diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml
index e811e41..99db8a8 100644
--- a/.github/workflows/rust.yml
+++ b/.github/workflows/rust.yml
@@ -14,7 +14,7 @@ jobs:
     steps:
     - uses: actions/checkout@v2
     - name: Install
-      run: rustup default nightly-2021-01-03
+      run: rustup default nightly-2021-01-31
     - name: Build
       run: cargo build --verbose
     - name: Run tests
diff --git a/Cargo.toml b/Cargo.toml
index 5dcb044..9226ae3 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -17,7 +17,7 @@ rand = "0.7.3"
 digest = "0.8.1"
 sha3 = "0.8.2"
 byteorder = "1.3.4"
-rayon = "1.3.0"
+rayon = { version = "1.3.0", optional = true }
 serde = { version = "1.0.106", features = ["derive"] }
 bincode = "1.2.1"
 subtle = { version = "^2.2.3", default-features = false }
@@ -52,5 +52,5 @@ name = "nizk"
 harness = false
 
 [features]
-multicore = []
+multicore = ["rayon"]
 profile = []
diff --git a/README.md b/README.md
index d3edaf5..0532604 100644
--- a/README.md
+++ b/README.md
@@ -82,7 +82,7 @@ Here is another example to use the NIZK variant of the Spartan proof system:
     let num_inputs = 10;
 
     // produce public parameters
-    let gens = NIZKGens::new(num_cons, num_vars);
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
 
     // ask the library to produce a synthentic R1CS instance
     let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
@@ -102,6 +102,7 @@ Here is another example to use the NIZK variant of the Spartan proof system:
 
 Finally, we provide an example that specifies a custom R1CS instance instead of using a synthetic instance
 ```rust
+#![allow(non_snake_case)]
 # extern crate curve25519_dalek;
 # extern crate libspartan;
 # extern crate merlin;
@@ -163,9 +164,9 @@ Finally, we provide an example that specifies a custom R1CS instance instead of
 
   // parameters of the R1CS instance rounded to the nearest power of two
   let num_cons = 4;
-  let num_vars = 8;
+  let num_vars = 5;
   let num_inputs = 2;
-  let num_non_zero_entries = 8;
+  let num_non_zero_entries = 5;
 
   // We will encode the above constraints into three matrices, where
   // the coefficients in the matrix are in the little-endian byte order
diff --git a/benches/nizk.rs b/benches/nizk.rs
index 42f2634..53d32cc 100644
--- a/benches/nizk.rs
+++ b/benches/nizk.rs
@@ -24,7 +24,7 @@ fn nizk_prove_benchmark(c: &mut Criterion) {
 
     let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
 
-    let gens = NIZKGens::new(num_cons, num_vars);
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
 
     let name = format!("NIZK_prove_{}", num_vars);
     group.bench_function(&name, move |b| {
@@ -54,7 +54,7 @@ fn nizk_verify_benchmark(c: &mut Criterion) {
     let num_inputs = 10;
     let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
 
-    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"example");
diff --git a/profiler/nizk.rs b/profiler/nizk.rs
index cb3f72d..e184dc9 100644
--- a/profiler/nizk.rs
+++ b/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");
diff --git a/src/dense_mlpoly.rs b/src/dense_mlpoly.rs
index f802f49..b30e253 100644
--- a/src/dense_mlpoly.rs
+++ b/src/dense_mlpoly.rs
@@ -149,7 +149,7 @@ impl DensePolynomial {
     assert_eq!(L_size * R_size, self.Z.len());
     let C = (0..L_size)
       .into_par_iter()
-      .map(|&i| {
+      .map(|i| {
         self.Z[R_size * i..R_size * (i + 1)]
           .commit(&blinds[i], gens)
           .compress()
diff --git a/src/lib.rs b/src/lib.rs
index 55cfdf6..36cae7e 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -10,10 +10,12 @@ extern crate curve25519_dalek;
 extern crate digest;
 extern crate merlin;
 extern crate rand;
-extern crate rayon;
 extern crate sha3;
 extern crate test;
 
+#[cfg(feature = "multicore")]
+extern crate rayon;
