relax requirements on the size of public IO and add a note about NIFS (…

…#294)

* relax requirements on the size of public IO

* add a note

src/nifs.rs

@@ -31,6 +31,12 @@ impl<E: Engine> NIFS<E> {
   /// a folded Relaxed R1CS instance-witness tuple `(U, W)` of the same shape `shape`,
   /// with the guarantee that the folded witness `W` satisfies the folded instance `U`
   /// if and only if `W1` satisfies `U1` and `W2` satisfies `U2`.
+  ///
+  /// Note that this code is tailored for use with Nova's IVC scheme, which enforces
+  /// certain requirements between the two instances that are folded.
+  /// In particular, it requires that `U1` and `U2` are such that the hash of `U1` is stored in the public IO of `U2`.
+  /// In this particular setting, this means that if `U2` is absorbed in the RO, it implicitly absorbs `U1` as well.
+  /// So the code below avoids absorbing `U1` in the RO.
   #[allow(clippy::too_many_arguments)]
   #[tracing::instrument(skip_all, level = "trace", name = "NIFS::prove")]
   pub fn prove(

src/r1cs/mod.rs

@@ -240,14 +240,13 @@ impl<E: Engine> R1CSShape<E> {
   }
 
   // Checks regularity conditions on the R1CSShape, required in Spartan-class SNARKs
-  // Returns false if num_cons, num_vars, or num_io are not powers of two, or if num_io > num_vars
+  // Returns false if num_cons or num_vars are not powers of two, or if num_io > num_vars
   #[inline]
   pub(crate) fn is_regular_shape(&self) -> bool {
     let cons_valid = self.num_cons.next_power_of_two() == self.num_cons;
     let vars_valid = self.num_vars.next_power_of_two() == self.num_vars;
-    let io_valid = self.num_io.next_power_of_two() == self.num_io;
     let io_lt_vars = self.num_io < self.num_vars;
-    cons_valid && vars_valid && io_valid && io_lt_vars
+    cons_valid && vars_valid && io_lt_vars
   }
 
   pub(crate) fn multiply_vec(
@@ -513,17 +512,17 @@ impl<E: Engine> R1CSShape<E> {
     Ok(CE::<E>::commit(ck, T))
   }
 
-  /// Pads the `R1CSShape` so that the number of variables is a power of two
+  /// Pads the `R1CSShape` so that the shape passes `is_regular_shape`
   /// Renumbers variables to accommodate padded variables
   pub fn pad(&self) -> Self {
-    // equalize the number of variables and constraints
-    let m = max(self.num_vars, self.num_cons).next_power_of_two();
-
     // check if the provided R1CSShape is already as required
-    if self.num_vars == m && self.num_cons == m {
+    if self.is_regular_shape() {
       return self.clone();
     }
 
+    // equalize the number of variables, constraints, and public IO
+    let m = max(max(self.num_vars, self.num_cons), self.num_io).next_power_of_two();
+
     // check if the number of variables are as expected, then
     // we simply set the number of constraints to the next power of two
     if self.num_vars == m {