楕円曲線のスカラー倍算

from ecc import FieldElement, Point
 
prime = 223
a = FieldElement(num=0, prime=prime)
b = FieldElement(num=7, prime=prime)
x = FieldElement(num=192, prime=prime)
y = FieldElement(num=105, prime=prime)
p = Point(x, y, a, b)
print(vars(p+p))

$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(49), ‘y’: FieldElement_223(71)}

p * p や 2*pとすると、以下のようなエラーとなってしまう。
$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(49), ‘y’: FieldElement_223(71)}
Traceback (most recent call last):
File “/home/vagrant/dev/blockchain/main.py”, line 10, in
print(vars(p*p))
TypeError: unsupported operand type(s) for *: ‘Point’ and ‘Point’

Traceback (most recent call last):
File “/home/vagrant/dev/blockchain/test.py”, line 9, in
print(p+p)
File “/home/vagrant/dev/blockchain/ecc.py”, line 89, in __add__
if self == other and self.y == 0 * self.x:
TypeError: unsupported operand type(s) for *: ‘int’ and ‘FieldElement’

他のパターン
x = FieldElement(num=143, prime=prime)
y = FieldElement(num=98, prime=prime)
$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(64), ‘y’: FieldElement_223(168)}

x = FieldElement(num=47, prime=prime)
y = FieldElement(num=71, prime=prime)
$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(36), ‘y’: FieldElement_223(111)}

4 * (47, 71) の場合
$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(194), ‘y’: FieldElement_223(51)}

8 * (47, 71) の場合
$ python3 main.py
{‘a’: FieldElement_223(0), ‘b’: FieldElement_223(7), ‘x’: FieldElement_223(116), ‘y’: FieldElement_223(55)}