+
 mod commitments;
 mod dense_mlpoly;
 mod errors;
@@ -31,6 +33,7 @@ mod timer;
 mod transcript;
 mod unipoly;
 
+use core::cmp::max;
 use errors::{ProofVerifyError, R1CSError};
 use merlin::Transcript;
 use r1csinstance::{
@@ -86,6 +89,22 @@ impl Assignment {
       assignment: assignment_scalar.unwrap(),
     })
   }
+
+  /// pads Assignment to the specified length
+  fn pad(&self, len: usize) -> VarsAssignment {
+    // check that the new length is higher than current length
+    assert!(len > self.assignment.len());
+
+    let padded_assignment = {
+      let mut padded_assignment = self.assignment.clone();
+      padded_assignment.extend(vec![Scalar::zero(); len - self.assignment.len()]);
+      padded_assignment
+    };
+
+    VarsAssignment {
+      assignment: padded_assignment,
+    }
+  }
 }
 
 /// `VarsAssignment` holds an assignment of values to variables in an `Instance`
@@ -109,20 +128,37 @@ impl Instance {
     B: &Vec<(usize, usize, [u8; 32])>,
     C: &Vec<(usize, usize, [u8; 32])>,
   ) -> Result<Instance, R1CSError> {
-    // check that num_cons is power of 2
-    if num_cons.next_power_of_two() != num_cons {
-      return Err(R1CSError::NonPowerOfTwoCons);
-    }
+    let (num_vars_padded, num_cons_padded) = {
+      let num_vars_padded = {
+        let mut num_vars_padded = num_vars;
 
-    // check that the number of variables is a power of 2
-    if num_vars.next_power_of_two() != num_vars {
-      return Err(R1CSError::NonPowerOfTwoVars);
-    }
+        // ensure that num_inputs + 1 <= num_vars
+        num_vars_padded = max(num_vars_padded, num_inputs + 1);
 
-    // check that num_inputs + 1 <= num_vars
-    if num_inputs >= num_vars {
-      return Err(R1CSError::InvalidNumberOfInputs);
-    }
+        // ensure that num_vars_padded a power of two
+        if num_vars_padded.next_power_of_two() != num_vars_padded {
+          num_vars_padded = num_vars_padded.next_power_of_two();
+        }
+        num_vars_padded
+      };
+
+      let num_cons_padded = {
+        let mut num_cons_padded = num_cons;
+
+        // ensure that num_cons_padded is at least 2
+        if num_cons_padded == 0 || num_cons_padded == 1 {
+          num_cons_padded = 2;
+        }
+
+        // ensure that num_cons_padded is power of 2
+        if num_cons.next_power_of_two() != num_cons {
+          num_cons_padded = num_cons.next_power_of_two();
+        }
+        num_cons_padded
+      };
+
+      (num_vars_padded, num_cons_padded)
+    };
 
     let bytes_to_scalar =
       |tups: &Vec<(usize, usize, [u8; 32])>| -> Result<Vec<(usize, usize, Scalar)>, R1CSError> {
@@ -142,11 +178,26 @@ impl Instance {
 
           let val = Scalar::from_bytes(&val_bytes);
           if val.is_some().unwrap_u8() == 1 {
-            mat.push((row, col, val.unwrap()));
+            // if col >= num_vars, it means that it is referencing a 1 or input in the satisfying
+            // assignment
+            if col >= num_vars {
+              mat.push((row, col + num_vars_padded - num_vars, val.unwrap()));
+            } else {
+              mat.push((row, col, val.unwrap()));
+            }
           } else {
             return Err(R1CSError::InvalidScalar);
           }
         }
+
+        // pad with additional constraints up until num_cons_padded if the original constraints were 0 or 1
+        // we do not need to pad otherwise because the dummy constraints are implicit in the sum-check protocol
+        if num_cons == 0 || num_cons == 1 {
+          for i in tups.len()..num_cons_padded {
+            mat.push((i, num_vars, Scalar::zero()));
+          }
+        }
+
         Ok(mat)
       };
 
@@ -166,8 +217,8 @@ impl Instance {
     }
 
     let inst = R1CSInstance::new(
-      num_cons,
-      num_vars,
+      num_cons_padded,
