/
cfrg.py
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/
cfrg.py
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# -*- coding: utf-8 -*-
# pylint: disable=line-too-long
#
# Copyright (c) 2015, Red Hat, Inc.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from .edwards import Point
class edwards25519(Point):
"""
>>> from . import find
>>> cls = find("edwards25519")
>>> find("ed25519")
<class 'rubenesque.curves.cfrg.edwards25519'>
Test basic math:
>>> cls().is_identity
True
>>> (-cls()).is_identity
True
>>> cls().is_valid
False
>>> (cls.generator() * 0).is_identity
True
>>> cls.generator() * 1 == cls.generator()
True
>>> cls.generator() + cls.generator() * 0 == cls.generator()
True
>>> cls.generator() + cls.generator() == cls.generator() * 2
True
>>> cls.generator() * 2 + cls.generator() == cls.generator() * 3
True
>>> cls.generator() * 2 - cls.generator() == cls.generator()
True
>>> cls.generator() * 6 / 3 == cls.generator() * 2
True
>>> edwards25519.generator()
edwards25519(216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A, 6666666666666666666666666666666666666666666666666666666666666658)
>>> edwards25519.generator() * 0x449a44ba44226a50185afcc10a4c1462dd5e46824b15163b9d7c52f06be346a0
edwards25519(1229EF6103B0AB43012C2DA513CC07CDB72A5DD0C37B3813D781B195A1BA7166, 1CC8FD645E6144B78000B7AEAE4A382FBAB72A08F9B6FB8A92C1BF3D7A032DBB)
>>> edwards25519.generator() + edwards25519.generator() * 0x449a44ba44226a50185afcc10a4c1462dd5e46824b15163b9d7c52f06be346a0
edwards25519(3318E20DB2054DE4687BADC30CC6BDC7406069B0DC3CD9F65E2ECBA364E4A077, 4641AE96F530129FA2107E9B79ED5893AD03C4EDDBFDB444ABC76FF629C6A973)
"""
a = -1
d = 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3
order = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
prime = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed
aliases = ("ed25519", )
cofactor = 8
@classmethod
def generator(cls):
return cls(
0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a,
0x6666666666666666666666666666666666666666666666666666666666666658
)
class edwards448(Point):
"""
>>> from . import find
>>> cls = find("edwards448")
>>> find("ed448")
<class 'rubenesque.curves.cfrg.edwards448'>
Test basic math:
>>> cls().is_identity
True
>>> (-cls()).is_identity
True
>>> cls().is_valid
False
>>> (cls.generator() * 0).is_identity
True
>>> cls.generator() * 1 == cls.generator()
True
>>> cls.generator() + cls.generator() * 0 == cls.generator()
True
>>> cls.generator() + cls.generator() == cls.generator() * 2
True
>>> cls.generator() * 2 + cls.generator() == cls.generator() * 3
True
>>> cls.generator() * 2 - cls.generator() == cls.generator()
True
>>> cls.generator() * 6 / 3 == cls.generator() * 2
True
>>> edwards448.generator()
edwards448(79A70B2B70400553AE7C9DF416C792C61128751AC92969240C25A07D728BDC93E21F7787ED6972249DE732F38496CD11698713093E9C04FC, 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE)
>>> edwards448.generator() * 0
edwards448(∞)
>>> edwards448.generator() * 1
edwards448(79A70B2B70400553AE7C9DF416C792C61128751AC92969240C25A07D728BDC93E21F7787ED6972249DE732F38496CD11698713093E9C04FC, 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE)
>>> edwards448.generator() + edwards448.generator() * 0
edwards448(79A70B2B70400553AE7C9DF416C792C61128751AC92969240C25A07D728BDC93E21F7787ED6972249DE732F38496CD11698713093E9C04FC, 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE)
TODO: More test vectors needed...
"""
d = 0xd78b4bdc7f0daf19f24f38c29373a2ccad46157242a50f37809b1da3412a12e79ccc9c81264cfe9ad080997058fb61c4243cc32dbaa156b9
order = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3
prime = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff
aliases = ("ed448", )
cofactor = 4
@classmethod
def generator(cls):
return cls(
0x79a70b2b70400553ae7c9df416c792c61128751ac92969240c25a07d728bdc93e21f7787ed6972249de732f38496cd11698713093e9c04fc,
0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffffffffffffffffffffffffffffffffffffffffffffffffffffe
)