pyecsca.ec.divpoly module¶
Provides functions for computing division polynomials and the multiplication-by-n map on an elliptic curve.
- a_invariants(curve)[source]¶
Compute the a-invariants of the curve.
- Parameters:
curve¶ (
EllipticCurve) – The elliptic curve (only ShortWeierstrass model).- Return type:
Tuple[Mod,...]- Returns:
A tuple of 5 a-invariants (a1, a2, a3, a4, a6).
- b_invariants(curve)[source]¶
Compute the b-invariants of the curve.
- Parameters:
curve¶ (
EllipticCurve) – The elliptic curve (only ShortWeierstrass model).- Return type:
Tuple[Mod,...]- Returns:
A tuple of 4 b-invariants (b2, b4, b6, b8).
- divpoly(curve, n, two_torsion_multiplicity=2)[source]¶
Compute the n-th division polynomial.
- Parameters:
curve¶ (
EllipticCurve) – Curve to compute on.n¶ (
int) – Scalar.two_torsion_multiplicity¶ (
int) – Same as sagemath.
- Return type:
Poly- Returns:
The division polynomial.
- mult_by_n(curve, n, x_only=False, use_pari=True)[source]¶
Compute the multiplication-by-n map on an elliptic curve.
- Parameters:
curve¶ (
EllipticCurve) – Curve to compute on.n¶ (
int) – Scalar.x_only¶ (
bool) – Whether to skip the my computation.use_pari¶ (
bool) – Whether to use the Pari version.
- Return type:
Tuple[Tuple[Poly,Poly],Optional[Tuple[Poly,Poly]]]- Returns:
A tuple (mx, my) where each is a tuple (numerator, denominator).