Add ecdsa Python library.

bin/python/ecdsa/__init__.py

@@ -0,0 +1,14 @@
+__all__ = ["curves", "der", "ecdsa", "ellipticcurve", "keys", "numbertheory",
+           "test_pyecdsa", "util", "six"]
+from .keys import SigningKey, VerifyingKey, BadSignatureError, BadDigestError
+from .curves import NIST192p, NIST224p, NIST256p, NIST384p, NIST521p, SECP256k1
+
+_hush_pyflakes = [SigningKey, VerifyingKey, BadSignatureError, BadDigestError,
+                  NIST192p, NIST224p, NIST256p, NIST384p, NIST521p, SECP256k1]
+del _hush_pyflakes
+
+# This code comes from http://github.com/warner/python-ecdsa
+
+from ._version import get_versions
+__version__ = get_versions()['version']
+del get_versions

bin/python/ecdsa/_version.py

@@ -0,0 +1,183 @@
+
+# This file helps to compute a version number in source trees obtained from
+# git-archive tarball (such as those provided by githubs download-from-tag
+# feature). Distribution tarballs (built by setup.py sdist) and build
+# directories (produced by setup.py build) will contain a much shorter file
+# that just contains the computed version number.
+
+# This file is released into the public domain. Generated by
+# versioneer-0.12 (https://github.com/warner/python-versioneer)
+
+# these strings will be replaced by git during git-archive
+git_refnames = " (HEAD, master)"
+git_full = "e7a6daff51221b8edd888cff404596ef90432869"
+
+# these strings are filled in when 'setup.py versioneer' creates _version.py
+tag_prefix = "python-ecdsa-"
+parentdir_prefix = "ecdsa-"
+versionfile_source = "ecdsa/_version.py"
+
+import os, sys, re, subprocess, errno
+
+def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
+    assert isinstance(commands, list)
+    p = None
+    for c in commands:
+        try:
+            # remember shell=False, so use git.cmd on windows, not just git
+            p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
+                                 stderr=(subprocess.PIPE if hide_stderr
+                                         else None))
+            break
+        except EnvironmentError:
+            e = sys.exc_info()[1]
+            if e.errno == errno.ENOENT:
+                continue
+            if verbose:
+                print("unable to run %s" % args[0])
+                print(e)
+            return None
+    else:
+        if verbose:
+            print("unable to find command, tried %s" % (commands,))
+        return None
+    stdout = p.communicate()[0].strip()
+    if sys.version >= '3':
+        stdout = stdout.decode()
+    if p.returncode != 0:
+        if verbose:
+            print("unable to run %s (error)" % args[0])
+        return None
+    return stdout
+
+
+def versions_from_parentdir(parentdir_prefix, root, verbose=False):
+    # Source tarballs conventionally unpack into a directory that includes
+    # both the project name and a version string.
+    dirname = os.path.basename(root)
+    if not dirname.startswith(parentdir_prefix):
+        if verbose:
+            print("guessing rootdir is '%s', but '%s' doesn't start with prefix '%s'" %
+                  (root, dirname, parentdir_prefix))
+        return None
+    return {"version": dirname[len(parentdir_prefix):], "full": ""}
+
+def git_get_keywords(versionfile_abs):
+    # the code embedded in _version.py can just fetch the value of these
+    # keywords. When used from setup.py, we don't want to import _version.py,
+    # so we do it with a regexp instead. This function is not used from
+    # _version.py.
+    keywords = {}
+    try:
+        f = open(versionfile_abs,"r")
+        for line in f.readlines():
+            if line.strip().startswith("git_refnames ="):
+                mo = re.search(r'=\s*"(.*)"', line)
+                if mo:
+                    keywords["refnames"] = mo.group(1)
+            if line.strip().startswith("git_full ="):
+                mo = re.search(r'=\s*"(.*)"', line)
+                if mo:
+                    keywords["full"] = mo.group(1)
+        f.close()
+    except EnvironmentError:
+        pass
+    return keywords
+
+def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
+    if not keywords:
+        return {} # keyword-finding function failed to find keywords
+    refnames = keywords["refnames"].strip()
+    if refnames.startswith("$Format"):
+        if verbose:
+            print("keywords are unexpanded, not using")
+        return {} # unexpanded, so not in an unpacked git-archive tarball
+    refs = set([r.strip() for r in refnames.strip("()").split(",")])
+    # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
+    # just "foo-1.0". If we see a "tag: " prefix, prefer those.
