Implement HyperNova's AugmentedFCircuit (#112)

- add LCCCS.hash methods (native & r1cs)
- add HyperNova's AugmentedFCircuit with tests

folding-schemes/src/folding/hypernova/mod.rs

@@ -1,6 +1,27 @@
 /// Implements the scheme described in [HyperNova](https://eprint.iacr.org/2023/573.pdf)
+use crate::ccs::CCS;
+use ark_ff::PrimeField;
+
 pub mod cccs;
 pub mod circuits;
 pub mod lcccs;
 pub mod nimfs;
 pub mod utils;
+
+/// Witness for the LCCCS & CCCS, containing the w vector, and the r_w used as randomness in the Pedersen commitment.
+#[derive(Debug, Clone, Eq, PartialEq)]
+pub struct Witness<F: PrimeField> {
+    pub w: Vec<F>,
+    pub r_w: F,
+}
+
+impl<F: PrimeField> Witness<F> {
+    pub fn new(w: Vec<F>) -> Self {
+        // note: at the current version, we don't use the blinding factors and we set them to 0
+        // always.
+        Self { w, r_w: F::zero() }
+    }
+    pub fn dummy(ccs: &CCS<F>) -> Self {
+        Witness::<F>::new(vec![F::zero(); ccs.n - ccs.l - 1])
+    }
+}