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align comments and fix numeration of steps

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Signed-off-by: Uncle Fatso <uncle.fatso@ghostchain.io>
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Uncle Fatso 2025-10-12 22:15:10 +03:00
parent abbb720857
commit 2b3eb14012
Signed by: f4ts0
GPG Key ID: 565F4F2860226EBB
1 changed files with 66 additions and 66 deletions
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src/libraries/ECMathProjective.sol
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@ -119,16 +119,16 @@ library EllipticCurveProjective {
uint256 t0 = mulmod(Y, Y, P); // 1. t0 ← Y · Y => (Y²) uint256 t0 = mulmod(Y, Y, P); // 1. t0 ← Y · Y => (Y²)
Z3 = mulmod(8, t0, P); // 2. Z3 ← t0 + t0 => (8Y²) Z3 = mulmod(8, t0, P); // 2. Z3 ← t0 + t0 => (8Y²)
uint256 t1 = mulmod(Y, Z, P); // 5. t1 ← Y · Z => (YZ) uint256 t1 = mulmod(Y, Z, P); // 3. t1 ← Y · Z => (YZ)
uint256 t2 = mulmod(Z, Z, P); // 6. t2 ← Z · Z => (Z²) uint256 t2 = mulmod(Z, Z, P); // 4. t2 ← Z · Z => (Z²)
t2 = mulmod(21, t2, P); // 7. t2 ← b3 · t2 => (3bZ²) t2 = mulmod(21, t2, P); // 5. t2 ← b3 · t2 => (3bZ²)
X3 = mulmod(t2, Z3, P); // 8. X3 ← t2 · Z3 => (3bZ²8Y²) X3 = mulmod(t2, Z3, P); // 6. X3 ← t2 · Z3 => (3bZ²8Y²)
Y3 = addmod(t0, t2, P); // 9. Y3 ← t0 + t2 => (Y² + 3bZ²) Y3 = addmod(t0, t2, P); // 7. Y3 ← t0 + t2 => (Y² + 3bZ²)
Z3 = mulmod(t1, Z3, P); // 10. Z3 ← t1 · Z3 => (YZ · 8Y² = 8Y³Z) Z3 = mulmod(t1, Z3, P); // 8. Z3 ← t1 · Z3 => (YZ · 8Y² = 8Y³Z)
t1 = addmod(t0, P - mulmod(3, t2, P), P); // 11. t1 ← t0 - (3 · t2) => (Y² - 9bZ²) t1 = addmod(t0, P - mulmod(3, t2, P), P); // 9. t1 ← t0 - (3 · t2) => (Y² - 9bZ²)
Y3 = addmod(X3, mulmod(t1, Y3, P), P); // 12. Y3 ← t1 · (t1 · Y3) => ((Y² - 9bZ²) · (Y² + 3bZ²)) Y3 = addmod(X3, mulmod(t1, Y3, P), P); // 10. Y3 ← t1 · (t1 · Y3) => ((Y² - 9bZ²) · (Y² + 3bZ²))
X3 = mulmod(t1, mulmod(X, Y, P), P); // 13. X3 ← t1 · (X1 · Y1) => ((Y² - 9bZ²) · XY) X3 = mulmod(t1, mulmod(X, Y, P), P); // 11. X3 ← t1 · (X1 · Y1) => ((Y² - 9bZ²) · XY)
X3 = addmod(X3, X3, P); // 14. X3 ← X3 + X3 => ((Y² - 9bZ²) · 2XY) X3 = addmod(X3, X3, P); // 12. X3 ← X3 + X3 => ((Y² - 9bZ²) · 2XY)
} }
function toAffine(uint256 x, uint256 y, uint256 z) internal pure returns (uint256 _x, uint256 _y) { function toAffine(uint256 x, uint256 y, uint256 z) internal pure returns (uint256 _x, uint256 _y) {