+    TAG = "tag: "
+    tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
+    if not tags:
+        # Either we're using git < 1.8.3, or there really are no tags. We use
+        # a heuristic: assume all version tags have a digit. The old git %d
+        # expansion behaves like git log --decorate=short and strips out the
+        # refs/heads/ and refs/tags/ prefixes that would let us distinguish
+        # between branches and tags. By ignoring refnames without digits, we
+        # filter out many common branch names like "release" and
+        # "stabilization", as well as "HEAD" and "master".
+        tags = set([r for r in refs if re.search(r'\d', r)])
+        if verbose:
+            print("discarding '%s', no digits" % ",".join(refs-tags))
+    if verbose:
+        print("likely tags: %s" % ",".join(sorted(tags)))
+    for ref in sorted(tags):
+        # sorting will prefer e.g. "2.0" over "2.0rc1"
+        if ref.startswith(tag_prefix):
+            r = ref[len(tag_prefix):]
+            if verbose:
+                print("picking %s" % r)
+            return { "version": r,
+                     "full": keywords["full"].strip() }
+    # no suitable tags, so we use the full revision id
+    if verbose:
+        print("no suitable tags, using full revision id")
+    return { "version": keywords["full"].strip(),
+             "full": keywords["full"].strip() }
+
+
+def git_versions_from_vcs(tag_prefix, root, verbose=False):
+    # this runs 'git' from the root of the source tree. This only gets called
+    # if the git-archive 'subst' keywords were *not* expanded, and
+    # _version.py hasn't already been rewritten with a short version string,
+    # meaning we're inside a checked out source tree.
+
+    if not os.path.exists(os.path.join(root, ".git")):
+        if verbose:
+            print("no .git in %s" % root)
+        return {}
+
+    GITS = ["git"]
+    if sys.platform == "win32":
+        GITS = ["git.cmd", "git.exe"]
+    stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
+                         cwd=root)
+    if stdout is None:
+        return {}
+    if not stdout.startswith(tag_prefix):
+        if verbose:
+            print("tag '%s' doesn't start with prefix '%s'" % (stdout, tag_prefix))
+        return {}
+    tag = stdout[len(tag_prefix):]
+    stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
+    if stdout is None:
+        return {}
+    full = stdout.strip()
+    if tag.endswith("-dirty"):
+        full += "-dirty"
+    return {"version": tag, "full": full}
+
+
+def get_versions(default={"version": "unknown", "full": ""}, verbose=False):
+    # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have
+    # __file__, we can work backwards from there to the root. Some
+    # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which
+    # case we can only use expanded keywords.
+
+    keywords = { "refnames": git_refnames, "full": git_full }
+    ver = git_versions_from_keywords(keywords, tag_prefix, verbose)
+    if ver:
+        return ver
+
+    try:
+        root = os.path.abspath(__file__)
+        # versionfile_source is the relative path from the top of the source
+        # tree (where the .git directory might live) to this file. Invert
+        # this to find the root from __file__.
