feat: nifs::protogalaxy from C::Base to C::Scalar

**Motivation**
We need consistent types for #369 between nifs <-> ivc protogalaxy modules

**Overview**
I had to make many types independent of the curve. Since for the random oracle logic we are byte-by-by-byte distilling from all fields to the target field anyway, I got rid of Scalar -> Base in favor of any field.

So now it can be both C::Base (for sangria) and C::Scalar (for cyclefold)

There are no other functional changes, only generic refactoring

src/ivc/consistency_markers_computation.rs

@@ -166,7 +166,7 @@ where
                 .absorb_field_iter(self.z_i.iter().copied())
                 .absorb(&relaxed)
                 .inspect(inspect)
-                .squeeze::<C>(NUM_CHALLENGE_BITS),
+                .squeeze::<C::ScalarExt>(NUM_CHALLENGE_BITS),
         )
         .unwrap()
     }

src/ivc/cyclefold/sfc/input/assigned.rs

@@ -437,7 +437,7 @@ pub struct Input<const ARITY: usize, F: PrimeField> {
 }
 
 impl<const A: usize, F: PrimeField> Input<A, F> {
-    fn assign_advice_from(
+    pub fn assign_advice_from(
         region: &mut RegionCtx<'_, F>,
         original: &super::Input<A, F>,
         main_gate_config: &MainGateConfig,

src/ivc/cyclefold/sfc/input/mod.rs

@@ -9,7 +9,7 @@ use crate::{
     poseidon::{AbsorbInRO, ROTrait},
 };
 
-mod assigned;
+pub mod assigned;
 
 #[derive(Debug, Clone)]
 pub struct BigUintPoint<F: PrimeField> {

src/ivc/cyclefold/sfc/mod.rs

@@ -7,7 +7,7 @@ use crate::{
         plonk::{Circuit, ConstraintSystem, Error as Halo2PlonkError},
     },
     ivc::{cyclefold, StepCircuit},
-    main_gate::{MainGate, MainGateConfig},
+    main_gate::{MainGate, MainGateConfig, RegionCtx},
     poseidon::ROTrait,
 };
 
@@ -83,9 +83,24 @@ impl<const ARITY: usize, C: CurveAffine, SC: StepCircuit<ARITY, C::ScalarExt>> C
 
     fn synthesize(
         &self,
-        _config: Self::Config,
-        _layouter: impl Layouter<C::ScalarExt>,
+        config: Self::Config,
+        mut layouter: impl Layouter<C::ScalarExt>,
     ) -> Result<(), Halo2PlonkError> {
+        layouter.assign_region(
+            || "sfc main",
+            |region| {
+                let mut region = RegionCtx::new(region, 0);
+
+                let _input = input::assigned::Input::assign_advice_from(
+                    &mut region,
+                    &self.input,
+                    &config.mg,
+                )?;
+
+                Ok(())
+            },
+        )?;
+
         todo!()
     }
 }