petrelic.petlib package

Submodules

petrelic.petlib.pairing module

This module provides a Python wrapper around RELIC’s pairings using petlib’s interface: operations in petrelic.native.pairings.G1 and petrelic.native.pairings.G2 are written additively, whereas operations in petrelic.native.pairings.GT are written multiplicatively.

class petrelic.petlib.pairing.BilinearGroupPair

Bases: object

A bilinear group pair.

Contains two origin groups G1, G2 and the image group GT. The underlying bplib.bp.BpGroup object is also embedded.

groups()

Returns the three groups in the following order : G1, G2, GT.

class petrelic.petlib.pairing.G1Elem

Bases: petrelic.native.pairing.G1Element

Element of the G1 group

export(compressed=True)

Serialize the element of G1 into a binary representation.

Example:

>>> generator = G1.generator()
>>> bin_repr = generator.to_binary()
>>> elem = G1Element.from_binary(bin_repr)
>>> generator == elem
True

classmethod from_binary(sbin, group=None)

Deserialize a binary representation of the element of G1.

Example:

>>> generator = G1.generator()
>>> bin_repr = generator.to_binary()
>>> elem = G1Element.from_binary(bin_repr)
>>> generator == elem
True

get_affine()

Return the affine coordinates (x,y) of this EC Point.

Example:

>>> generator = G1.generator()
>>> x, y = generator.get_affine_coordinates()
>>> x
Bn(3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507)
>>> y
Bn(1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569)

group

alias of G1Group

is_infinite()

Check if the object is the neutral element of G1.

Example:

>>> generator = G1.generator()
>>> order = G1.order()
>>> elem = order * generator
>>> elem.is_neutral_element()
True

pair(other)

Computes bilinear pairing with self and otherwise

Examples:

>>> G1 = G1Group()
>>> G2 = G2Group()
>>> GT = GTGroup()
>>> G1.generator().pair(G2.generator()) == GT.generator()
True

>>> p = 100 * G1.generator()
>>> q = 200 * G2.generator()
>>> p.pair(q) == GT.generator() ** 20000
True

pt_add(other)

Add two points together.

This method is aliased by a + b.

Examples:

>>> a = 10 * G1.generator()
>>> b = 40 * G1.generator()
>>> a + b == 50 * G1.generator()
True
>>> a.add(b) == 50 * G1.generator()
True

pt_add_inplace(other)

Inplace add another point.

Examples:

>>> a = 10 * G1.generator()
>>> b = 10 * G1.generator()
>>> a += 3 * G1.generator()
>>> _ = b.iadd(3 * G1.generator())
>>> a == b
True
>>> a == 13 * G1.generator()
True

pt_double()

Return double of the current element

Example:

>>> generator = G1.generator()
>>> elem = generator.double()
>>> elem == 2 * generator
True

pt_double_inplace()

Inplace double the current element.

Example:

>>> generator = G1.generator()
>>> elem = G1.generator()
>>> _ = elem.idouble()
>>> elem == 2 * generator
True

pt_eq(other)

Check point equality.

pt_mul(other)

Multiply point by a scalar

This method is aliased by n * pt.

Examples:

>>> g = G1.generator()
>>> g + g == 2 * g
True

pt_mul_inplace(other)

Inplace point multiplication by a scalar

Examples:

>>> a = G1.generator()
>>> b = G1.generator()
>>> a *= 10
>>> _ = b.imul(10)
>>> a == b
True
>>> a == 10 * G1.generator()
True

pt_neg()

Return the inverse of the element.

Examples:

>>> a = 30
>>> elem = a * G1.generator()
>>> -elem == elem.inverse()
True
>>> elem.inverse() == (G1.order() - a) * G1.generator()
True

pt_neg_inplace()

Inplace inverse of the current element

Examples:

>>> a = 30
>>> elem1 = a * G1.generator()
>>> elem2 = a * G1.generator()
>>> _ = elem1.iinverse()
>>> elem1 == elem2.inverse()
True

pt_sub(other)

Substract two points

This method is aliased by a - b.

Examples:

>>> a = 50 * G1.generator()
>>> b = 13 * G1.generator()
>>> a - b == 37 * G1.generator()
True
>>> a.sub(b) == 37 * G1.generator()
True

class petrelic.petlib.pairing.G1Group

Bases: petrelic.native.pairing.G1

G1 group

check_point(pt)

Ensures the point is on the curve.

Example:

>>> G = G1Group()
>>> G.check_point(G.generator())
True
>>> G.check_point(G.infinite())
True

classmethod infinite()

The point at infinity.

Alias for G1.neutral_element()

class petrelic.petlib.pairing.G2Elem

Bases: petrelic.native.pairing.G2Element

Element of the G2 group

export(compressed=True)

Serialize the element of G2 into a binary representation.

Example:

>>> generator = G2.generator()
>>> bin_repr = generator.to_binary()
>>> elem = G2Element.from_binary(bin_repr)
>>> generator == elem
True

classmethod from_binary(sbin, group=None)

Deserialize a binary representation of the element of G2.

Example:

>>> generator = G2.generator()
>>> bin_repr = generator.to_binary()
>>> elem = G2Element.from_binary(bin_repr)
>>> generator == elem
True

group

alias of G1Group

is_infinite()

Check if the object is the neutral element of G2.

