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"""
This module includes some utility functions.
The methods most typically used are the sigencode and sigdecode functions
to be used with :func:`~ecdsa.keys.SigningKey.sign` and
:func:`~ecdsa.keys.VerifyingKey.verify`
respectively. See the :func:`sigencode_strings`, :func:`sigdecode_string`,
:func:`sigencode_der`, :func:`sigencode_strings_canonize`,
:func:`sigencode_string_canonize`, :func:`sigencode_der_canonize`,
:func:`sigdecode_strings`, :func:`sigdecode_string`, and
:func:`sigdecode_der` functions.
"""
from __future__ import division
import os
import math
import binascii
import sys
from hashlib import sha256
from six import PY2, int2byte, next
from . import der
from ._compat import normalise_bytes
# RFC5480:
# The "unrestricted" algorithm identifier is:
# id-ecPublicKey OBJECT IDENTIFIER ::= {
# iso(1) member-body(2) us(840) ansi-X9-62(10045) keyType(2) 1 }
oid_ecPublicKey = (1, 2, 840, 10045, 2, 1)
encoded_oid_ecPublicKey = der.encode_oid(*oid_ecPublicKey)
# RFC5480:
# The ECDH algorithm uses the following object identifier:
# id-ecDH OBJECT IDENTIFIER ::= {
# iso(1) identified-organization(3) certicom(132) schemes(1)
# ecdh(12) }
oid_ecDH = (1, 3, 132, 1, 12)
# RFC5480:
# The ECMQV algorithm uses the following object identifier:
# id-ecMQV OBJECT IDENTIFIER ::= {
# iso(1) identified-organization(3) certicom(132) schemes(1)
# ecmqv(13) }
oid_ecMQV = (1, 3, 132, 1, 13)
if sys.version_info >= (3,): # pragma: no branch
def entropy_to_bits(ent_256):
"""Convert a bytestring to string of 0's and 1's"""
return bin(int.from_bytes(ent_256, "big"))[2:].zfill(len(ent_256) * 8)
else:
def entropy_to_bits(ent_256):
"""Convert a bytestring to string of 0's and 1's"""
return "".join(bin(ord(x))[2:].zfill(8) for x in ent_256)
if sys.version_info < (2, 7): # pragma: no branch
# Can't add a method to a built-in type so we are stuck with this
def bit_length(x):
return len(bin(x)) - 2
else:
def bit_length(x):
return x.bit_length() or 1
def orderlen(order):
return (1 + len("%x" % order)) // 2 # bytes
def randrange(order, entropy=None):
"""Return a random integer k such that 1 <= k < order, uniformly
distributed across that range. Worst case should be a mean of 2 loops at
(2**k)+2.
Note that this function is not declared to be forwards-compatible: we may
change the behavior in future releases. The entropy= argument (which
should get a callable that behaves like os.urandom) can be used to
achieve stability within a given release (for repeatable unit tests), but
should not be used as a long-term-compatible key generation algorithm.
"""
assert order > 1
if entropy is None:
entropy = os.urandom
upper_2 = bit_length(order - 2)
upper_256 = upper_2 // 8 + 1
while True: # I don't think this needs a counter with bit-wise randrange
ent_256 = entropy(upper_256)
ent_2 = entropy_to_bits(ent_256)
rand_num = int(ent_2[:upper_2], base=2) + 1
if 0 < rand_num < order:
return rand_num
class PRNG:
# this returns a callable which, when invoked with an integer N, will
# return N pseudorandom bytes. Note: this is a short-term PRNG, meant
# primarily for the needs of randrange_from_seed__trytryagain(), which
# only needs to run it a few times per seed. It does not provide
# protection against state compromise (forward security).
def __init__(self, seed):
self.generator = self.block_generator(seed)
def __call__(self, numbytes):
a = [next(self.generator) for i in range(numbytes)]
if PY2: # pragma: no branch
return "".join(a)
else:
return bytes(a)
def block_generator(self, seed):
counter = 0
while True:
for byte in sha256(
("prng-%d-%s" % (counter, seed)).encode()
).digest():
yield byte
counter += 1
def randrange_from_seed__overshoot_modulo(seed, order):