+        for i in range(len(versionfile_source.split(os.sep))):
+            root = os.path.dirname(root)
+    except NameError:
+        return default
+
+    return (git_versions_from_vcs(tag_prefix, root, verbose)
+            or versions_from_parentdir(parentdir_prefix, root, verbose)
+            or default)

bin/python/ecdsa/curves.py

@@ -0,0 +1,53 @@
+from __future__ import division
+
+from . import der, ecdsa
+
+class UnknownCurveError(Exception):
+    pass
+
+def orderlen(order):
+    return (1+len("%x"%order))//2 # bytes
+
+# the NIST curves
+class Curve:
+    def __init__(self, name, openssl_name,
+                 curve, generator, oid):
+        self.name = name
+        self.openssl_name = openssl_name # maybe None
+        self.curve = curve
+        self.generator = generator
+        self.order = generator.order()
+        self.baselen = orderlen(self.order)
+        self.verifying_key_length = 2*self.baselen
+        self.signature_length = 2*self.baselen
+        self.oid = oid
+        self.encoded_oid = der.encode_oid(*oid)
+
+NIST192p = Curve("NIST192p", "prime192v1",
+                 ecdsa.curve_192, ecdsa.generator_192,
+                 (1, 2, 840, 10045, 3, 1, 1))
+NIST224p = Curve("NIST224p", "secp224r1",
+                 ecdsa.curve_224, ecdsa.generator_224,
+                 (1, 3, 132, 0, 33))
+NIST256p = Curve("NIST256p", "prime256v1",
+                 ecdsa.curve_256, ecdsa.generator_256,
+                 (1, 2, 840, 10045, 3, 1, 7))
+NIST384p = Curve("NIST384p", "secp384r1",
+                 ecdsa.curve_384, ecdsa.generator_384,
+                 (1, 3, 132, 0, 34))
+NIST521p = Curve("NIST521p", "secp521r1",
+                 ecdsa.curve_521, ecdsa.generator_521,
+                 (1, 3, 132, 0, 35))
+SECP256k1 = Curve("SECP256k1", "secp256k1",
+                  ecdsa.curve_secp256k1, ecdsa.generator_secp256k1,
+                  (1, 3, 132, 0, 10))
+
+curves = [NIST192p, NIST224p, NIST256p, NIST384p, NIST521p, SECP256k1]
+
+def find_curve(oid_curve):
+    for c in curves:
+        if c.oid == oid_curve:
+            return c
+    raise UnknownCurveError("I don't know about the curve with oid %s."
+                            "I only know about these: %s" %
+                            (oid_curve, [c.name for c in curves]))

bin/python/ecdsa/der.py

@@ -0,0 +1,199 @@
+from __future__ import division
+
+import binascii
+import base64
+from .six import int2byte, b, integer_types, text_type
+
+class UnexpectedDER(Exception):
+    pass
+
+def encode_constructed(tag, value):
+    return int2byte(0xa0+tag) + encode_length(len(value)) + value
+def encode_integer(r):
+    assert r >= 0 # can't support negative numbers yet
+    h = ("%x" % r).encode()
+    if len(h) % 2:
+        h = b("0") + h
+    s = binascii.unhexlify(h)
+    num = s[0] if isinstance(s[0], integer_types) else ord(s[0])
+    if num <= 0x7f:
+        return b("\x02") + int2byte(len(s)) + s
+    else:
+        # DER integers are two's complement, so if the first byte is
+        # 0x80-0xff then we need an extra 0x00 byte to prevent it from
+        # looking negative.
