413 lines
18 KiB
Python
413 lines
18 KiB
Python
# coding: utf-8
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# PyGOST -- Pure Python GOST cryptographic functions library
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# Copyright (C) 2015-2023 Sergey Matveev <stargrave@stargrave.org>
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, version 3 of the License.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with this program. If not, see <http://www.gnu.org/licenses/>.
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"""GOST R 34.10 public-key signature function.
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This is implementation of GOST R 34.10-2001 (:rfc:`5832`), GOST R
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34.10-2012 (:rfc:`7091`). The difference between 2001 and 2012 is the
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key, digest and signature lengths.
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"""
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from os import urandom
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from pygost.utils import bytes2long
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from pygost.utils import hexdec
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from pygost.utils import long2bytes
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from pygost.utils import modinvert
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def point_size(point):
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"""Determine is it either 256 or 512 bit point
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"""
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return (512 // 8) if point.bit_length() > 256 else (256 // 8)
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class GOST3410Curve(object):
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"""GOST 34.10 validated curve
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>>> curve = CURVES["id-GostR3410-2001-TestParamSet"]
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>>> prv = prv_unmarshal(urandom(32))
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>>> signature = sign(curve, prv, GOST341194(data).digest())
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>>> pub = public_key(curve, prv)
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>>> verify(curve, pub, GOST341194(data).digest(), signature)
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True
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:param long p: characteristic of the underlying prime field
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:param long q: elliptic curve subgroup order
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:param long a, b: coefficients of the equation of the elliptic curve in
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the canonical form
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:param long x, y: the coordinate of the point P (generator of the
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subgroup of order q) of the elliptic curve in
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the canonical form
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:param long e, d: coefficients of the equation of the elliptic curve in
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the twisted Edwards form
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:param str name: human-readable curve name
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"""
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def __init__(self, p, q, a, b, x, y, cofactor=1, e=None, d=None, name=None):
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self.p = p
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self.q = q
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self.a = a
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self.b = b
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self.x = x
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self.y = y
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self.cofactor = cofactor
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self.e = e
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self.d = d
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if not self.contains((x, y)):
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raise ValueError("Invalid parameters")
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self._st = None
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self.name = name
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@property
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def point_size(self):
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return point_size(self.p)
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def __repr__(self):
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return "<%s: %s>" % (self.__class__.__name__, self.name)
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def pos(self, v):
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"""Make positive number
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"""
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if v < 0:
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return v + self.p
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return v
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def contains(self, point):
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"""Is point on the curve?
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:type point: (long, long)
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"""
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x, y = point
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r1 = y * y % self.p
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r2 = ((x * x + self.a) * x + self.b) % self.p
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return r1 == self.pos(r2)
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def _add(self, p1x, p1y, p2x, p2y):
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if p1x == p2x and p1y == p2y:
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# double
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t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
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else:
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tx = self.pos(p2x - p1x) % self.p
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ty = self.pos(p2y - p1y) % self.p
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t = (ty * modinvert(tx, self.p)) % self.p
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tx = self.pos(t * t - p1x - p2x) % self.p
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ty = self.pos(t * (p1x - tx) - p1y) % self.p
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return tx, ty
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def exp(self, degree, x=None, y=None):
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x = x or self.x
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y = y or self.y
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tx = x
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ty = y
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if degree == 0:
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raise ValueError("Bad degree value")
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degree -= 1
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while degree != 0:
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if degree & 1 == 1:
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tx, ty = self._add(tx, ty, x, y)
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degree = degree >> 1
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x, y = self._add(x, y, x, y)
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return tx, ty
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def st(self):
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"""Compute s/t parameters for twisted Edwards curve points conversion
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"""
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if self.e is None or self.d is None:
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raise ValueError("Non twisted Edwards curve")
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if self._st is not None:
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return self._st
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self._st = (
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self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
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(self.e + self.d) * modinvert(6, self.p) % self.p,
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)
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return self._st
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CURVES = {
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"GostR3410_2001_ParamSet_cc": GOST3410Curve(
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p=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003C7")),
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q=bytes2long(hexdec("5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85")),
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a=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003c4")),
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b=bytes2long(hexdec("2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c")),
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x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