# hash the data, then turn the digest into a number in [1,order).
#
# We use David-Sarah Hopwood's suggestion: turn it into a number that's
# sufficiently larger than the group order, then modulo it down to fit.
# This should give adequate (but not perfect) uniformity, and simple
# code. There are other choices: try-try-again is the main one.
base = PRNG(seed)(2 * orderlen(order))
number = (int(binascii.hexlify(base), 16) % (order - 1)) + 1
assert 1 <= number < order, (1, number, order)
return number
def lsb_of_ones(numbits):
return (1 << numbits) - 1
def bits_and_bytes(order):
bits = int(math.log(order - 1, 2) + 1)
bytes = bits // 8
extrabits = bits % 8
return bits, bytes, extrabits
# the following randrange_from_seed__METHOD() functions take an
# arbitrarily-sized secret seed and turn it into a number that obeys the same
# range limits as randrange() above. They are meant for deriving consistent
# signing keys from a secret rather than generating them randomly, for
# example a protocol in which three signing keys are derived from a master
# secret. You should use a uniformly-distributed unguessable seed with about
# curve.baselen bytes of entropy. To use one, do this:
# seed = os.urandom(curve.baselen) # or other starting point
# secexp = ecdsa.util.randrange_from_seed__trytryagain(sed, curve.order)
# sk = SigningKey.from_secret_exponent(secexp, curve)
def randrange_from_seed__truncate_bytes(seed, order, hashmod=sha256):
# hash the seed, then turn the digest into a number in [1,order), but
# don't worry about trying to uniformly fill the range. This will lose,
# on average, four bits of entropy.
bits, _bytes, extrabits = bits_and_bytes(order)
if extrabits:
_bytes += 1
base = hashmod(seed).digest()[:_bytes]
base = "\x00" * (_bytes - len(base)) + base
number = 1 + int(binascii.hexlify(base), 16)
assert 1 <= number < order
return number
def randrange_from_seed__truncate_bits(seed, order, hashmod=sha256):
# like string_to_randrange_truncate_bytes, but only lose an average of
# half a bit
bits = int(math.log(order - 1, 2) + 1)
maxbytes = (bits + 7) // 8
base = hashmod(seed).digest()[:maxbytes]
base = "\x00" * (maxbytes - len(base)) + base
topbits = 8 * maxbytes - bits
if topbits:
base = int2byte(ord(base[0]) & lsb_of_ones(topbits)) + base[1:]
number = 1 + int(binascii.hexlify(base), 16)
assert 1 <= number < order
return number
def randrange_from_seed__trytryagain(seed, order):
# figure out exactly how many bits we need (rounded up to the nearest
# bit), so we can reduce the chance of looping to less than 0.5 . This is
# specified to feed from a byte-oriented PRNG, and discards the
# high-order bits of the first byte as necessary to get the right number
# of bits. The average number of loops will range from 1.0 (when
# order=2**k-1) to 2.0 (when order=2**k+1).
assert order > 1
bits, bytes, extrabits = bits_and_bytes(order)
generate = PRNG(seed)
while True:
extrabyte = b""
if extrabits:
extrabyte = int2byte(ord(generate(1)) & lsb_of_ones(extrabits))
guess = string_to_number(extrabyte + generate(bytes)) + 1
if 1 <= guess < order:
return guess
def number_to_string(num, order):
l = orderlen(order)
fmt_str = "%0" + str(2 * l) + "x"
string = binascii.unhexlify((fmt_str % num).encode())
assert len(string) == l, (len(string), l)
return string
def number_to_string_crop(num, order):
l = orderlen(order)
fmt_str = "%0" + str(2 * l) + "x"
string = binascii.unhexlify((fmt_str % num).encode())
return string[:l]
def string_to_number(string):
return int(binascii.hexlify(string), 16)
def string_to_number_fixedlen(string, order):
l = orderlen(order)
assert len(string) == l, (len(string), l)
return int(binascii.hexlify(string), 16)
def sigencode_strings(r, s, order):
"""
Encode the signature to a pair of strings in a tuple
Encodes signature into raw encoding (:term:`raw encoding`) with the
``r`` and ``s`` parts of the signature encoded separately.
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: raw encoding of ECDSA signature
:rtype: tuple(bytes, bytes)
"""
r_str = number_to_string(r, order)
s_str = number_to_string(s, order)
return (r_str, s_str)
def sigencode_string(r, s, order):
"""
Encode the signature to raw format (:term:`raw encoding`)
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: raw encoding of ECDSA signature
:rtype: bytes
"""
# for any given curve, the size of the signature numbers is
# fixed, so just use simple concatenation
r_str, s_str = sigencode_strings(r, s, order)
return r_str + s_str
def sigencode_der(r, s, order):
"""
Encode the signature into the ECDSA-Sig-Value structure using :term:`DER`.
Encodes the signature to the following :term:`ASN.1` structure::
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: DER encoding of ECDSA signature
:rtype: bytes
"""
return der.encode_sequence(der.encode_integer(r), der.encode_integer(s))
def _canonize(s, order):
"""
Internal function for ensuring that the ``s`` value of a signature is in
the "canonical" format.
:param int s: the second parameter of ECDSA signature
:param int order: the order of the curve over which the signatures was
computed
:return: canonical value of s
:rtype: int
"""
if s > order // 2:
s = order - s
return s
def sigencode_strings_canonize(r, s, order):
"""
Encode the signature to a pair of strings in a tuple
Encodes signature into raw encoding (:term:`raw encoding`) with the
``r`` and ``s`` parts of the signature encoded separately.
Makes sure that the signature is encoded in the canonical format, where
the ``s`` parameter is always smaller than ``order / 2``.
Most commonly used in bitcoin.
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: raw encoding of ECDSA signature
:rtype: tuple(bytes, bytes)
"""
s = _canonize(s, order)
return sigencode_strings(r, s, order)
def sigencode_string_canonize(r, s, order):
"""
Encode the signature to raw format (:term:`raw encoding`)
Makes sure that the signature is encoded in the canonical format, where
the ``s`` parameter is always smaller than ``order / 2``.
