check that the public keys lie on the curve.?

[Noname400]

hello, tell me how to check that the public keys lie on the curve.?
and how to check that after the operation of multiplication I left the border of the curve?

[tomato42]

All the public methods in VerifyingKey check if the public key lies on the curve, it's controlled by the validate_point option like:

python-ecdsa/src/ecdsa/keys.py

Lines 202 to 204 in b3b27cd

	def from_public_point(
	cls, point, curve=NIST192p, hashfunc=sha1, validate_point=True
	):

or:

python-ecdsa/src/ecdsa/keys.py

Lines 286 to 293 in b3b27cd

	def from_string(
	cls,
	string,
	curve=NIST192p,
	hashfunc=sha1,
	validate_point=True,
	valid_encodings=None,
	):

and how to check that after the operation of multiplication I left the border of the curve?

if a point was on the curve before multiplication, then the result will be on the curve...

You can double check that on high level, by exporting the point to a byte string and then create a new VerifyingKey instance, that will verify if it is on curve still.

On low level, you need to get the CurveFp() and call contains_point() for short Weierstrass curves:

python-ecdsa/src/ecdsa/ellipticcurve.py

Line 131 in b3b27cd

def contains_point(self, x, y):

or the contains_point() of CurveEdTw() for twisted Edwards curves:

python-ecdsa/src/ecdsa/ellipticcurve.py

Line 197 in b3b27cd

def contains_point(self, x, y):