From 3bb8e37b07474a45a7e0ca386173c0b0ab0b17ac Mon Sep 17 00:00:00 2001
From: Nikesh Nazareth <business@nikeshnazareth.com>
Date: Sun, 4 Jul 2021 14:34:28 +1000
Subject: [PATCH 1/2] Correct pairing docstrings

The pairing functions use precompile 0x8, defined in EIP-197.

The EIP states:
Elements a * i + b of F_p^2 are encoded as two elements of F_p, (a, b)
So the imaginary component should be specified first.

Additionally, it checks whether e(a1, b1) * ... * e(ak, bk) = 1

The docstrings currently list real components first and invert the
first pairing term. This commit corrects them.
---
 contracts/BN256G1.sol | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/contracts/BN256G1.sol b/contracts/BN256G1.sol
index c4955de..e1ee321 100644
--- a/contracts/BN256G1.sol
+++ b/contracts/BN256G1.sol
@@ -91,21 +91,21 @@ library BN256G1 {
       PP);
   }
 
-  /// @dev Checks if e(P, Q) = e (R,S).
+  /// @dev Checks if 1 = e(P, Q)*e (R,S).
   /// @param input: 12 values of 256 bits each:
   ///  *) x-coordinate of point P
   ///  *) y-coordinate of point P
-  ///  *) x real coordinate of point Q
   ///  *) x imaginary coordinate of point Q
-  ///  *) y real coordinate of point Q
+  ///  *) x real coordinate of point Q
   ///  *) y imaginary coordinate of point Q
+  ///  *) y real coordinate of point Q
   ///  *) x-coordinate of point R
   ///  *) y-coordinate of point R
-  ///  *) x real coordinate of point S
   ///  *) x imaginary coordinate of point S
-  ///  *) y real coordinate of point S
+  ///  *) x real coordinate of point S
   ///  *) y imaginary coordinate of point S
-  /// @return true if e(P, Q) = e (R,S).
+  ///  *) y real coordinate of point S
+  /// @return true if 1 = e(P, Q)*e (R,S).
   function bn256CheckPairing(uint256[12] memory input) internal returns (bool) {
     uint256[1] memory result;
     bool success;
@@ -121,22 +121,22 @@ library BN256G1 {
     return result[0] == 1;
   }
 
-  /// @dev Checks if e(P, Q) = e (R,S)*e(T,U)...
+  /// @dev Checks if 1 = e(P, Q)*e (R,S)*e(T,U)...
   /// @param input: A modulo 6 length array of values of 256 bits each:
   ///  *) x-coordinate of point P
   ///  *) y-coordinate of point P
-  ///  *) x real coordinate of point Q
   ///  *) x imaginary coordinate of point Q
-  ///  *) y real coordinate of point Q
+  ///  *) x real coordinate of point Q
   ///  *) y imaginary coordinate of point Q
+  ///  *) y real coordinate of point Q
   ///  *) x-coordinate of point R
   ///  *) y-coordinate of point R
-  ///  *) x real coordinate of point S
   ///  *) x imaginary coordinate of point S
-  ///  *) y real coordinate of point S
+  ///  *) x real coordinate of point S
   ///  *) y imaginary coordinate of point S
+  ///  *) y real coordinate of point S
   ///  *) and so forth with additional pairing checks
-  /// @return true if e(input[0,1], input[2,3,4,5]) = e(input[6,7], input[8,9,10,11])*e(input[12,13], input[14,15,16,17])...
+  /// @return true if 1 = e(input[0,1], input[2,3,4,5])*e(input[6,7], input[8,9,10,11])*e(input[12,13], input[14,15,16,17])...
   function bn256CheckPairingBatch(uint256[] memory input) internal returns (bool) {
     uint256[1] memory result;
     bool success;

From d8c9e029a8d6a98cda8f0dfe3c0abc2224fb6211 Mon Sep 17 00:00:00 2001
From: Nikesh Nazareth <business@nikeshnazareth.com>
Date: Sun, 4 Jul 2021 14:43:18 +1000
Subject: [PATCH 2/2] Fix spacing

---
 contracts/BN256G1.sol | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/contracts/BN256G1.sol b/contracts/BN256G1.sol
index e1ee321..d6b5202 100644
--- a/contracts/BN256G1.sol
+++ b/contracts/BN256G1.sol
@@ -91,7 +91,7 @@ library BN256G1 {
       PP);
   }
 
-  /// @dev Checks if 1 = e(P, Q)*e (R,S).
+  /// @dev Checks if 1 = e(P, Q)*e(R, S).
   /// @param input: 12 values of 256 bits each:
   ///  *) x-coordinate of point P
   ///  *) y-coordinate of point P
@@ -105,7 +105,7 @@ library BN256G1 {
   ///  *) x real coordinate of point S
   ///  *) y imaginary coordinate of point S
   ///  *) y real coordinate of point S
-  /// @return true if 1 = e(P, Q)*e (R,S).
+  /// @return true if 1 = e(P, Q)*e(R, S).
   function bn256CheckPairing(uint256[12] memory input) internal returns (bool) {
     uint256[1] memory result;
     bool success;