refactor: streamline some traits and bounds (#207)

* refactor: Remove redundant PrimeField bound in various modules

* refactor: Refactor main Group trait to use group::Group

- the main Group trait now uses ::zkcrypto::group::Group
- Refactored the usage of generic type associated 'Scalar' across multiple files and functions from 'G::Scalar' to fully qualified '<G as Group>::Scalar'.
- No new features were added, functionality remained the same, changes were mostly aimed at improving type inference and handling.

* Revert "refactor: Refactor main Group trait to use group::Group"

This reverts commit 5ee0590588.

src/bellperson/r1cs.rs

@@ -28,10 +28,7 @@ pub trait NovaShape {
   fn r1cs_shape(&self) -> (R1CSShape<G>, CommitmentKey<G>);
 }
 
-impl<G: Group> NovaWitness<G> for SatisfyingAssignment<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> NovaWitness<G> for SatisfyingAssignment<G> {
   fn r1cs_instance_and_witness(
     &self,
     shape: &R1CSShape<G>,
@@ -48,10 +45,7 @@ where
   }
 }
 
-impl<G: Group> NovaShape<G> for ShapeCS<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> NovaShape<G> for ShapeCS<G> {
   fn r1cs_shape(&self) -> (R1CSShape<G>, CommitmentKey<G>) {
     let mut A: Vec<(usize, usize, G::Scalar)> = Vec::new();
     let mut B: Vec<(usize, usize, G::Scalar)> = Vec::new();

src/bellperson/shape_cs.rs

@@ -48,10 +48,7 @@ impl Ord for OrderedVariable {
 
 #[allow(clippy::upper_case_acronyms)]
 /// `ShapeCS` is a `ConstraintSystem` for creating `R1CSShape`s for a circuit.
-pub struct ShapeCS<G: Group>
-where
-  G::Scalar: PrimeField + Field,
-{
+pub struct ShapeCS<G: Group> {
   named_objects: HashMap<String, NamedObject>,
   current_namespace: Vec<String>,
   #[allow(clippy::type_complexity)]
@@ -92,10 +89,7 @@ fn proc_lc(
   map
 }
 
-impl<G: Group> ShapeCS<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> ShapeCS<G> {
   /// Create a new, default `ShapeCS`,
   pub fn new() -> Self {
     ShapeCS::default()
@@ -216,10 +210,7 @@ where
   }
 }
 
-impl<G: Group> Default for ShapeCS<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> Default for ShapeCS<G> {
   fn default() -> Self {
     let mut map = HashMap::new();
     map.insert("ONE".into(), NamedObject::Var(ShapeCS::<G>::one()));
@@ -233,10 +224,7 @@ where
   }
 }
 
-impl<G: Group> ConstraintSystem<G::Scalar> for ShapeCS<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> ConstraintSystem<G::Scalar> for ShapeCS<G> {
   type Root = Self;
 
   fn alloc<F, A, AR>(&mut self, annotation: A, _f: F) -> Result<Variable, SynthesisError>

src/bellperson/solver.rs

@@ -1,7 +1,7 @@
 //! Support for generating R1CS witness using bellperson.
 
 use crate::traits::Group;
-use ff::{Field, PrimeField};
+use ff::Field;
 
 use bellperson::{
   multiexp::DensityTracker, ConstraintSystem, Index, LinearCombination, SynthesisError, Variable,
@@ -9,10 +9,7 @@ use bellperson::{
 
 /// A `ConstraintSystem` which calculates witness values for a concrete instance of an R1CS circuit.
 #[derive(PartialEq)]
-pub struct SatisfyingAssignment<G: Group>
-where
-  G::Scalar: PrimeField,
-{
+pub struct SatisfyingAssignment<G: Group> {
   // Density of queries
   a_aux_density: DensityTracker,
   b_input_density: DensityTracker,
@@ -29,10 +26,7 @@ where
 }
 use std::fmt;
 
-impl<G: Group> fmt::Debug for SatisfyingAssignment<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> fmt::Debug for SatisfyingAssignment<G> {
   fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
     fmt
       .debug_struct("SatisfyingAssignment")
@@ -69,10 +63,7 @@ where
   }
 }
 
-impl<G: Group> ConstraintSystem<G::Scalar> for SatisfyingAssignment<G>
-where
-  G::Scalar: PrimeField,
-{
+impl<G: Group> ConstraintSystem<G::Scalar> for SatisfyingAssignment<G> {
   type Root = Self;
 
   fn new() -> Self {

src/traits/mod.rs

@@ -41,8 +41,7 @@ pub trait Group:
     + for<'de> Deserialize<'de>;
 
   /// A type representing an element of the scalar field of the group
-  type Scalar: PrimeField
-    + PrimeFieldBits
+  type Scalar: PrimeFieldBits
     + PrimeFieldExt
     + Send
     + Sync