+        return b("\x02") + int2byte(len(s)+1) + b("\x00") + s
+
+def encode_bitstring(s):
+    return b("\x03") + encode_length(len(s)) + s
+def encode_octet_string(s):
+    return b("\x04") + encode_length(len(s)) + s
+def encode_oid(first, second, *pieces):
+    assert first <= 2
+    assert second <= 39
+    encoded_pieces = [int2byte(40*first+second)] + [encode_number(p)
+                                                    for p in pieces]
+    body = b('').join(encoded_pieces)
+    return b('\x06') + encode_length(len(body)) + body
+def encode_sequence(*encoded_pieces):
+    total_len = sum([len(p) for p in encoded_pieces])
+    return b('\x30') + encode_length(total_len) + b('').join(encoded_pieces)
+def encode_number(n):
+    b128_digits = []
+    while n:
+        b128_digits.insert(0, (n & 0x7f) | 0x80)
+        n = n >> 7
+    if not b128_digits:
+        b128_digits.append(0)
+    b128_digits[-1] &= 0x7f
+    return b('').join([int2byte(d) for d in b128_digits])
+
+def remove_constructed(string):
+    s0 = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+    if (s0 & 0xe0) != 0xa0:
+        raise UnexpectedDER("wanted constructed tag (0xa0-0xbf), got 0x%02x"
+                            % s0)
+    tag = s0 & 0x1f
+    length, llen = read_length(string[1:])
+    body = string[1+llen:1+llen+length]
+    rest = string[1+llen+length:]
+    return tag, body, rest
+
+def remove_sequence(string):
+    if not string.startswith(b("\x30")):
+        n = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+        raise UnexpectedDER("wanted sequence (0x30), got 0x%02x" % n)
+    length, lengthlength = read_length(string[1:])
+    endseq = 1+lengthlength+length
+    return string[1+lengthlength:endseq], string[endseq:]
+
+def remove_octet_string(string):
+    if not string.startswith(b("\x04")):
+        n = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+        raise UnexpectedDER("wanted octetstring (0x04), got 0x%02x" % n)
+    length, llen = read_length(string[1:])
+    body = string[1+llen:1+llen+length]
+    rest = string[1+llen+length:]
+    return body, rest
+
+def remove_object(string):
+    if not string.startswith(b("\x06")):
+        n = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+        raise UnexpectedDER("wanted object (0x06), got 0x%02x" % n)
+    length, lengthlength = read_length(string[1:])
+    body = string[1+lengthlength:1+lengthlength+length]
+    rest = string[1+lengthlength+length:]
+    numbers = []
+    while body:
+        n, ll = read_number(body)
+        numbers.append(n)
+        body = body[ll:]
+    n0 = numbers.pop(0)
+    first = n0//40
+    second = n0-(40*first)
+    numbers.insert(0, first)
+    numbers.insert(1, second)
+    return tuple(numbers), rest
+
+def remove_integer(string):
+    if not string.startswith(b("\x02")):
+        n = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+        raise UnexpectedDER("wanted integer (0x02), got 0x%02x" % n)
+    length, llen = read_length(string[1:])
+    numberbytes = string[1+llen:1+llen+length]
+    rest = string[1+llen+length:]
+    nbytes = numberbytes[0] if isinstance(numberbytes[0], integer_types) else ord(numberbytes[0])
+    assert nbytes < 0x80 # can't support negative numbers yet
+    return int(binascii.hexlify(numberbytes), 16), rest
+
+def read_number(string):
+    number = 0
+    llen = 0
+    # base-128 big endian, with b7 set in all but the last byte
+    while True:
+        if llen > len(string):
+            raise UnexpectedDER("ran out of length bytes")
+        number = number << 7
+        d = string[llen] if isinstance(string[llen], integer_types) else ord(string[llen])
+        number += (d & 0x7f)
+        llen += 1
+        if not d & 0x80:
+            break
+    return number, llen
+
+def encode_length(l):
+    assert l >= 0
+    if l < 0x80:
+        return int2byte(l)
+    s = ("%x" % l).encode()
+    if len(s)%2:
+        s = b("0")+s
+    s = binascii.unhexlify(s)
+    llen = len(s)
+    return int2byte(0x80|llen) + s
+
+def read_length(string):
+    num = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+    if not (num & 0x80):
+        # short form
+        return (num & 0x7f), 1
+    # else long-form: b0&0x7f is number of additional base256 length bytes,
+    # big-endian
+    llen = num & 0x7f
+    if llen > len(string)-1:
+        raise UnexpectedDER("ran out of length bytes")
+    return int(binascii.hexlify(string[1:1+llen]), 16), 1+llen
+
+def remove_bitstring(string):
+    num = string[0] if isinstance(string[0], integer_types) else ord(string[0])
+    if not string.startswith(b("\x03")):
+        raise UnexpectedDER("wanted bitstring (0x03), got 0x%02x" % num)
+    length, llen = read_length(string[1:])
+    body = string[1+llen:1+llen+length]
+    rest = string[1+llen+length:]
+    return body, rest
+
+# SEQUENCE([1, STRING(secexp), cont[0], OBJECT(curvename), cont[1], BINTSTRING)
+
+
+# signatures: (from RFC3279)
+#  ansi-X9-62  OBJECT IDENTIFIER ::= {
+#       iso(1) member-body(2) us(840) 10045 }
+#
+#  id-ecSigType OBJECT IDENTIFIER  ::=  {
+#       ansi-X9-62 signatures(4) }
+#  ecdsa-with-SHA1  OBJECT IDENTIFIER ::= {
+#       id-ecSigType 1 }
+## so 1,2,840,10045,4,1
+## so 0x42, .. ..
