Add public input absorption

kimchi/src/prover.rs

@@ -254,7 +254,7 @@ where
         //~    and $0$ for the rest.
         let public = witness[0][0..index.cs.public].to_vec();
         let public_poly = -Evaluations::<G::ScalarField, D<G::ScalarField>>::from_vec_and_domain(
-            public,
+            public.clone(),
             index.cs.domain.d1,
         )
         .interpolate();
@@ -279,6 +279,9 @@ where
         //~    This is why we need to absorb the commitment to the public polynomial at this point.
         absorb_commitment(&mut fq_sponge, &public_comm);
 
+        //~ 1. (NEW) Absorb the public input.
+        fq_sponge.absorb_fr(&public);
+
         //~ 1. Commit to the witness columns by creating `COLUMNS` hidding commitments.
         //~
         //~    Note: since the witness is in evaluation form,

kimchi/src/verifier.rs

@@ -147,6 +147,9 @@ where
         //~ 1. Absorb the commitment of the public input polynomial with the Fq-Sponge.
         absorb_commitment(&mut fq_sponge, public_comm);
 
+        //~ 1. (NEW) Absorb the public input (TODO: remove unwrap).
+        fq_sponge.absorb_fr(public_input.unwrap());
+
         //~ 1. Absorb the commitments to the registers / witness columns with the Fq-Sponge.
         self.commitments
             .w_comm