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y=bytes2long(hexdec("a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c")),
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),
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"id-GostR3410-2001-TestParamSet": GOST3410Curve(
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p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000431")),
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q=bytes2long(hexdec("8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3")),
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a=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000007")),
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b=bytes2long(hexdec("5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E")),
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x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
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y=bytes2long(hexdec("08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8")),
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),
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"id-tc26-gost-3410-12-256-paramSetA": GOST3410Curve(
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p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
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q=bytes2long(hexdec("400000000000000000000000000000000FD8CDDFC87B6635C115AF556C360C67")),
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a=bytes2long(hexdec("C2173F1513981673AF4892C23035A27CE25E2013BF95AA33B22C656F277E7335")),
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b=bytes2long(hexdec("295F9BAE7428ED9CCC20E7C359A9D41A22FCCD9108E17BF7BA9337A6F8AE9513")),
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x=bytes2long(hexdec("91E38443A5E82C0D880923425712B2BB658B9196932E02C78B2582FE742DAA28")),
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y=bytes2long(hexdec("32879423AB1A0375895786C4BB46E9565FDE0B5344766740AF268ADB32322E5C")),
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cofactor=4,
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e=0x01,
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d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
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),
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"id-tc26-gost-3410-12-256-paramSetB": GOST3410Curve(
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p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
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q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")),
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a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94")),
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b=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000a6")),
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x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
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y=bytes2long(hexdec("8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14")),
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),
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"id-tc26-gost-3410-12-256-paramSetC": GOST3410Curve(
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p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C99")),
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q=bytes2long(hexdec("800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F")),
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a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C96")),
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b=bytes2long(hexdec("3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B")),
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x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
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y=bytes2long(hexdec("3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC")),
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),
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"id-tc26-gost-3410-12-256-paramSetD": GOST3410Curve(
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p=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B")),
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q=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9")),
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a=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598")),
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b=bytes2long(hexdec("000000000000000000000000000000000000000000000000000000000000805a")),
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x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000000")),
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y=bytes2long(hexdec("41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67")),
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),
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"id-tc26-gost-3410-12-512-paramSetTest": GOST3410Curve(
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p=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DF1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373")),
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q=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DA82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF")),
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a=7,
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b=bytes2long(hexdec("1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC")),
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x=bytes2long(hexdec("24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A")),
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y=bytes2long(hexdec("2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E")),
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),
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"id-tc26-gost-3410-12-512-paramSetA": GOST3410Curve(
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p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
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q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")),
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a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4")),
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b=bytes2long(hexdec("E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760")),
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x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003")),
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y=bytes2long(hexdec("7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4")),
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),
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"id-tc26-gost-3410-12-512-paramSetB": GOST3410Curve(
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p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F")),
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q=bytes2long(hexdec("800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD")),
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a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C")),
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b=bytes2long(hexdec("687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116")),
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x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002")),
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y=bytes2long(hexdec("1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD")),
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),
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"id-tc26-gost-3410-12-512-paramSetC": GOST3410Curve(
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p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
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q=bytes2long(hexdec("3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC98CDBA46506AB004C33A9FF5147502CC8EDA9E7A769A12694623CEF47F023ED")),
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a=bytes2long(hexdec("DC9203E514A721875485A529D2C722FB187BC8980EB866644DE41C68E143064546E861C0E2C9EDD92ADE71F46FCF50FF2AD97F951FDA9F2A2EB6546F39689BD3")),
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b=bytes2long(hexdec("B4C4EE28CEBC6C2C8AC12952CF37F16AC7EFB6A9F69F4B57FFDA2E4F0DE5ADE038CBC2FFF719D2C18DE0284B8BFEF3B52B8CC7A5F5BF0A3C8D2319A5312557E1")),
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x=bytes2long(hexdec("E2E31EDFC23DE7BDEBE241CE593EF5DE2295B7A9CBAEF021D385F7074CEA043AA27272A7AE602BF2A7B9033DB9ED3610C6FB85487EAE97AAC5BC7928C1950148")),
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y=bytes2long(hexdec("F5CE40D95B5EB899ABBCCFF5911CB8577939804D6527378B8C108C3D2090FF9BE18E2D33E3021ED2EF32D85822423B6304F726AA854BAE07D0396E9A9ADDC40F")),
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cofactor=4,
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e=0x01,
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d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
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),
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}
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CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
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CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetC"]
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CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetD"]
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CURVES["id-GostR3410-2001-CryptoPro-XchA-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