+
+#  Ecdsa-Sig-Value  ::=  SEQUENCE  {
+#       r     INTEGER,
+#       s     INTEGER  }
+
+# id-public-key-type OBJECT IDENTIFIER  ::= { ansi-X9.62 2 }
+#
+# id-ecPublicKey OBJECT IDENTIFIER ::= { id-publicKeyType 1 }
+
+# I think the secp224r1 identifier is (t=06,l=05,v=2b81040021)
+#  secp224r1 OBJECT IDENTIFIER ::= {
+#  iso(1) identified-organization(3) certicom(132) curve(0) 33 }
+# and the secp384r1 is (t=06,l=05,v=2b81040022)
+#  secp384r1 OBJECT IDENTIFIER ::= {
+#  iso(1) identified-organization(3) certicom(132) curve(0) 34 }
+
+def unpem(pem):
+    if isinstance(pem, text_type):
+        pem = pem.encode()
+
+    d = b("").join([l.strip() for l in pem.split(b("\n"))
+                    if l and not l.startswith(b("-----"))])
+    return base64.b64decode(d)
+def topem(der, name):
+    b64 = base64.b64encode(der)
+    lines = [("-----BEGIN %s-----\n" % name).encode()]
+    lines.extend([b64[start:start+64]+b("\n")
+                  for start in range(0, len(b64), 64)])
+    lines.append(("-----END %s-----\n" % name).encode())
+    return b("").join(lines)
+

bin/python/ecdsa/ecdsa.py

@@ -0,0 +1,576 @@
+#! /usr/bin/env python
+
+"""
+Implementation of Elliptic-Curve Digital Signatures.
+
+Classes and methods for elliptic-curve signatures:
+private keys, public keys, signatures,
+NIST prime-modulus curves with modulus lengths of
+192, 224, 256, 384, and 521 bits.
+
+Example:
+
+  # (In real-life applications, you would probably want to
+  # protect against defects in SystemRandom.)
+  from random import SystemRandom
+  randrange = SystemRandom().randrange
+
+  # Generate a public/private key pair using the NIST Curve P-192:
+
+  g = generator_192
+  n = g.order()
+  secret = randrange( 1, n )
+  pubkey = Public_key( g, g * secret )
+  privkey = Private_key( pubkey, secret )
+
+  # Signing a hash value:
+
+  hash = randrange( 1, n )
+  signature = privkey.sign( hash, randrange( 1, n ) )
+
+  # Verifying a signature for a hash value:
+
+  if pubkey.verifies( hash, signature ):
+    print_("Demo verification succeeded.")
+  else:
+    print_("*** Demo verification failed.")
+
+  # Verification fails if the hash value is modified:
+
+  if pubkey.verifies( hash-1, signature ):
+    print_("**** Demo verification failed to reject tampered hash.")
+  else:
+    print_("Demo verification correctly rejected tampered hash.")
+
+Version of 2009.05.16.
+
+Revision history:
+      2005.12.31 - Initial version.
+      2008.11.25 - Substantial revisions introducing new classes.
+      2009.05.16 - Warn against using random.randrange in real applications.
+      2009.05.17 - Use random.SystemRandom by default.
+
+Written in 2005 by Peter Pearson and placed in the public domain.
+"""
+
+from .six import int2byte, b, print_
+from . import ellipticcurve
+from . import numbertheory
+import random
+
+
+
+class Signature( object ):
+  """ECDSA signature.
+  """
+  def __init__( self, r, s ):
+    self.r = r
+    self.s = s
+
+
+
+class Public_key( object ):
+  """Public key for ECDSA.
