def __mul__(self, scalar: int):
"""Multiply a :class:`Point` on an elliptic curve by an integer.
Args:
| self (:class:`Point`): a point :math:`P` on the curve
| other (int): an integer :math:`d \in \mathbb{Z_q}` where :math:`q` is the order of
the curve that :math:`P` is on
Returns:
:class:`Point`: A point :math:`R` such that :math:`R = P * d`
"""
validate_type(scalar, int)
if scalar == 0:
return self.IDENTITY_ELEMENT
x, y = curvemath.mul(str(self.x), str(self.y), str(scalar),
str(self.curve.p), str(self.curve.a),
str(self.curve.b), str(self.curve.q),
str(self.curve.gx), str(self.curve.gy))
x = int(x)
y = int(y)
if x == 0 and y == 0:
return self.IDENTITY_ELEMENT
return Point(x, y, self.curve)
def __mul__(self, scalar):
"""Multiply a :class:`Point`s on an elliptic curve by an integer.
Args:
| self (fastecdsa.point.Point): a point :math:`P` on the curve
| other (long): an integer :math:`d \in \mathbb{Z_q}` where :math:`q` is the order of
the curve that :math:`P` is on
Returns:
fastecdsa.point.Point: A point :math:`R` such that :math:`R = P * d`
"""
try:
d = int(scalar) % self.curve.q
except ValueError:
raise TypeError('Curve point multiplication must be by an integer')
else:
x, y = curvemath.mul(
str(self.x),
str(self.y),
str(d),
str(self.curve.p),
str(self.curve.a),
str(self.curve.b),
str(self.curve.q),
str(self.curve.gx),
str(self.curve.gy)
)
return Point(int(x), int(y), self.curve)
def __mul__(self, scalar):
e = scalar
if self.__order: e = e % self.__order
if e == 0:
return INFINITY
if self == INFINITY: return INFINITY
try:
d = int(scalar) % self.__order
except ValueError:
raise TypeError('Curve point multiplication must be by an integer')
else:
x, y = curvemath.mul(
str(self.__x),
str(self.__y),
str(d),
str(self.__curve.p()),
str(self.__curve.a()),
str(self.__curve.b()),
str(self.__order),
# hardcode secp256k1 generator x and y. TODO: refactor
str(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
),
str(0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
))
return Point(self.curve(), int(x), int(y), self.order())