From 6f66fd3f9d959fa04bcbcf1e10c9bdc2ed80c7f8 Mon Sep 17 00:00:00 2001
From: Sean Bowe <ewillbefull@gmail.com>
Date: Tue, 20 Feb 2018 16:11:48 -0700
Subject: [PATCH] Express x and y coordinates from lookup as linear
 combinations.

---
 src/circuit/lookup.rs        | 22 ++++++++++++----------
 src/circuit/pedersen_hash.rs |  2 +-
 2 files changed, 13 insertions(+), 11 deletions(-)

diff --git a/src/circuit/lookup.rs b/src/circuit/lookup.rs
index e433cd0..e002609 100644
--- a/src/circuit/lookup.rs
+++ b/src/circuit/lookup.rs
@@ -169,24 +169,26 @@ pub fn lookup3_xy_with_conditional_negation<E: Engine, CS>(
     synth::<E, _>(2, coords.iter().map(|c| &c.0), &mut x_coeffs);
     synth::<E, _>(2, coords.iter().map(|c| &c.1), &mut y_coeffs);
 
+    let precomp = Boolean::and(cs.namespace(|| "precomp"), &bits[0], &bits[1])?;
+
     cs.enforce(
         || "x-coordinate lookup",
-        |lc| lc + (x_coeffs[0b01], one)
-                + &bits[1].lc::<E>(one, x_coeffs[0b11]),
-        |lc| lc + &bits[0].lc::<E>(one, E::Fr::one()),
+        |lc| lc + (x_coeffs[0b00], one)
+                + &bits[0].lc::<E>(one, x_coeffs[0b01])
+                + &bits[1].lc::<E>(one, x_coeffs[0b10])
+                + &precomp.lc::<E>(one, x_coeffs[0b11]),
+        |lc| lc + one,
         |lc| lc + res_x.get_variable()
-                - (x_coeffs[0b00], one)
-                - &bits[1].lc::<E>(one, x_coeffs[0b10])
     );
 
     cs.enforce(
         || "y-coordinate lookup",
-        |lc| lc + (y_coeffs[0b01], one)
-                + &bits[1].lc::<E>(one, y_coeffs[0b11]),
-        |lc| lc + &bits[0].lc::<E>(one, E::Fr::one()),
+        |lc| lc + (y_coeffs[0b00], one)
+                + &bits[0].lc::<E>(one, y_coeffs[0b01])
+                + &bits[1].lc::<E>(one, y_coeffs[0b10])
+                + &precomp.lc::<E>(one, y_coeffs[0b11]),
+        |lc| lc + one,
         |lc| lc + res_y.get_variable()
-                - (y_coeffs[0b00], one)
-                - &bits[1].lc::<E>(one, y_coeffs[0b10])
     );
 
     let final_y = res_y.conditionally_negate(&mut cs, &bits[2])?;
diff --git a/src/circuit/pedersen_hash.rs b/src/circuit/pedersen_hash.rs
index 55f9cfb..68aab98 100644
--- a/src/circuit/pedersen_hash.rs
+++ b/src/circuit/pedersen_hash.rs
@@ -155,7 +155,7 @@ mod test {
         ).unwrap();
 
         assert!(cs.is_satisfied());
-        assert_eq!(cs.num_constraints(), 1551);
+        assert_eq!(cs.num_constraints(), 1721);
     }
 
     #[test]