Remove Montgomery point doubling implementation in the circuit.

src/circuit/mont.rs

@@ -650,109 +650,6 @@ impl<E: JubjubEngine> MontgomeryPoint<E> {
             y: yprime
         })
     }
-
-    /// Performs an affine point doubling, not defined for
-    /// the point of order two (0, 0).
-    pub fn double<CS>(
-        &self,
-        mut cs: CS,
-        params: &E::Params
-    ) -> Result<Self, SynthesisError>
-        where CS: ConstraintSystem<E>
-    {
-        // Square x
-        let xx = self.x.square(&mut cs)?;
-
-        // Compute lambda = (3.xx + 2.A.x + 1) / 2.y
-        let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
-            let mut t0 = *xx.get_value().get()?;
-            let mut t1 = t0;
-            t0.double(); // t0 = 2.xx
-            t0.add_assign(&t1); // t0 = 3.xx
-            t1 = *self.x.get_value().get()?; // t1 = x
-            t1.mul_assign(params.montgomery_2a()); // t1 = 2.A.x
-            t0.add_assign(&t1);
-            t0.add_assign(&E::Fr::one());
-            t1 = *self.y.get_value().get()?; // t1 = y
-            t1.double(); // t1 = 2.y
-            match t1.inverse() {
-                Some(t1) => {
-                    t0.mul_assign(&t1);
-
-                    Ok(t0)
-                },
-                None => {
-                    Err(SynthesisError::DivisionByZero)
-                }
-            }
-        })?;
-
-        // (2.y) * (lambda) = (3.xx + 2.A.x + 1)
-        let one = CS::one();
-        cs.enforce(
-            || "evaluate lambda",
-            |lc| lc + self.y.get_variable()
-                    + self.y.get_variable(),
-
-            |lc| lc + lambda.get_variable(),
-
-            |lc| lc + xx.get_variable()
-                    + xx.get_variable()
-                    + xx.get_variable()
-                    + (*params.montgomery_2a(), self.x.get_variable())
-                    + one
-        );
-
-        // Compute x' = (lambda^2) - A - 2.x
-        let xprime = AllocatedNum::alloc(cs.namespace(|| "xprime"), || {
-            let mut t0 = *lambda.get_value().get()?;
-            t0.square();
-            t0.sub_assign(params.montgomery_a());
-            t0.sub_assign(self.x.get_value().get()?);
-            t0.sub_assign(self.x.get_value().get()?);
-
-            Ok(t0)
-        })?;
-
-        // (lambda) * (lambda) = (A + 2.x + x')
-        cs.enforce(
-            || "evaluate xprime",
-            |lc| lc + lambda.get_variable(),
-            |lc| lc + lambda.get_variable(),
-            |lc| lc + (*params.montgomery_a(), one)
-                    + self.x.get_variable()
-                    + self.x.get_variable()
-                    + xprime.get_variable()
-        );
-
-        // Compute y' = -(y + lambda(x' - x))
-        let yprime = AllocatedNum::alloc(cs.namespace(|| "yprime"), || {
-            let mut t0 = *xprime.get_value().get()?;
-            t0.sub_assign(self.x.get_value().get()?);
-            t0.mul_assign(lambda.get_value().get()?);
-            t0.add_assign(self.y.get_value().get()?);
-            t0.negate();
-
-            Ok(t0)
-        })?;
-
-        // y' + y = lambda(x - x')
-        cs.enforce(
-            || "evaluate yprime",
-            |lc| lc + self.x.get_variable()
-                    - xprime.get_variable(),
-
-            |lc| lc + lambda.get_variable(),
-
-            |lc| lc + yprime.get_variable()
-                    + self.y.get_variable()
-        );
-
-        Ok(MontgomeryPoint {
-            x: xprime,
-            y: yprime
-        })
-    }
 }
 
 #[cfg(test)]
@@ -863,27 +760,6 @@ mod test {
         }
     }
 
-    #[test]
-    fn test_doubling_order_2() {
-        let params = &JubjubBls12::new();
-
-        let mut cs = TestConstraintSystem::<Bls12>::new();
-
-        let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
-            Ok(Fr::zero())
-        }).unwrap();
-        let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
-            Ok(Fr::zero())
-        }).unwrap();
-
-        let p = MontgomeryPoint {
-            x: x,
-            y: y
-        };
-
-        assert!(p.double(&mut cs, params).is_err());
-    }
-
     #[test]
     fn test_edwards_fixed_base_multiplication()  {
         let params = &JubjubBls12::new();
@@ -1222,60 +1098,4 @@ mod test {
             assert_eq!(cs.which_is_unsatisfied(), Some("addition/evaluate lambda"));
         }
     }
-
-    #[test]
-    fn test_montgomery_doubling() {
-        let params = &JubjubBls12::new();
-        let rng = &mut XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
-
-        for _ in 0..100 {
-            let p = loop {
-                let x: Fr = rng.gen();
-                let s: bool = rng.gen();
-
-                if let Some(p) = montgomery::Point::<Bls12, _>::get_for_x(x, s, params) {
-                    break p;
-                }
-            };
-
-            let p2 = p.double(params);
-
-            let (x0, y0) = p.into_xy().unwrap();
-            let (x1, y1) = p2.into_xy().unwrap();
-
-            let mut cs = TestConstraintSystem::<Bls12>::new();
-
-            let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
-                Ok(x0)
-            }).unwrap();
-            let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
-                Ok(y0)
-            }).unwrap();
-
-            let p = MontgomeryPoint {
-                x: x,
-                y: y
-            };
-
-            let p2 = p.double(cs.namespace(|| "doubling"), params).unwrap();
-
-            assert!(cs.is_satisfied());
-
-            assert!(p2.x.get_value().unwrap() == x1);
-            assert!(p2.y.get_value().unwrap() == y1);
-
-            cs.set("doubling/yprime/num", rng.gen());
-            assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate yprime"));
-            cs.set("doubling/yprime/num", y1);
-            assert!(cs.is_satisfied());
-
-            cs.set("doubling/xprime/num", rng.gen());
-            assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate xprime"));
-            cs.set("doubling/xprime/num", x1);
-            assert!(cs.is_satisfied());
-
-            cs.set("doubling/lambda/num", rng.gen());
-            assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate lambda"));
-        }
-    }
 }