Most commonly used in bitcoin.
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: raw encoding of ECDSA signature
:rtype: bytes
"""
s = _canonize(s, order)
return sigencode_string(r, s, order)
def sigencode_der_canonize(r, s, order):
"""
Encode the signature into the ECDSA-Sig-Value structure using :term:`DER`.
Makes sure that the signature is encoded in the canonical format, where
the ``s`` parameter is always smaller than ``order / 2``.
Most commonly used in bitcoin.
Encodes the signature to the following :term:`ASN.1` structure::
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
It's expected that this function will be used as a ``sigencode=`` parameter
in :func:`ecdsa.keys.SigningKey.sign` method.
:param int r: first parameter of the signature
:param int s: second parameter of the signature
:param int order: the order of the curve over which the signature was
computed
:return: DER encoding of ECDSA signature
:rtype: bytes
"""
s = _canonize(s, order)
return sigencode_der(r, s, order)
class MalformedSignature(Exception):
"""
Raised by decoding functions when the signature is malformed.
Malformed in this context means that the relevant strings or integers
do not match what a signature over provided curve would create. Either
because the byte strings have incorrect lengths or because the encoded
values are too large.
"""
pass
def sigdecode_string(signature, order):
"""
Decoder for :term:`raw encoding` of ECDSA signatures.
raw encoding is a simple concatenation of the two integers that comprise
the signature, with each encoded using the same amount of bytes depending
on curve size/order.
It's expected that this function will be used as the ``sigdecode=``
parameter to the :func:`ecdsa.keys.VerifyingKey.verify` method.
:param signature: encoded signature
:type signature: bytes like object
:param order: order of the curve over which the signature was computed
:type order: int
:raises MalformedSignature: when the encoding of the signature is invalid
:return: tuple with decoded ``r`` and ``s`` values of signature
:rtype: tuple of ints
"""
signature = normalise_bytes(signature)
l = orderlen(order)
if not len(signature) == 2 * l:
raise MalformedSignature(
"Invalid length of signature, expected {0} bytes long, "
"provided string is {1} bytes long".format(2 * l, len(signature))
)
r = string_to_number_fixedlen(signature[:l], order)
s = string_to_number_fixedlen(signature[l:], order)
return r, s
def sigdecode_strings(rs_strings, order):
"""
Decode the signature from two strings.
First string needs to be a big endian encoding of ``r``, second needs to
be a big endian encoding of the ``s`` parameter of an ECDSA signature.
It's expected that this function will be used as the ``sigdecode=``
parameter to the :func:`ecdsa.keys.VerifyingKey.verify` method.
:param list rs_strings: list of two bytes-like objects, each encoding one
parameter of signature
:param int order: order of the curve over which the signature was computed
:raises MalformedSignature: when the encoding of the signature is invalid
:return: tuple with decoded ``r`` and ``s`` values of signature
:rtype: tuple of ints
"""
if not len(rs_strings) == 2:
raise MalformedSignature(
"Invalid number of strings provided: {0}, expected 2".format(
len(rs_strings)
)
)
(r_str, s_str) = rs_strings
r_str = normalise_bytes(r_str)
s_str = normalise_bytes(s_str)
l = orderlen(order)
if not len(r_str) == l:
raise MalformedSignature(
"Invalid length of first string ('r' parameter), "
"expected {0} bytes long, provided string is {1} "
"bytes long".format(l, len(r_str))
)
if not len(s_str) == l:
raise MalformedSignature(
"Invalid length of second string ('s' parameter), "
"expected {0} bytes long, provided string is {1} "
"bytes long".format(l, len(s_str))
)
r = string_to_number_fixedlen(r_str, order)
s = string_to_number_fixedlen(s_str, order)
return r, s
def sigdecode_der(sig_der, order):
"""
Decoder for DER format of ECDSA signatures.
DER format of signature is one that uses the :term:`ASN.1` :term:`DER`
rules to encode it as a sequence of two integers::
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
It's expected that this function will be used as as the ``sigdecode=``
parameter to the :func:`ecdsa.keys.VerifyingKey.verify` method.
:param sig_der: encoded signature
:type sig_der: bytes like object
:param order: order of the curve over which the signature was computed
:type order: int
:raises UnexpectedDER: when the encoding of signature is invalid
:return: tuple with decoded ``r`` and ``s`` values of signature
:rtype: tuple of ints
"""
sig_der = normalise_bytes(sig_der)
# return der.encode_sequence(der.encode_integer(r), der.encode_integer(s))
rs_strings, empty = der.remove_sequence(sig_der)
if empty != b"":
raise der.UnexpectedDER(
"trailing junk after DER sig: %s" % binascii.hexlify(empty)
)
r, rest = der.remove_integer(rs_strings)
s, empty = der.remove_integer(rest)
if empty != b"":
raise der.UnexpectedDER(
"trailing junk after DER numbers: %s" % binascii.hexlify(empty)
)
return r, s