivc_trivial() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+    test_ivc_trivial_with::<G1, G2>();
+  }
+
+  fn test_ivc_nontrivial_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+  {
     let circuit_primary = TrivialTestCircuit::default();
     let circuit_secondary = CubicCircuit::default();
 
@@ -950,14 +969,30 @@ mod tests {
     assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::ONE]);
     let mut zn_secondary_direct = vec![<G2 as Group>::Scalar::ZERO];
     for _i in 0..num_steps {
-      zn_secondary_direct = CubicCircuit::default().output(&zn_secondary_direct);
+      zn_secondary_direct = circuit_secondary.clone().output(&zn_secondary_direct);
     }
     assert_eq!(zn_secondary, zn_secondary_direct);
     assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
   }
 
   #[test]
-  fn test_ivc_nontrivial_with_compression() {
+  fn test_ivc_nontrivial() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+
+    test_ivc_nontrivial_with::<G1, G2>();
+  }
+
+  fn test_ivc_nontrivial_with_compression_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+    // this is due to the reliance on CommitmentKeyExtTrait as a bound in ipa_pc
+    <G1::CE as CommitmentEngineTrait<G1>>::CommitmentKey:
+      CommitmentKeyExtTrait<G1, CE = <G1 as Group>::CE>,
+    <G2::CE as CommitmentEngineTrait<G2>>::CommitmentKey:
+      CommitmentKeyExtTrait<G2, CE = <G2 as Group>::CE>,
+  {
     let circuit_primary = TrivialTestCircuit::default();
     let circuit_secondary = CubicCircuit::default();
 
@@ -1012,16 +1047,16 @@ mod tests {
     assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::ONE]);
     let mut zn_secondary_direct = vec![<G2 as Group>::Scalar::ZERO];
     for _i in 0..num_steps {
-      zn_secondary_direct = CubicCircuit::default().output(&zn_secondary_direct);
+      zn_secondary_direct = circuit_secondary.clone().output(&zn_secondary_direct);
     }
     assert_eq!(zn_secondary, zn_secondary_direct);
     assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
 
     // produce the prover and verifier keys for compressed snark
-    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
+    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1<G1>, S2<G2>>::setup(&pp).unwrap();
 
     // produce a compressed SNARK
-    let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
+    let res = CompressedSNARK::<_, _, _, _, S1<G1>, S2<G2>>::prove(&pp, &pk, &recursive_snark);
     assert!(res.is_ok());
     let compressed_snark = res.unwrap();
 
@@ -1036,7 +1071,23 @@ mod tests {
   }
 
   #[test]
-  fn test_ivc_nontrivial_with_spark_compression() {
+  fn test_ivc_nontrivial_with_compression() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+
+    test_ivc_nontrivial_with_compression_with::<G1, G2>();
+  }
+
+  fn test_ivc_nontrivial_with_spark_compression_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+    // this is due to the reliance on CommitmentKeyExtTrait as a bound in ipa_pc
+    <G1::CE as CommitmentEngineTrait<G1>>::CommitmentKey:
+      CommitmentKeyExtTrait<G1, CE = <G1 as Group>::CE>,
+    <G2::CE as CommitmentEngineTrait<G2>>::CommitmentKey:
+      CommitmentKeyExtTrait<G2, CE = <G2 as Group>::CE>,
+  {
     let circuit_primary = TrivialTestCircuit::default();
     let circuit_secondary = CubicCircuit::default();
 
@@ -1097,14 +1148,13 @@ mod tests {
     assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(2460515u64)]);
 
     // run the compressed snark with Spark compiler
-    type S1Prime = spartan::pp::RelaxedR1CSSNARK<G1, EE1>;
-    type S2Prime = spartan::pp::RelaxedR1CSSNARK<G2, EE2>;
 
     // produce the prover and verifier keys for compressed snark
-    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1Prime, S2Prime>::setup(&pp).unwrap();
+    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1Prime<G1>, S2Prime<G2>>::setup(&pp).unwrap();
 
     // produce a compressed SNARK
-    let res = CompressedSNARK::<_, _, _, _, S1Prime, S2Prime>::prove(&pp, &pk, &recursive_snark);
+    let res =
+      CompressedSNARK::<_, _, _, _, S1Prime<G1>, S2Prime<G2>>::prove(&pp, &pk, &recursive_snark);
     assert!(res.is_ok());
     let compressed_snark = res.unwrap();
 
