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# Bug: multiplication of Point by negative const produces wrong results

See original GitHub issue
``````from fastecdsa.curve import P256
from fastecdsa.point import Point

xs = 0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9
S = Point(xs, ys, curve=P256)

print(S)
# X: 0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9
# (On curve <P256>)
print((-1)*S)
# X: 0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9
# (On curve <P256>)
print(-S)
# X: 0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9
# Y: 0x3f6c517f0c91ac8003fe5a552e1999a68fd217f1ac313a8949caf4dbcfbd5da9
# (On curve <P256>)
print((-1-P256.q)*S)
# X: 0x2754ffb5ff6ff19af1bb2fe0ef25a22d3a28731031d319afa9bf707c3595d58d
# Y: 0x3832af93a61dc91177c094f3c1723e5a3f4e29cc9fbc862da05be393b54a9a9e
# (On curve <P256>)

``````

version 2.1.5

### Issue Analytics

• State:
• Created 2 years ago

1reaction
AntonKueltzcommented, Dec 17, 2021

Revisiting this issue - given that the fallback code is needed anyway I’m in favor of keeping things as they are and not introducing an additional cofactor field. If anyone has objections we can discuss here.

1reaction
bbbrumleycommented, Jul 14, 2021

Just to be clear: you cannot always calculate the cofactor like I give in the pointer. So in the end, you need the fallback code anyway – i.e. no scalar reduction, and sign considerations – which is what you’ve merged already.

For curves already built into fastecdsa, this doesn’t matter because `h` is a precomputed constant. It’s only a question of custom curves instantiated with the `Curve` class.

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