+      num_vars_padded,
       num_inputs,
       &A_scalar.unwrap(),
       &B_scalar.unwrap(),
@@ -183,15 +234,31 @@ impl Instance {
     vars: &VarsAssignment,
     inputs: &InputsAssignment,
   ) -> Result<bool, R1CSError> {
-    if vars.assignment.len() != self.inst.get_num_vars() {
-      return Err(R1CSError::InvalidNumberOfVars);
+    if vars.assignment.len() > self.inst.get_num_vars() {
+      return Err(R1CSError::InvalidNumberOfInputs);
     }
 
     if inputs.assignment.len() != self.inst.get_num_inputs() {
       return Err(R1CSError::InvalidNumberOfInputs);
     }
 
-    Ok(self.inst.is_sat(&vars.assignment, &inputs.assignment))
+    // we might need to pad variables
+    let padded_vars = {
+      let num_padded_vars = self.inst.get_num_vars();
+      let num_vars = vars.assignment.len();
+      let padded_vars = if num_padded_vars > num_vars {
+        vars.pad(num_padded_vars)
+      } else {
+        vars.clone()
+      };
+      padded_vars
+    };
+
+    Ok(
+      self
+        .inst
+        .is_sat(&padded_vars.assignment, &inputs.assignment),
+    )
   }
 
   /// Constructs a new synthetic R1CS `Instance` and an associated satisfying assignment
@@ -217,12 +284,21 @@ pub struct SNARKGens {
 
 impl SNARKGens {
   /// Constructs a new `SNARKGens` given the size of the R1CS statement
+  /// `num_nz_entries` specifies the maximum number of non-zero entries in any of the three R1CS matrices
   pub fn new(num_cons: usize, num_vars: usize, num_inputs: usize, num_nz_entries: usize) -> Self {
-    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars);
+    let num_vars_padded = {
+      let mut num_vars_padded = max(num_vars, num_inputs + 1);
+      if num_vars_padded != num_vars_padded.next_power_of_two() {
+        num_vars_padded = num_vars_padded.next_power_of_two();
+      }
+      num_vars_padded
+    };
+
+    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars_padded);
     let gens_r1cs_eval = R1CSCommitmentGens::new(
       b"gens_r1cs_eval",
       num_cons,
-      num_vars,
+      num_vars_padded,
       num_inputs,
       num_nz_entries,
     );
@@ -276,14 +352,29 @@ impl SNARK {
     let mut random_tape = RandomTape::new(b"proof");
     transcript.append_protocol_name(SNARK::protocol_name());
     let (r1cs_sat_proof, rx, ry) = {
-      let (proof, rx, ry) = R1CSProof::prove(
-        &inst.inst,
-        vars.assignment,
-        &inputs.assignment,
-        &gens.gens_r1cs_sat,
-        transcript,
-        &mut random_tape,
-      );
+      let (proof, rx, ry) = {
+        // we might need to pad variables
+        let padded_vars = {
+          let num_padded_vars = inst.inst.get_num_vars();
+          let num_vars = vars.assignment.len();
+          let padded_vars = if num_padded_vars > num_vars {
+            vars.pad(num_padded_vars)
+          } else {
+            vars
+          };
+          padded_vars
+        };
+
+        R1CSProof::prove(
+          &inst.inst,
+          padded_vars.assignment,
+          &inputs.assignment,
+          &gens.gens_r1cs_sat,
+          transcript,
+          &mut random_tape,
+        )
+      };
+
       let proof_encoded: Vec<u8> = bincode::serialize(&proof).unwrap();
       Timer::print(&format!("len_r1cs_sat_proof {:?}", proof_encoded.len()));
 
@@ -378,8 +469,16 @@ pub struct NIZKGens {
 
 impl NIZKGens {
   /// Constructs a new `NIZKGens` given the size of the R1CS statement
-  pub fn new(num_cons: usize, num_vars: usize) -> Self {
-    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars);
+  pub fn new(num_cons: usize, num_vars: usize, num_inputs: usize) -> Self {
+    let num_vars_padded = {
+      let mut num_vars_padded = max(num_vars, num_inputs + 1);
+      if num_vars_padded != num_vars_padded.next_power_of_two() {
