public void TestPairing()
{
var standardResult = Bn128Pairing.Pair(Bn128Curve.G2, Bn128Curve.G1);
var negativeG1Result = Bn128Pairing.Pair(Bn128Curve.G2, Bn128Curve.G1.Negate());
Assert.Equal(Fp12.OneValue, standardResult * negativeG1Result);
var negativeG2Result = Bn128Pairing.Pair(Bn128Curve.G2.Negate(), Bn128Curve.G1);
Assert.Equal(Fp12.OneValue, standardResult * negativeG1Result);
Assert.Equal(Fp12.OneValue, standardResult.Pow(Bn128Curve.N));
var twoTimesG1Result = Bn128Pairing.Pair(Bn128Curve.G2, Bn128Curve.G1.Multiply(2));
Assert.Equal(standardResult * standardResult, twoTimesG1Result);
Assert.NotEqual(standardResult, twoTimesG1Result);
Assert.NotEqual(standardResult, negativeG2Result);
Assert.NotEqual(twoTimesG1Result, negativeG2Result);
var twoTimesG2Result = Bn128Pairing.Pair(Bn128Curve.G2.Multiply(2), Bn128Curve.G1);
Assert.Equal(standardResult * standardResult, twoTimesG2Result);
var final1 = Bn128Pairing.Pair(Bn128Curve.G2.Multiply(27), Bn128Curve.G1.Multiply(37));
var final2 = Bn128Pairing.Pair(Bn128Curve.G2, Bn128Curve.G1.Multiply(999));
Assert.Equal(final1, final2);
}
private static EVMExecutionResult Precompile_ECPairing(MeadowEVM evm)
{
// Verify we're past the byzantium fork
if (evm.Version < EthereumRelease.Byzantium)
{
return(new EVMExecutionResult(evm, null, true));
}
const int PAIRING_SIZE_PER_POINT = 192;
// Verify our messatge data is divisible by our size per point.
if (evm.Message.Data.Length % PAIRING_SIZE_PER_POINT != 0)
{
throw new EVMException($"ECPairing precompile failed because the call data was not divisible by the size per point ({PAIRING_SIZE_PER_POINT}).");
}
// Charge the gas for the precompile operation before processing.
BigInteger gasCharge = GasDefinitions.GAS_PRECOMPILE_ECPAIRING_BASE + ((evm.Message.Data.Length / PAIRING_SIZE_PER_POINT) * GasDefinitions.GAS_PRECOMPILE_ECPAIRING_PER_POINT);
evm.GasState.Deduct(gasCharge);
// Obtain a memory representation of our data.
Span <byte> messageData = new Span <byte>(evm.Message.Data);
// Define some constant variables for arithmetic.
FpVector3 <Fp2> zero = new FpVector3 <Fp2>(Fp2.OneValue, Fp2.OneValue, Fp2.ZeroValue);
Fp12 exponent = Fp12.OneValue;
// Loop for each point in our data
for (int i = 0; i < evm.Message.Data.Length; i += PAIRING_SIZE_PER_POINT)
{
// Obtain our component data
BigInteger x1 = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 0, EVMDefinitions.WORD_SIZE));
BigInteger y1 = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 32, EVMDefinitions.WORD_SIZE));
BigInteger x2_i = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 64, EVMDefinitions.WORD_SIZE));
BigInteger x2_r = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 96, EVMDefinitions.WORD_SIZE));
BigInteger y2_i = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 128, EVMDefinitions.WORD_SIZE));
BigInteger y2_r = BigIntegerConverter.GetBigInteger(messageData.Slice(i + 160, EVMDefinitions.WORD_SIZE));
// Parse and verify our point.
FpVector3 <Fp> point1 = ParsePoint(x1, y1);
if (point1 == null)
{
throw new EVMException("ECPairing precompile failed because point 1 was deemed invalid when parsing.");
}
// If our coordinates exceed our modulo divisor, they are invalid.
if (x2_i >= Bn128Curve.P || x2_r >= Bn128Curve.P || y2_i >= Bn128Curve.P || y2_r >= Bn128Curve.P)
{
throw new EVMException("ECPairing precompile failed because point 2 was deemed invalid when parsing.");
}
Fp2 x2 = new Fp2(x2_r, x2_i);
Fp2 y2 = new Fp2(y2_r, y2_i);
FpVector3 <Fp2> point2 = null;
if (x2 == Fp2.ZeroValue && y2 == Fp2.ZeroValue)
{
// Our point is the zero point.
point2 = zero;
}
else
{
// Initialize our point from components.
point2 = new FpVector3 <Fp2>(x2, y2, Fp2.OneValue);
// Verify our desired point is on the curve
if (!point2.IsOnCurveCheck(Bn128Curve.B2))
{
throw new EVMException("ECPairing precompile failed because point 2 was not on the curve.");
}
}
// Verify multiplying by the curve order is non-zero.
if (point2.Multiply(Bn128Curve.N).Z != Fp2.ZeroValue)
{
throw new EVMException("ECPairing precompile failed because point 2 was deemed invalid. Points multiplied by the curve order should equal infinity (zero).");
}
// Pair our points and multiply the exponent by them.
exponent *= Bn128Pairing.Pair(point2, point1, false);
}
// Return our result
bool returnStatus = Bn128Pairing.FinalExponentiate(exponent) == Fp12.OneValue;
byte[] returnData = BigIntegerConverter.GetBytes(returnStatus ? 1 : 0, EVMDefinitions.WORD_SIZE);
return(new EVMExecutionResult(evm, returnData, true));
}