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CURVES["id-GostR3410-2001-CryptoPro-XchB-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
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CURVES["id-tc26-gost-3410-2012-256-paramSetA"] = CURVES["id-tc26-gost-3410-12-256-paramSetA"]
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CURVES["id-tc26-gost-3410-2012-256-paramSetB"] = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
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CURVES["id-tc26-gost-3410-2012-256-paramSetC"] = CURVES["id-tc26-gost-3410-12-256-paramSetC"]
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CURVES["id-tc26-gost-3410-2012-256-paramSetD"] = CURVES["id-tc26-gost-3410-12-256-paramSetD"]
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CURVES["id-tc26-gost-3410-2012-512-paramSetTest"] = CURVES["id-tc26-gost-3410-12-512-paramSetTest"]
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CURVES["id-tc26-gost-3410-2012-512-paramSetA"] = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
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CURVES["id-tc26-gost-3410-2012-512-paramSetB"] = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
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CURVES["id-tc26-gost-3410-2012-512-paramSetC"] = CURVES["id-tc26-gost-3410-12-512-paramSetC"]
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for _name, _curve in CURVES.items():
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_curve.name = _name
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DEFAULT_CURVE = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
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def public_key(curve, prv, mask=None):
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"""Generate public key from the private one
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:param GOST3410Curve curve: curve to use
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:param long prv: private key
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:returns: public key's parts, X and Y
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:rtype: (long, long)
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"""
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pub = curve.exp(prv)
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if mask is not None:
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pub = curve.exp(mask, pub[0], pub[1])
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return pub
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def sign(curve, prv, digest, rand=None, mask=None):
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"""Calculate signature for provided digest
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:param GOST3410Curve curve: curve to use
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:param long prv: private key
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:param digest: digest for signing
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:type digest: bytes, 32 or 64 bytes
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:param rand: optional predefined random data used for k/r generation
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:type rand: bytes, 32 or 64 bytes
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:returns: signature, BE(S) || BE(R)
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:rtype: bytes, 64 or 128 bytes
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"""
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size = curve.point_size
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q = curve.q
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e = bytes2long(digest) % q
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if e == 0:
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e = 1
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while True:
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if rand is None:
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rand = urandom(size)
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elif len(rand) != size:
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raise ValueError("rand length != %d" % size)
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k = bytes2long(rand) % q
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if k == 0:
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continue
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r, y = curve.exp(k)
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if mask is not None:
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r, y = curve.exp(mask, x=r, y=y)
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r %= q
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if r == 0:
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continue
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d = prv * r
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k *= e
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s = d + k
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if mask is not None:
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s *= mask
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s %= q
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if s == 0:
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continue
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break
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return long2bytes(s, size) + long2bytes(r, size)
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def verify(curve, pub, digest, signature):
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"""Verify provided digest with the signature
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:param GOST3410Curve curve: curve to use
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:type pub: (long, long)
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:param digest: digest needed to check
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:type digest: bytes, 32 or 64 bytes
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:param signature: signature to verify with
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:type signature: bytes, 64 or 128 bytes
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:rtype: bool
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"""
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size = curve.point_size
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if len(signature) != size * 2:
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raise ValueError("Invalid signature length")
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q = curve.q
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p = curve.p
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s = bytes2long(signature[:size])
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r = bytes2long(signature[size:])
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if r <= 0 or r >= q or s <= 0 or s >= q:
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return False
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e = bytes2long(digest) % curve.q
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if e == 0:
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e = 1
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v = modinvert(e, q)
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z1 = s * v % q
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z2 = q - r * v % q
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p1x, p1y = curve.exp(z1)
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q1x, q1y = curve.exp(z2, pub[0], pub[1])
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lm = q1x - p1x
|
|
if lm < 0:
|
|
lm += p
|
|
lm = modinvert(lm, p)
|
|
z1 = q1y - p1y
|
|
lm = lm * z1 % p
|
|
lm = lm * lm % p
|
|
lm = lm - p1x - q1x
|
|
lm = lm % p
|
|
if lm < 0:
|
|
lm += p
|
|
lm %= q
|
|
# This is not constant time comparison!
|
|
return lm == r
|
|
|
|
|
|
def prv_unmarshal(prv):
|
|
"""Unmarshal little-endian private key
|
|
|
|
:param bytes prv: serialized private key
|
|
:rtype: long
|
|
|
|
It is advisable to use :py:func:`pygost.gost3410.prv_marshal` to
|
|
assure that key i in curve's Q field for better compatibility with
|
|
some implementations.
|
|
"""
|
|
return bytes2long(prv[::-1])
|
|
|
|
|
|
def prv_marshal(curve, prv):
|
|
"""Marshal little-endian private key
|
|
|
|
:param GOST3410Curve curve: curve to use
|
|
:param long prv: serialized private key
|
|
:rtype: bytes
|
|
|
|
Key is in curve's Q field.
|
|
"""
|
|
return long2bytes(prv % curve.q, point_size(prv))[::-1]
|
|
|
|
|
|
def pub_marshal(pub):
|
|
"""Marshal public key
|
|
|
|
:type pub: (long, long)
|
|
:rtype: bytes
|
|
:returns: LE(X) || LE(Y)
|
|
"""
|
|
size = point_size(pub[0])
|
|
return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
|
|
|
|
|
|
def pub_unmarshal(pub):
|
|
"""Unmarshal public key
|
|
|
|
:param pub: LE(X) || LE(Y)
|
|
:type pub: bytes
|
|
:rtype: (long, long)
|
|
"""
|
|
size = len(pub) // 2
|
|
pub = pub[::-1]
|
|
return (bytes2long(pub[size:]), bytes2long(pub[:size]))
|
|
|
|
|
|
def uv2xy(curve, u, v):
|
|
"""Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
|
|
"""
|
|
s, t = curve.st()
|
|
k1 = (s * (1 + v)) % curve.p
|
|
k2 = curve.pos(1 - v)
|
|
x = t + k1 * modinvert(k2, curve.p)
|
|
y = k1 * modinvert(u * k2, curve.p)
|
|
return x % curve.p, y % curve.p
|
|
|
|
|
|
def xy2uv(curve, x, y):
|
|
"""Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
|
|
"""
|
|
s, t = curve.st()
|
|
xmt = curve.pos(x - t)
|
|
u = xmt * modinvert(y, curve.p)
|
|
v = curve.pos(xmt - s) * modinvert(xmt + s, curve.p)
|
|
return u % curve.p, v % curve.p
|