+  """
+
+  def __init__( self, generator, point ):
+    """generator is the Point that generates the group,
+    point is the Point that defines the public key.
+    """
+
+    self.curve = generator.curve()
+    self.generator = generator
+    self.point = point
+    n = generator.order()
+    if not n:
+      raise RuntimeError("Generator point must have order.")
+    if not n * point == ellipticcurve.INFINITY:
+      raise RuntimeError("Generator point order is bad.")
+    if point.x() < 0 or n <= point.x() or point.y() < 0 or n <= point.y():
+      raise RuntimeError("Generator point has x or y out of range.")
+
+
+  def verifies( self, hash, signature ):
+    """Verify that signature is a valid signature of hash.
+    Return True if the signature is valid.
+    """
+
+    # From X9.62 J.3.1.
+
+    G = self.generator
+    n = G.order()
+    r = signature.r
+    s = signature.s
+    if r < 1 or r > n-1: return False
+    if s < 1 or s > n-1: return False
+    c = numbertheory.inverse_mod( s, n )
+    u1 = ( hash * c ) % n
+    u2 = ( r * c ) % n
+    xy = u1 * G + u2 * self.point
+    v = xy.x() % n
+    return v == r
+
+
+
+class Private_key( object ):
+  """Private key for ECDSA.
+  """
+
+  def __init__( self, public_key, secret_multiplier ):
+    """public_key is of class Public_key;
+    secret_multiplier is a large integer.
+    """
+
+    self.public_key = public_key
+    self.secret_multiplier = secret_multiplier
+
+  def sign( self, hash, random_k ):
+    """Return a signature for the provided hash, using the provided
+    random nonce.  It is absolutely vital that random_k be an unpredictable
+    number in the range [1, self.public_key.point.order()-1].  If
+    an attacker can guess random_k, he can compute our private key from a
+    single signature.  Also, if an attacker knows a few high-order
+    bits (or a few low-order bits) of random_k, he can compute our private
+    key from many signatures.  The generation of nonces with adequate
+    cryptographic strength is very difficult and far beyond the scope
+    of this comment.
+
+    May raise RuntimeError, in which case retrying with a new
+    random value k is in order.
+    """
+
+    G = self.public_key.generator
+    n = G.order()
+    k = random_k % n
+    p1 = k * G
+    r = p1.x()
+    if r == 0: raise RuntimeError("amazingly unlucky random number r")
+    s = ( numbertheory.inverse_mod( k, n ) * \
+          ( hash + ( self.secret_multiplier * r ) % n ) ) % n
+    if s == 0: raise RuntimeError("amazingly unlucky random number s")
+    return Signature( r, s )
+
+
+
+def int_to_string( x ):
+  """Convert integer x into a string of bytes, as per X9.62."""
+  assert x >= 0
+  if x == 0: return b('\0')
+  result = []
+  while x:
+    ordinal = x & 0xFF
+    result.append(int2byte(ordinal))
+    x >>= 8
+
+  result.reverse()
+  return b('').join(result)
+
+
+def string_to_int( s ):
+  """Convert a string of bytes into an integer, as per X9.62."""
+  result = 0
+  for c in s:
+    if not isinstance(c, int): c = ord( c )
+    result = 256 * result + c
+  return result
+
+
+def digest_integer( m ):
+  """Convert an integer into a string of bytes, compute
+     its SHA-1 hash, and convert the result to an integer."""
+  #
+  # I don't expect this function to be used much. I wrote
+  # it in order to be able to duplicate the examples
+  # in ECDSAVS.
+  #
+  from hashlib import sha1
+  return string_to_int( sha1( int_to_string( m ) ).digest() )
+
+
+def point_is_valid( generator, x, y ):
+  """Is (x,y) a valid public key based on the specified generator?"""
+
+  # These are the tests specified in X9.62.
