diff --git a/src/circuit/boolean.rs b/src/circuit/boolean.rs
index 239d404..f06fc99 100644
--- a/src/circuit/boolean.rs
+++ b/src/circuit/boolean.rs
@@ -375,35 +375,44 @@ impl Boolean {
         where E: Engine,
               CS: ConstraintSystem<E>
     {
-        let c = Self::xor(&mut cs, a, b)?;
-
-        match c {
-            Boolean::Constant(false) => {
-                Ok(())
+        match (a, b) {
+            (&Boolean::Constant(a), &Boolean::Constant(b)) => {
+                if a == b {
+                    Ok(())
+                } else {
+                    Err(SynthesisError::Unsatisfiable)
+                }
             },
-            Boolean::Constant(true) => {
-                Err(SynthesisError::Unsatisfiable)
-            },
-            Boolean::Is(ref res) => {
+            (&Boolean::Constant(true), a) | (a, &Boolean::Constant(true)) => {
                 cs.enforce(
-                    || "enforce equals zero",
+                    || "enforce equal to one",
                     |lc| lc,
                     |lc| lc,
-                    |lc| lc + res.get_variable()
+                    |lc| lc + CS::one() - &a.lc(CS::one(), E::Fr::one())
                 );
 
                 Ok(())
             },
-            Boolean::Not(ref res) => {
+            (&Boolean::Constant(false), a) | (a, &Boolean::Constant(false)) => {
                 cs.enforce(
-                    || "enforce equals one",
+                    || "enforce equal to zero",
                     |lc| lc,
                     |lc| lc,
-                    |lc| lc + CS::one() - res.get_variable()
+                    |_| a.lc(CS::one(), E::Fr::one())
                 );
 
                 Ok(())
             },
+            (a, b) => {
+                cs.enforce(
+                    || "enforce equal",
+                    |lc| lc,
+                    |lc| lc,
+                    |_| a.lc(CS::one(), E::Fr::one()) - &b.lc(CS::one(), E::Fr::one())
+                );
+
+                Ok(())
+            }
         }
     }
 
@@ -636,24 +645,88 @@ mod test {
             for b_bool in [false, true].iter().cloned() {
                 for a_neg in [false, true].iter().cloned() {
                     for b_neg in [false, true].iter().cloned() {
-                        let mut cs = TestConstraintSystem::<Bls12>::new();
+                        {
+                            let mut cs = TestConstraintSystem::<Bls12>::new();
 
-                        let mut a = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_bool)).unwrap());
-                        let mut b = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_bool)).unwrap());
+                            let mut a = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_bool)).unwrap());
+                            let mut b = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_bool)).unwrap());
 
-                        if a_neg {
-                            a = a.not();
+                            if a_neg {
+                                a = a.not();
+                            }
+                            if b_neg {
+                                b = b.not();
+                            }
+
+                            Boolean::enforce_equal(&mut cs, &a, &b).unwrap();
+
+                            assert_eq!(
+                                cs.is_satisfied(),
+                                (a_bool ^ a_neg) == (b_bool ^ b_neg)
+                            );
                         }
-                        if b_neg {
-                            b = b.not();
+                        {
+                            let mut cs = TestConstraintSystem::<Bls12>::new();
+
+                            let mut a = Boolean::Constant(a_bool);
+                            let mut b = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_bool)).unwrap());
+
+                            if a_neg {
+                                a = a.not();
+                            }
+                            if b_neg {
+                                b = b.not();
+                            }
+
+                            Boolean::enforce_equal(&mut cs, &a, &b).unwrap();
+
+                            assert_eq!(
+                                cs.is_satisfied(),
+                                (a_bool ^ a_neg) == (b_bool ^ b_neg)
+                            );
                         }
+                        {
+                            let mut cs = TestConstraintSystem::<Bls12>::new();
 
-                        Boolean::enforce_equal(&mut cs, &a, &b).unwrap();
+                            let mut a = Boolean::from(AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_bool)).unwrap());
+                            let mut b = Boolean::Constant(b_bool);
 
-                        assert_eq!(
-                            cs.is_satisfied(),
-                            (a_bool ^ a_neg) == (b_bool ^ b_neg)
-                        );
+                            if a_neg {
+                                a = a.not();
+                            }
+                            if b_neg {
+                                b = b.not();
+                            }
+
+                            Boolean::enforce_equal(&mut cs, &a, &b).unwrap();
+
+                            assert_eq!(
+                                cs.is_satisfied(),
+                                (a_bool ^ a_neg) == (b_bool ^ b_neg)
+                            );
+                        }
+                        {
+                            let mut cs = TestConstraintSystem::<Bls12>::new();
+
+                            let mut a = Boolean::Constant(a_bool);
+                            let mut b = Boolean::Constant(b_bool);
+
+                            if a_neg {
+                                a = a.not();
+                            }
+                            if b_neg {
+                                b = b.not();
+                            }
+
+                            let result = Boolean::enforce_equal(&mut cs, &a, &b);
+
+                            if (a_bool ^ a_neg) == (b_bool ^ b_neg) {
+                                assert!(result.is_ok());
+                                assert!(cs.is_satisfied());
+                            } else {
+                                assert!(result.is_err());
+                            }
+                        }
                     }
                 }
             }