@@ -1119,7 +1169,23 @@ mod tests {
   }
 
   #[test]
-  fn test_ivc_nondet_with_compression() {
+  fn test_ivc_nontrivial_with_spark_compression() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+
+    test_ivc_nontrivial_with_spark_compression_with::<G1, G2>();
+  }
+
+  fn test_ivc_nondet_with_compression_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+    // this is due to the reliance on CommitmentKeyExtTrait as a bound in ipa_pc
+    <G1::CE as CommitmentEngineTrait<G1>>::CommitmentKey:
+      CommitmentKeyExtTrait<G1, CE = <G1 as Group>::CE>,
+    <G2::CE as CommitmentEngineTrait<G2>>::CommitmentKey:
+      CommitmentKeyExtTrait<G2, CE = <G2 as Group>::CE>,
+  {
     // y is a non-deterministic advice representing the fifth root of the input at a step.
     #[derive(Clone, Debug)]
     struct FifthRootCheckingCircuit<F: PrimeField> {
@@ -1252,10 +1318,10 @@ mod tests {
     assert!(res.is_ok());
 
     // produce the prover and verifier keys for compressed snark
-    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
+    let (pk, vk) = CompressedSNARK::<_, _, _, _, S1<G1>, S2<G2>>::setup(&pp).unwrap();
 
     // produce a compressed SNARK
-    let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
+    let res = CompressedSNARK::<_, _, _, _, S1<G1>, S2<G2>>::prove(&pp, &pk, &recursive_snark);
     assert!(res.is_ok());
     let compressed_snark = res.unwrap();
 
@@ -1265,7 +1331,18 @@ mod tests {
   }
 
   #[test]
-  fn test_ivc_base() {
+  fn test_ivc_nondet_with_compression() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+
+    test_ivc_nondet_with_compression_with::<G1, G2>();
+  }
+
+  fn test_ivc_base_with<G1, G2>()
+  where
+    G1: Group<Base = <G2 as Group>::Scalar>,
+    G2: Group<Base = <G1 as Group>::Scalar>,
+  {
     // produce public parameters
     let pp = PublicParams::<
       G1,
@@ -1302,4 +1379,12 @@ mod tests {
     assert_eq!(zn_primary, vec![<G1 as Group>::Scalar::ONE]);
     assert_eq!(zn_secondary, vec![<G2 as Group>::Scalar::from(5u64)]);
   }
+
+  #[test]
+  fn test_ivc_base() {
+    type G1 = pasta_curves::pallas::Point;
+    type G2 = pasta_curves::vesta::Point;
+
+    test_ivc_base_with::<G1, G2>();
+  }
 }
diff --git a/src/nifs.rs b/src/nifs.rs
index 0993349..2187a5d 100644
--- a/src/nifs.rs
+++ b/src/nifs.rs
@@ -162,8 +162,10 @@ mod tests {
     Ok(())
   }
 
-  #[test]
-  fn test_tiny_r1cs_bellperson() {
+  fn test_tiny_r1cs_bellperson_with<G>()
+  where
+    G: Group,
+  {
     use crate::bellperson::{
       r1cs::{NovaShape, NovaWitness},
       shape_cs::ShapeCS,
@@ -179,7 +181,7 @@ mod tests {
 
     // Now get the instance and assignment for one instance
     let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
-    let _ = synthesize_tiny_r1cs_bellperson(&mut cs, Some(S::from(5)));
+    let _ = synthesize_tiny_r1cs_bellperson(&mut cs, Some(G::Scalar::from(5)));
     let (U1, W1) = cs.r1cs_instance_and_witness(&shape, &ck).unwrap();
 
     // Make sure that the first instance is satisfiable
@@ -187,7 +189,7 @@ mod tests {
 
     // Now get the instance and assignment for second instance
     let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
-    let _ = synthesize_tiny_r1cs_bellperson(&mut cs, Some(S::from(135)));
+    let _ = synthesize_tiny_r1cs_bellperson(&mut cs, Some(G::Scalar::from(135)));
     let (U2, W2) = cs.r1cs_instance_and_witness(&shape, &ck).unwrap();
 
     // Make sure that the second instance is satisfiable
@@ -206,8 +208,13 @@ mod tests {
     );
   }
 
+  #[test]
+  fn test_tiny_r1cs_bellperson() {
+    test_tiny_r1cs_bellperson_with::<G>();
+  }
+
   #[allow(clippy::too_many_arguments)]
-  fn execute_sequence(
+  fn execute_sequence<G>(
     ck: &CommitmentKey<G>,
     ro_consts: &<<G as Group>::RO as ROTrait<<G as Group>::Base, <G as Group>::Scalar>>::Constants,
     pp_digest: &<G as Group>::Scalar,
@@ -216,7 +223,9 @@ mod tests {
     W1: &R1CSWitness<G>,
     U2: &R1CSInstance<G>,
     W2: &R1CSWitness<G>,
-  ) {
+  ) where
+    G: Group,
+  {
     // produce a default running instance
     let mut r_W = RelaxedR1CSWitness::default(shape);
     let mut r_U = RelaxedR1CSInstance::default(ck, shape);
diff --git a/src/provider/keccak.rs b/src/provider/keccak.rs
index 2629e7c..a4daf18 100644
--- a/src/provider/keccak.rs
+++ b/src/provider/keccak.rs
@@ -101,10 +101,7 @@ mod tests {
   use ff::PrimeField;
   use sha3::{Digest, Keccak256};
 
