| | |
- builtins.object
-
- FiniteGroupElement
-
- ClassGroupForm
- EllipticCurvePoint
-
- EdwardsCurvePoint
-
- EdwardsAffine
- EdwardsExtended
- EdwardsProjective
- WeierstrassCurvePoint
-
- WeierstrassAffine
- WeierstrassJacobian
- WeierstrassProjective
- QuadraticResidue
- SchnorrGroupElement
- SymmetricGroupElement
class ClassGroupForm(FiniteGroupElement) |
| |
ClassGroupForm(value=None, check=True)
Common base class for class groups of imaginary quadratic fields.
Represented by primitive positive definite forms (a,b,c) of discriminant D<0.
That is, all forms (a,b,c) with D=b^2-4ac<0 satisfying gcd(a,b,c)=1 and a>0.
|
| |
- Method resolution order:
- ClassGroupForm
- FiniteGroupElement
- builtins.object
Methods defined here:
- __getitem__(self, key)
- __init__(self, value=None, check=True)
- Create a binary quadratic form (a,b,c).
Invariant: form (a,b,c) is reduced.
Class methods defined here:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in the first coefficient of a form.
- equality(f1, f2, /) from builtins.type
- Return a == b.
- inversion(f, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(f1, f2, /) from builtins.type
- Return a @ b.
- operation2(f, /) from builtins.type
- Return a @ a.
Data and other attributes defined here:
- __annotations__ = {'discriminant': <class 'int'>}
- bit_length = None
- gap = None
- is_abelian = True
- is_multiplicative = True
- order = None
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_additive = False
- is_cyclic = None
|
class EdwardsAffine(EdwardsCurvePoint) |
| |
EdwardsAffine(value=None, check=True)
Edwards curves with affine coordinates.
|
| |
- Method resolution order:
- EdwardsAffine
- EdwardsCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add Edwards points using affine coordinates (projective with z=1).
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = True
Methods inherited from EdwardsCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from EdwardsCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from EdwardsCurvePoint:
- a = None
- d = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
|
class EdwardsCurvePoint(EllipticCurvePoint) |
| |
EdwardsCurvePoint(value=None, check=True)
Common base class for (twisted) Edwards curves.
|
| |
- Method resolution order:
- EdwardsCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods defined here:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes defined here:
- __annotations__ = {}
- a = None
- d = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
- normalize(self)
- Convert to unique affine representation.
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
- oblivious = None
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
|
class EdwardsExtended(EdwardsCurvePoint) |
| |
EdwardsExtended(value=None, check=True)
Edwards curves with extended coordinates.
|
| |
- Method resolution order:
- EdwardsExtended
- EdwardsCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add (twisted a=-1) Edwards points in extended projective coordinates.
- operation2(pt, /) from builtins.type
- Doubling (twisted a=-1) Edwards point in extended projective coordinates.
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = True
Methods inherited from EdwardsCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from EdwardsCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from EdwardsCurvePoint:
- a = None
- d = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
|
class EdwardsProjective(EdwardsCurvePoint) |
| |
EdwardsProjective(value=None, check=True)
Edwards curves with projective coordinates.
|
| |
- Method resolution order:
- EdwardsProjective
- EdwardsCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add Edwards points with (homogeneous) projective coordinates.
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = True
Methods inherited from EdwardsCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from EdwardsCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from EdwardsCurvePoint:
- a = None
- d = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
|
class EllipticCurvePoint(FiniteGroupElement) |
| |
Common base class for elliptic curve groups.
|
| |
- Method resolution order:
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- __getitem__(self, key)
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Readonly properties defined here:
- x
- y
- z
Data and other attributes defined here:
- __annotations__ = {'field': <class 'type'>}
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
- oblivious = None
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
|
class FiniteGroupElement(builtins.object) |
| |
Abstract base class for finite groups.
Overview Python operators for group operation, inverse, and repeated operation:
- default notation: @, ~, ^ (matmul, invert, xor).
- additive notation: +, -, * (add, sub, mul)
- multiplicative notation: *, 1/ (or, **-1), ** (mul, truediv (or, pow), pow)
|
| |
Methods defined here:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods defined here:
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods defined here:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors defined here:
- value
Data and other attributes defined here:
- __annotations__ = {'value': <class 'object'>}
- generator = None
- identity = None
- is_abelian = None
- is_additive = False
- is_cyclic = None
- is_multiplicative = False
- order = None
|
class QuadraticResidue(FiniteGroupElement) |
| |
QuadraticResidue(value=1, check=True)
Common base class for groups of quadratic residues modulo an odd prime.
Quadratic residues modulo p represented by GF(p)* elements.
|
| |
- Method resolution order:
- QuadraticResidue
- FiniteGroupElement
- builtins.object
Methods defined here:
- __init__(self, value=1, check=True)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
Class methods defined here:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in a quadratic residue.
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- repeat(a, n) from builtins.type
- Return nth @-power of a (written a^n), for any integer n.
Data and other attributes defined here:
- __annotations__ = {'field': <class 'type'>}
- gap = None
- is_abelian = True
- is_cyclic = True
- is_multiplicative = True
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- operation2(a, /) from builtins.type
- Return a @ a.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_additive = False
- order = None
|
class SchnorrGroupElement(FiniteGroupElement) |
| |
SchnorrGroupElement(value=1, check=True)
Common base class for prime-order subgroups of the multiplicative group of a finite field.
|
| |
- Method resolution order:
- SchnorrGroupElement
- FiniteGroupElement
- builtins.object
Methods defined here:
- __init__(self, value=1, check=True)
- Initialize self. See help(type(self)) for accurate signature.
