ethereum.forks.constantinople.vm.precompiled_contracts.alt_bn128

Ethereum Virtual Machine (EVM) ALT_BN128 CONTRACTS.

.. contents:: Table of Contents :backlinks: none :local:

Introduction

Implementation of the ALT_BN128 precompiled contracts.

bytes_to_g1

Decode 64 bytes to a point on the curve.

Parameters

data : The bytes data to decode.

Returns

point : Point3D A point on the curve.

Raises

InvalidParameter Either a field element is invalid or the point is not on the curve.

def bytes_to_g1(​data: Bytes​) -> Point3D[FQ]:
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    """
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    Decode 64 bytes to a point on the curve.
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    Parameters
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    ----------
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    data :
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        The bytes data to decode.
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    Returns
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    -------
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    point : Point3D
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        A point on the curve.
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    Raises
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    ------
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    InvalidParameter
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        Either a field element is invalid or the point is not on the curve.
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    """
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    if len(data) != 64:
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        raise InvalidParameter("Input should be 64 bytes long")
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    x_bytes = buffer_read(data, U256(0), U256(32))
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    x = int(U256.from_be_bytes(x_bytes))
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    y_bytes = buffer_read(data, U256(32), U256(32))
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    y = int(U256.from_be_bytes(y_bytes))
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    if x >= field_modulus:
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        raise InvalidParameter("Invalid field element")
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    if y >= field_modulus:
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        raise InvalidParameter("Invalid field element")
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    z = 1
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    if x == 0 and y == 0:
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        z = 0
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    point = (FQ(x), FQ(y), FQ(z))
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    # Check if the point is on the curve
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    if not is_on_curve(point, b):
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        raise InvalidParameter("Point is not on curve")
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    return point

bytes_to_g2

Decode 128 bytes to a G2 point.

Parameters

data : The bytes data to decode.

Returns

point : Point2D A point on the curve.

Raises

InvalidParameter Either a field element is invalid or the point is not on the curve.

def bytes_to_g2(​data: Bytes​) -> Point3D[FQ2]:
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    """
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    Decode 128 bytes to a G2 point.
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    Parameters
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    ----------
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    data :
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        The bytes data to decode.
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    Returns
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    -------
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    point : Point2D
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        A point on the curve.
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    Raises
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    ------
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    InvalidParameter
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        Either a field element is invalid or the point is not on the curve.
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    """
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    if len(data) != 128:
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        raise InvalidParameter("G2 should be 128 bytes long")
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    x0_bytes = buffer_read(data, U256(0), U256(32))
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    x0 = int(U256.from_be_bytes(x0_bytes))
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    x1_bytes = buffer_read(data, U256(32), U256(32))
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    x1 = int(U256.from_be_bytes(x1_bytes))
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    y0_bytes = buffer_read(data, U256(64), U256(32))
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    y0 = int(U256.from_be_bytes(y0_bytes))
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    y1_bytes = buffer_read(data, U256(96), U256(32))
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    y1 = int(U256.from_be_bytes(y1_bytes))
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    if x0 >= field_modulus or x1 >= field_modulus:
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        raise InvalidParameter("Invalid field element")
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    if y0 >= field_modulus or y1 >= field_modulus:
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        raise InvalidParameter("Invalid field element")
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    x = FQ2((x1, x0))
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    y = FQ2((y1, y0))
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    z = (1, 0)
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    if x == FQ2((0, 0)) and y == FQ2((0, 0)):
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        z = (0, 0)
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    point = (x, y, FQ2(z))
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    # Check if the point is on the curve
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    if not is_on_curve(point, b2):
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        raise InvalidParameter("Point is not on curve")
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    return point

alt_bn128_add

The ALT_BN128 addition precompiled contract.

Parameters

evm : The current EVM frame.

def alt_bn128_add(​evm: Evm​) -> None:
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    """
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    The ALT_BN128 addition precompiled contract.
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    Parameters
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    ----------
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    evm :
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        The current EVM frame.
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    """
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    data = evm.message.data
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    # GAS
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    charge_gas(evm, Uint(500))
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    # OPERATION
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    try:
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        p0 = bytes_to_g1(buffer_read(data, U256(0), U256(64)))
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        p1 = bytes_to_g1(buffer_read(data, U256(64), U256(64)))
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    except InvalidParameter as e:
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        raise OutOfGasError from e
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    p = add(p0, p1)
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    x, y = normalize(p)
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    evm.output = Uint(x).to_be_bytes32() + Uint(y).to_be_bytes32()

alt_bn128_mul

The ALT_BN128 multiplication precompiled contract.

Parameters

evm : The current EVM frame.

def alt_bn128_mul(​evm: Evm​) -> None:
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    """
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    The ALT_BN128 multiplication precompiled contract.
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    Parameters
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    ----------
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    evm :
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        The current EVM frame.
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    """
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    data = evm.message.data
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    # GAS
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    charge_gas(evm, Uint(40000))
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    # OPERATION
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    try:
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        p0 = bytes_to_g1(buffer_read(data, U256(0), U256(64)))
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    except InvalidParameter as e:
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        raise OutOfGasError from e
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    n = int(U256.from_be_bytes(buffer_read(data, U256(64), U256(32))))
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    p = multiply(p0, n)
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    x, y = normalize(p)
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    evm.output = Uint(x).to_be_bytes32() + Uint(y).to_be_bytes32()

alt_bn128_pairing_check

The ALT_BN128 pairing check precompiled contract.

Parameters

evm : The current EVM frame.

def alt_bn128_pairing_check(​evm: Evm​) -> None:
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    """
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    The ALT_BN128 pairing check precompiled contract.
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    Parameters
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    ----------
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    evm :
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        The current EVM frame.
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    """
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    data = evm.message.data
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    # GAS
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    charge_gas(evm, Uint(80000 * (len(data) // 192) + 100000))
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    # OPERATION
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    if len(data) % 192 != 0:
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        raise OutOfGasError
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    result = FQ12.one()
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    for i in range(len(data) // 192):
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        try:
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            p = bytes_to_g1(buffer_read(data, U256(192 * i), U256(64)))
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            q = bytes_to_g2(buffer_read(data, U256(192 * i + 64), U256(128)))
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        except InvalidParameter as e:
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            raise OutOfGasError from e
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        if not is_inf(multiply(p, curve_order)):
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            raise OutOfGasError
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        if not is_inf(multiply(q, curve_order)):
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            raise OutOfGasError
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        result *= pairing(q, p)
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    if result == FQ12.one():
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        evm.output = U256(1).to_be_bytes32()
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    else:
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        evm.output = U256(0).to_be_bytes32()