Bw6-761 optimized Miller loop (#155)

Cargo.toml

@@ -68,10 +68,10 @@ debug-assertions = true
 debug = true
 
 [patch.crates-io]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-poly = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-algebra-bench-templates = { git = "https://github.com/arkworks-rs/algebra/" }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
+ark-poly = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
+ark-algebra-bench-templates = { git = "https://github.com/arkworks-rs/algebra/", branch = "bw6-optimization" }
 ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std/" }

bw6_761/src/curves/mod.rs

@@ -21,20 +21,19 @@ impl BW6Config for Config {
     const X: BigInteger = BigInt!("0x8508c00000000001");
     /// `x` is positive.
     const X_IS_NEGATIVE: bool = false;
+    // X
+    const ATE_LOOP_COUNT_1: &'static [u64] = &[0x8508c00000000001];
     // (X-1)/3
     const X_MINUS_1_DIV_3: BigInteger = BigInt!("0x2c58400000000000");
     // X+1
-    const ATE_LOOP_COUNT_1: &'static [u64] = &[0x8508c00000000002];
     const ATE_LOOP_COUNT_1_IS_NEGATIVE: bool = false;
-    // X^3-X^2-X
+    // X^2-X-1
     const ATE_LOOP_COUNT_2: &'static [i8] = &[
         -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
-        0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0,
-        1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1,
-        0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
+        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,
+        0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0,
+        0, 1, 0, 1, 0, 0, 0, 1,
     ];
     const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
     const TWIST_TYPE: TwistType = TwistType::M;

bw6_767/src/curves/mod.rs

@@ -19,22 +19,19 @@ impl BW6Config for Config {
     // X is the same as in bls12_381
     const X: BigInteger = BigInt!("0xd201000000010000");
     const X_IS_NEGATIVE: bool = true;
-    // [(-X)+1]/3, since X < 0
+    // X
+    const ATE_LOOP_COUNT_1: &'static [u64] = &[0xd201000000010000];
     const X_MINUS_1_DIV_3: BigInteger = BigInt!("0x460055555555aaab");
-    // -[(-X)+1]
-    const ATE_LOOP_COUNT_1: &'static [u64] = &[0xd20100000000ffff];
     const ATE_LOOP_COUNT_1_IS_NEGATIVE: bool = true;
-    // -[(-X)^3-(-X)^2-(-X)] in 2-NAF
+    // X^2-X-1
     const ATE_LOOP_COUNT_2: &'static [i8] = &[
-        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0,
-        -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1,
-        0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0,
-        0, 0, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0,
-        0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0,
-        1, 0, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 1,
+        -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
+        1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 1,
+        0, 0, 0, -1, 0, -1, 0, -1, 0, 1,
     ];
-    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = true;
+    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
     const TWIST_TYPE: TwistType = TwistType::M;
     const H_T: i64 = -4;
     const H_Y: i64 = -6;