Arbitrary number of variables and contraints (#34)

* This commit makes adding an arbitrary number of variables and inputs possible and removes the
  implementation leaking to the interface for

  num_inps + 1 <= num_vars, num_vars: a power of 2, num_cons: a power of 2, but not 1.

  1. When creating a new R1CS Instance throught the public interface,
     it is required # constraints and # of vars be a power of 2. I remove
     that requirement by padding with dummy constraints and vars until the nearest
     power of 2.
  2. The sumcheck protocol in src/sumcheck.rs does not work for 1 constraint, even
     though 1 is a power of 2. I have to pad to a minimum of two constraints.
  3. Added a test in src/r1csproof.rs called test_padded_constraints.

* Move test to src/lib.rs

* Remove padding metadata

* remove unused use

* Simplify padding to power of 2

* run cargo fmt

* Fix indexing bug

* Rayon is optional, depending on 'multicore' feature

* Update rust toolchain

* cargo fmt

* cleaner to track num_vars_padded and num_cons_padded

* cleanup

* further cleanup

* Cleanup & comments

* small fixes

* adjust code for padding constraints

* fix a bug with pad call

* add comment about num_nz_entries

* extend padding to NIZK methods

extend padding to NIZK methods

Co-authored-by: Lef Ioannidis <elefthei@seas.upenn.edu>
Co-authored-by: Srinath Setty <srinath@microsoft.com>

profiler/nizk.rs

@@ -27,7 +27,7 @@ pub fn main() {
     let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
 
     // produce public generators
-    let gens = NIZKGens::new(num_cons, num_vars);
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
 
     // produce a proof of satisfiability
     let mut prover_transcript = Transcript::new(b"nizk_example");