+
+  n = generator.order()
+  curve = generator.curve()
+  if x < 0 or n <= x or y < 0 or n <= y:
+    return False
+  if not curve.contains_point( x, y ):
+    return False
+  if not n*ellipticcurve.Point( curve, x, y ) == \
+     ellipticcurve.INFINITY:
+    return False
+  return True
+
+
+
+# NIST Curve P-192:
+_p = 6277101735386680763835789423207666416083908700390324961279
+_r = 6277101735386680763835789423176059013767194773182842284081
+# s = 0x3045ae6fc8422f64ed579528d38120eae12196d5L
+# c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65L
+_b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
+_Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
+_Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
+
+curve_192 = ellipticcurve.CurveFp( _p, -3, _b )
+generator_192 = ellipticcurve.Point( curve_192, _Gx, _Gy, _r )
+
+
+# NIST Curve P-224:
+_p = 26959946667150639794667015087019630673557916260026308143510066298881
+_r = 26959946667150639794667015087019625940457807714424391721682722368061
+# s = 0xbd71344799d5c7fcdc45b59fa3b9ab8f6a948bc5L
+# c = 0x5b056c7e11dd68f40469ee7f3c7a7d74f7d121116506d031218291fbL
+_b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
+_Gx =0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
+_Gy = 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
+
+curve_224 = ellipticcurve.CurveFp( _p, -3, _b )
+generator_224 = ellipticcurve.Point( curve_224, _Gx, _Gy, _r )
+
+# NIST Curve P-256:
+_p = 115792089210356248762697446949407573530086143415290314195533631308867097853951
+_r = 115792089210356248762697446949407573529996955224135760342422259061068512044369
+# s = 0xc49d360886e704936a6678e1139d26b7819f7e90L
+# c = 0x7efba1662985be9403cb055c75d4f7e0ce8d84a9c5114abcaf3177680104fa0dL
+_b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
+_Gx = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
+_Gy = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
+
+curve_256 = ellipticcurve.CurveFp( _p, -3, _b )
+generator_256 = ellipticcurve.Point( curve_256, _Gx, _Gy, _r )
+
+# NIST Curve P-384:
+_p = 39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319
+_r = 39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643
+# s = 0xa335926aa319a27a1d00896a6773a4827acdac73L
+# c = 0x79d1e655f868f02fff48dcdee14151ddb80643c1406d0ca10dfe6fc52009540a495e8042ea5f744f6e184667cc722483L
+_b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
+_Gx = 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7
+_Gy = 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f
+
+curve_384 = ellipticcurve.CurveFp( _p, -3, _b )
+generator_384 = ellipticcurve.Point( curve_384, _Gx, _Gy, _r )
+
+# NIST Curve P-521:
+_p = 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151
+_r = 6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449
+# s = 0xd09e8800291cb85396cc6717393284aaa0da64baL
+# c = 0x0b48bfa5f420a34949539d2bdfc264eeeeb077688e44fbf0ad8f6d0edb37bd6b533281000518e19f1b9ffbe0fe9ed8a3c2200b8f875e523868c70c1e5bf55bad637L
+_b = 0x051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
+_Gx = 0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
+_Gy = 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
+
+curve_521 = ellipticcurve.CurveFp( _p, -3, _b )
+generator_521 = ellipticcurve.Point( curve_521, _Gx, _Gy, _r )
+
+# Certicom secp256-k1
+_a  = 0x0000000000000000000000000000000000000000000000000000000000000000
+_b  = 0x0000000000000000000000000000000000000000000000000000000000000007
+_p  = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
+_Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
+_Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
+_r  = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
+
+curve_secp256k1 = ellipticcurve.CurveFp( _p, _a, _b)
+generator_secp256k1 = ellipticcurve.Point( curve_secp256k1, _Gx, _Gy, _r)
+
+
+
+def __main__():
+  class TestFailure(Exception): pass
+
+  def test_point_validity( generator, x, y, expected ):
+    """generator defines the curve; is (x,y) a point on
+       this curve? "expected" is True if the right answer is Yes."""
+    if point_is_valid( generator, x, y ) == expected:
+      print_("Point validity tested as expected.")
+    else:
+      raise TestFailure("*** Point validity test gave wrong result.")