Example:

>>> generator = G2.generator()
>>> order = G2.order()
>>> elem = order * generator
>>> elem.is_neutral_element()
True

pt_add(other)

Add two points together.

This method is aliased by a + b.

Examples:

>>> a = 10 * G2.generator()
>>> b = 40 * G2.generator()
>>> a + b == 50 * G2.generator()
True
>>> a.add(b) == 50 * G2.generator()
True

pt_add_inplace(other)

Add two points together.

This method is aliased by a + b.

Examples:

>>> a = 10 * G2.generator()
>>> b = 40 * G2.generator()
>>> a + b == 50 * G2.generator()
True
>>> a.add(b) == 50 * G2.generator()
True

pt_double()

Return double of the current element

Example:

>>> generator = G2.generator()
>>> elem = generator.double()
>>> elem == 2 * generator
True

pt_double_inplace()

Inplace double the current element.

Example:

>>> generator = G2.generator()
>>> elem = G2.generator()
>>> _ = elem.idouble()
>>> elem == 2 * generator
True

pt_eq(other)

Check that the points on the EC are equal.

pt_mul(other)

Multiply point by a scalar

This method is aliased by n * pt.

Examples:

>>> g = G2.generator()
>>> g + g == 2 * g
True

pt_mul_inplace(other)

Inplace point multiplication by a scalar

Examples:

>>> a = G2.generator()
>>> b = G2.generator()
>>> a *= 10
>>> _ = b.imul(10)
>>> a == b
True
>>> a == 10 * G2.generator()
True

pt_neg()

Return the inverse of the element.

Examples:

>>> a = 30
>>> elem = a * G2.generator()
>>> -elem == elem.inverse()
True
>>> elem.inverse() == (G2.order() - a) * G2.generator()
True

pt_neg_inplace()

Inplace inverse of the current element

Examples:

>>> a = 30
>>> elem1 = a * G2.generator()
>>> elem2 = a * G2.generator()
>>> _ = elem1.iinverse()
>>> elem1 == elem2.inverse()
True

pt_sub(other)

Substract two points

This method is aliased by a - b.

Examples:

>>> a = 50 * G2.generator()
>>> b = 13 * G2.generator()
>>> a - b == 37 * G2.generator()
True
>>> a.sub(b) == 37 * G2.generator()
True

class petrelic.petlib.pairing.G2Group

Bases: petrelic.native.pairing.G2

G2 group

check_point(pt)

Ensures the point is on the curve.

Example:

>>> G = G2Group()
>>> G.check_point(G.generator())
True
>>> G.check_point(G.infinite())
True

classmethod infinite()

The point at infinity.

Alias for G2.neutral_element()

class petrelic.petlib.pairing.GTElem

Bases: petrelic.native.pairing.GTElement

GT element

exp(other)

Raise element to the power of a scalar

This method is aliased by el ** n.

Examples:

>>> g = GT.generator()
>>> g * g == g ** 2
True
>>> g * g == g.pow(2)
True

exp_inplace(other)

Inplace raise element to the power of a scalar

Examples:

>>> g = GT.generator()
>>> a = GT.generator()
>>> _ = a.ipow(3)
>>> g * g * g == a
True

export(compressed=True)

Serialize the element of GT into a binary representation.

Example:

>>> generator = GT.generator()
>>> bin_repr = generator.to_binary()
>>> elem = GTElement.from_binary(bin_repr)
>>> generator == elem
True

classmethod from_binary(sbin, group=None)

Create an element from a byte sequence.

It accepts (but ignores) group as extra argument.

Example:

>>> G = GTGroup()
>>> byte_string = G.generator().export()                # Export EC point as byte string
>>> GTElem.from_binary(byte_string, G) == G.generator()    # Import EC point from binary string
True
>>> GTElem.from_binary(byte_string) == G.generator()    # Import EC point from binary string
True

group

alias of GTGroup

inv()

Return the inverse of the element.

Examples:

>>> a = 30
>>> elem = GT.generator() ** a
>>> elem.inverse() == GT.generator() ** (G1.order() - a)
True

inv_inplace()

Inplace inverse of the current element

Examples:

>>> a = 30
>>> elem1 = GT.generator() ** a
>>> elem2 = GT.generator() ** a
>>> _ = elem1.iinverse()
>>> elem1 == elem2.inverse()
True

mul_inplace(other)

Inplace multiplication by another element

Examples:

>>> a = GT.generator() ** 10
>>> b = GT.generator() ** 10
>>> a *= GT.generator() ** 3
>>> _ = b.imul(GT.generator() ** 3)
>>> a == b
True
>>> a == GT.generator() ** 13
True

sqr()

Return the square of the current element

Example:

>>> generator = GT.generator()
>>> elem = generator.square()
>>> elem == generator ** 2
True

sqr_inplace()

Inplace square of the current element.

Example:

>>> elem = GT.generator()
>>> _ = elem.isquare()
>>> elem == GT.generator() ** 2
True

class petrelic.petlib.pairing.GTGroup

Bases: petrelic.native.pairing.GT

GT group

check_elem(pt)

Ensures the element is an element of the group

Example:

>>> G = GTGroup()
>>> G.check_elem(G.generator())
True
>>> G.check_elem(G.unity())
True

Module contents