- __int__(self)
Class methods defined here:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in group element g^m.
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- repeat(a, n) from builtins.type
- Return nth @-power of a (written a^n), for any integer n.
Data and other attributes defined here:
- __annotations__ = {'field': <class 'type'>}
- is_abelian = True
- is_cyclic = True
- is_multiplicative = True
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- operation2(a, /) from builtins.type
- Return a @ a.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_additive = False
- order = None
|
class SymmetricGroupElement(FiniteGroupElement) |
| |
SymmetricGroupElement(value=None, check=True)
Common base class for symmetric groups.
Symmetric groups contains all permutations of a fixed length (degree).
Permutations of {0,...,n-1} represented as length-n tuples with unique
entries in {0,...,n-1}, n>=0.
|
| |
- Method resolution order:
- SymmetricGroupElement
- FiniteGroupElement
- builtins.object
Methods defined here:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods defined here:
- equality(p, q, /) from builtins.type
- Return a == b.
- inversion(p, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(p, q, /) from builtins.type
- First p then q.
Data and other attributes defined here:
- __annotations__ = {}
- degree = None
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_abelian = None
- is_additive = False
- is_cyclic = None
- is_multiplicative = False
- order = None
|
class WeierstrassAffine(WeierstrassCurvePoint) |
| |
WeierstrassAffine(value=None, check=True)
Short Weierstrass curves with affine coordinates.
|
| |
- Method resolution order:
- WeierstrassAffine
- WeierstrassCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add Weierstrass points with affine coordinates.
- operation2(pt, /) from builtins.type
- Double Weierstrass point with affine coordinates.
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = False
Methods inherited from WeierstrassCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from WeierstrassCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from WeierstrassCurvePoint:
- a = None
- b = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
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class WeierstrassCurvePoint(EllipticCurvePoint) |
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WeierstrassCurvePoint(value=None, check=True)
Common base class for (short) Weierstrass curves.
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- Method resolution order:
- WeierstrassCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods defined here:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes defined here:
- __annotations__ = {}
- a = None
- b = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
- normalize(self)
- Convert to unique affine representation.
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
- oblivious = None
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Class methods inherited from FiniteGroupElement:
- equality(a, b, /) from builtins.type
- Return a == b.
- inversion(a, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(a, b, /) from builtins.type
- Return a @ b.
- operation2(a, /) from builtins.type
- Return a @ a.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
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class WeierstrassJacobian(WeierstrassCurvePoint) |
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WeierstrassJacobian(value=None, check=True)
Short Weierstrass curves with Jacobian coordinates.
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- Method resolution order:
- WeierstrassJacobian
- WeierstrassCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add Weierstrass points with Jacobian coordinates.
- operation2(pt, /) from builtins.type
- Double Weierstrass point with Jacobian coordinates.
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = False
Methods inherited from WeierstrassCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from WeierstrassCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from WeierstrassCurvePoint:
- a = None
- b = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
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class WeierstrassProjective(WeierstrassCurvePoint) |
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WeierstrassProjective(value=None, check=True)
Short Weierstrass curves with projective coordinates.
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- Method resolution order:
- WeierstrassProjective
- WeierstrassCurvePoint
- EllipticCurvePoint
- FiniteGroupElement
- builtins.object
Methods defined here:
- normalize(self)
- Convert to unique affine representation.
Class methods defined here:
- equality(pt1, pt2, /) from builtins.type
- Return a == b.
- inversion(pt, /) from builtins.type
- Return @-inverse of a (written ~a).
- operation(pt1, pt2, /) from builtins.type
- Add Weierstrass points with projective coordinates.
- operation2(pt, /) from builtins.type
- Double Weierstrass point with projective coordinates.
Data and other attributes defined here:
- __annotations__ = {}
- oblivious = True
Methods inherited from WeierstrassCurvePoint:
- __init__(self, value=None, check=True)
- Initialize self. See help(type(self)) for accurate signature.
Class methods inherited from WeierstrassCurvePoint:
- ysquared(x) from builtins.type
- Return value of y^2 as a function of x, for a point (x, y) on the curve.
Data and other attributes inherited from WeierstrassCurvePoint:
- a = None
- b = None
Methods inherited from EllipticCurvePoint:
- __getitem__(self, key)
Class methods inherited from EllipticCurvePoint:
- decode(M, Z) from builtins.type
- encode(m) from builtins.type
- Encode message m in x-coordinate of a point on the curve.
Readonly properties inherited from EllipticCurvePoint:
- x
- y
- z
Data and other attributes inherited from EllipticCurvePoint:
- gap = None
- is_abelian = True
- is_additive = True
- is_multiplicative = False
Methods inherited from FiniteGroupElement:
- __add__(self, other)
- __eq__(self, other)
- Return self==value.
- __hash__(self)
- Make finite group elements hashable (e.g., for LRU caching).
- __invert__(self)
- __matmul__(self, other)
- __mul__(self, other)
- __neg__(self)
- __pow__(self, other)
- __repr__(self)
- Return repr(self).
- __rmul__(self, other)
- __rtruediv__(self, other)
- __sub__(self, other)
- __truediv__(self, other)
- __xor__(self, other)
- inverse(self)
- For convenience.
Static methods inherited from FiniteGroupElement:
- repeat(a, n)
- Return nth @-power of a (written a^n), for any integer n.
Data descriptors inherited from FiniteGroupElement:
- value
Data and other attributes inherited from FiniteGroupElement:
- generator = None
- identity = None
- is_cyclic = None
- order = None
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