-  type G = pasta_curves::pallas::Point;
-
-  #[test]
-  fn test_keccak_transcript() {
+  fn test_keccak_transcript_with<G: Group>() {
     let mut transcript: Keccak256Transcript<G> = Keccak256Transcript::new(b"test");
 
     // two scalars
@@ -136,6 +133,12 @@ mod tests {
     );
   }
 
+  #[test]
+  fn test_keccak_transcript() {
+    type G = pasta_curves::pallas::Point;
+    test_keccak_transcript_with::<G>()
+  }
+
   #[test]
   fn test_keccak_example() {
     let mut hasher = Keccak256::new();
diff --git a/src/provider/poseidon.rs b/src/provider/poseidon.rs
index eee606d..2445984 100644
--- a/src/provider/poseidon.rs
+++ b/src/provider/poseidon.rs
@@ -201,27 +201,31 @@ where
 #[cfg(test)]
 mod tests {
   use super::*;
-  type S = pasta_curves::pallas::Scalar;
-  type B = pasta_curves::vesta::Scalar;
-  type G = pasta_curves::pallas::Point;
   use crate::{
     bellperson::solver::SatisfyingAssignment, constants::NUM_CHALLENGE_BITS,
-    gadgets::utils::le_bits_to_num,
+    gadgets::utils::le_bits_to_num, traits::Group,
   };
   use ff::Field;
   use rand::rngs::OsRng;
 
-  #[test]
-  fn test_poseidon_ro() {
+  fn test_poseidon_ro_with<G: Group>()
+  where
+    // we can print the field elements we get from G's Base & Scalar fields,
+    // and compare their byte representations
+    <<G as Group>::Base as PrimeField>::Repr: std::fmt::Debug,
+    <<G as Group>::Scalar as PrimeField>::Repr: std::fmt::Debug,
+    <<G as Group>::Base as PrimeField>::Repr: PartialEq<<<G as Group>::Scalar as PrimeField>::Repr>,
+  {
     // Check that the number computed inside the circuit is equal to the number computed outside the circuit
     let mut csprng: OsRng = OsRng;
-    let constants = PoseidonConstantsCircuit::new();
+    let constants = PoseidonConstantsCircuit::<G::Scalar>::new();
     let num_absorbs = 32;
-    let mut ro: PoseidonRO<S, B> = PoseidonRO::new(constants.clone(), num_absorbs);
-    let mut ro_gadget: PoseidonROCircuit<S> = PoseidonROCircuit::new(constants, num_absorbs);
+    let mut ro: PoseidonRO<G::Scalar, G::Base> = PoseidonRO::new(constants.clone(), num_absorbs);
+    let mut ro_gadget: PoseidonROCircuit<G::Scalar> =
+      PoseidonROCircuit::new(constants, num_absorbs);
     let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
     for i in 0..num_absorbs {
-      let num = S::random(&mut csprng);
+      let num = G::Scalar::random(&mut csprng);
       ro.absorb(num);
       let num_gadget =
         AllocatedNum::alloc(cs.namespace(|| format!("data {i}")), || Ok(num)).unwrap();
@@ -235,4 +239,11 @@ mod tests {
     let num2 = le_bits_to_num(&mut cs, num2_bits).unwrap();
     assert_eq!(num.to_repr(), num2.get_value().unwrap().to_repr());
   }
+
+  #[test]
+  fn test_poseidon_ro() {
+    type G = pasta_curves::pallas::Point;
+
+    test_poseidon_ro_with::<G>()
+  }
 }
diff --git a/src/spartan/pp.rs b/src/spartan/pp.rs
index 08dc6f7..70c4c71 100644
--- a/src/spartan/pp.rs
+++ b/src/spartan/pp.rs
@@ -2191,8 +2191,6 @@ impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>, C: StepCircuit<G::Scala
 #[cfg(test)]
 mod tests {
   use super::*;
-  type G = pasta_curves::pallas::Point;
-  type EE = crate::provider::ipa_pc::EvaluationEngine<G>;
   use ::bellperson::{gadgets::num::AllocatedNum, ConstraintSystem, SynthesisError};
   use core::marker::PhantomData;
   use ff::PrimeField;
@@ -2248,6 +2246,13 @@ mod tests {
 
   #[test]
   fn test_spartan_snark() {
+    type G = pasta_curves::pallas::Point;
+    type EE = crate::provider::ipa_pc::EvaluationEngine<G>;
+
+    test_spartan_snark_with::<G, EE>();
+  }
+
+  fn test_spartan_snark_with<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>>() {
     let circuit = CubicCircuit::default();
 
     // produce keys