+        num_vars_padded = num_vars_padded.next_power_of_two();
+      }
+      num_vars_padded
+    };
+
+    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars_padded);
     NIZKGens { gens_r1cs_sat }
   }
 }
@@ -410,9 +509,21 @@ impl NIZK {
     let mut random_tape = RandomTape::new(b"proof");
     transcript.append_protocol_name(NIZK::protocol_name());
     let (r1cs_sat_proof, rx, ry) = {
+      // we might need to pad variables
+      let padded_vars = {
+        let num_padded_vars = inst.inst.get_num_vars();
+        let num_vars = vars.assignment.len();
+        let padded_vars = if num_padded_vars > num_vars {
+          vars.pad(num_padded_vars)
+        } else {
+          vars
+        };
+        padded_vars
+      };
+
       let (proof, rx, ry) = R1CSProof::prove(
         &inst.inst,
-        vars.assignment,
+        padded_vars.assignment,
         &input.assignment,
         &gens.gens_r1cs_sat,
         transcript,
@@ -544,4 +655,85 @@ mod tests {
     assert_eq!(inst.is_err(), true);
     assert_eq!(inst.err(), Some(R1CSError::InvalidScalar));
   }
+
+  #[test]
+  fn test_padded_constraints() {
+    // parameters of the R1CS instance
+    let num_cons = 1;
+    let num_vars = 0;
+    let num_inputs = 3;
+    let num_non_zero_entries = 3;
+
+    // We will encode the above constraints into three matrices, where
+    // the coefficients in the matrix are in the little-endian byte order
+    let mut A: Vec<(usize, usize, [u8; 32])> = Vec::new();
+    let mut B: Vec<(usize, usize, [u8; 32])> = Vec::new();
+    let mut C: Vec<(usize, usize, [u8; 32])> = Vec::new();
+
+    // Create a^2 + b + 13
+    A.push((0, num_vars + 2, Scalar::one().to_bytes())); // 1*a
+    B.push((0, num_vars + 2, Scalar::one().to_bytes())); // 1*a
+    C.push((0, num_vars + 1, Scalar::one().to_bytes())); // 1*z
+    C.push((0, num_vars, (-Scalar::from(13u64)).to_bytes())); // -13*1
+    C.push((0, num_vars + 3, (-Scalar::one()).to_bytes())); // -1*b
+
+    // Var Assignments (Z_0 = 16 is the only output)
+    let vars = vec![Scalar::zero().to_bytes(); num_vars];
+
+    // create an InputsAssignment (a = 1, b = 2)
+    let mut inputs = vec![Scalar::zero().to_bytes(); num_inputs];
+    inputs[0] = Scalar::from(16u64).to_bytes();
+    inputs[1] = Scalar::from(1u64).to_bytes();
+    inputs[2] = Scalar::from(2u64).to_bytes();
+
+    let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
+    let assignment_vars = VarsAssignment::new(&vars).unwrap();
+
+    // Check if instance is satisfiable
+    let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
+    let res = inst.is_sat(&assignment_vars, &assignment_inputs);
+    assert_eq!(res.unwrap(), true, "should be satisfied");
+
+    // SNARK public params
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
+
+    // create a commitment to the R1CS instance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a SNARK
+    let mut prover_transcript = Transcript::new(b"snark_example");
+    let proof = SNARK::prove(
+      &inst,
+      &decomm,
+      assignment_vars.clone(),
+      &assignment_inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the SNARK
+    let mut verifier_transcript = Transcript::new(b"snark_example");
+    assert!(proof
+      .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+
+    // NIZK public params
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
+
+    // produce a NIZK
+    let mut prover_transcript = Transcript::new(b"nizk_example");
+    let proof = NIZK::prove(
+      &inst,
+      assignment_vars,
+      &assignment_inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the NIZK
+    let mut verifier_transcript = Transcript::new(b"nizk_example");
+    assert!(proof
+      .verify(&inst, &assignment_inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+  }
 }