+
+  def test_signature_validity( Msg, Qx, Qy, R, S, expected ):
+    """Msg = message, Qx and Qy represent the base point on
+       elliptic curve c192, R and S are the signature, and
+       "expected" is True iff the signature is expected to be valid."""
+    pubk = Public_key( generator_192,
+                       ellipticcurve.Point( curve_192, Qx, Qy ) )
+    got = pubk.verifies( digest_integer( Msg ), Signature( R, S ) )
+    if got == expected:
+      print_("Signature tested as expected: got %s, expected %s." % \
+            ( got, expected ))
+    else:
+      raise TestFailure("*** Signature test failed: got %s, expected %s." % \
+                        ( got, expected ))
+
+  print_("NIST Curve P-192:")
+
+  p192 = generator_192
+
+  # From X9.62:
+
+  d = 651056770906015076056810763456358567190100156695615665659
+  Q = d * p192
+  if Q.x() != 0x62B12D60690CDCF330BABAB6E69763B471F994DD702D16A5:
+    raise TestFailure("*** p192 * d came out wrong.")
+  else:
+    print_("p192 * d came out right.")
+
+  k = 6140507067065001063065065565667405560006161556565665656654
+  R = k * p192
+  if R.x() != 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD \
+     or R.y() != 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835:
+    raise TestFailure("*** k * p192 came out wrong.")
+  else:
+    print_("k * p192 came out right.")
+
+  u1 = 2563697409189434185194736134579731015366492496392189760599
+  u2 = 6266643813348617967186477710235785849136406323338782220568
+  temp = u1 * p192 + u2 * Q
+  if temp.x() != 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD \
+     or temp.y() != 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835:
+    raise TestFailure("*** u1 * p192 + u2 * Q came out wrong.")
+  else:
+    print_("u1 * p192 + u2 * Q came out right.")
+
+  e = 968236873715988614170569073515315707566766479517
+  pubk = Public_key( generator_192, generator_192 * d )
+  privk = Private_key( pubk, d )
+  sig = privk.sign( e, k )
+  r, s = sig.r, sig.s
+  if r != 3342403536405981729393488334694600415596881826869351677613 \
+     or s != 5735822328888155254683894997897571951568553642892029982342:
+    raise TestFailure("*** r or s came out wrong.")
+  else:
+    print_("r and s came out right.")
+
+  valid = pubk.verifies( e, sig )
+  if valid: print_("Signature verified OK.")
+  else: raise TestFailure("*** Signature failed verification.")
+
+  valid = pubk.verifies( e-1, sig )
+  if not valid: print_("Forgery was correctly rejected.")
+  else: raise TestFailure("*** Forgery was erroneously accepted.")
+
+  print_("Testing point validity, as per ECDSAVS.pdf B.2.2:")
+
+  test_point_validity( \
+    p192, \
+    0xcd6d0f029a023e9aaca429615b8f577abee685d8257cc83a, \
+    0x00019c410987680e9fb6c0b6ecc01d9a2647c8bae27721bacdfc, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0x00017f2fce203639e9eaf9fb50b81fc32776b30e3b02af16c73b, \
+    0x95da95c5e72dd48e229d4748d4eee658a9a54111b23b2adb, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0x4f77f8bc7fccbadd5760f4938746d5f253ee2168c1cf2792, \
+    0x000147156ff824d131629739817edb197717c41aab5c2a70f0f6, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0xc58d61f88d905293bcd4cd0080bcb1b7f811f2ffa41979f6, \
+    0x8804dc7a7c4c7f8b5d437f5156f3312ca7d6de8a0e11867f, \
+    True )
+
+  test_point_validity(
+    p192, \
+    0xcdf56c1aa3d8afc53c521adf3ffb96734a6a630a4a5b5a70, \
+    0x97c1c44a5fb229007b5ec5d25f7413d170068ffd023caa4e, \
+    True )
+
+  test_point_validity(
+    p192, \
+    0x89009c0dc361c81e99280c8e91df578df88cdf4b0cdedced, \
+    0x27be44a529b7513e727251f128b34262a0fd4d8ec82377b9, \
+    True )
+
+  test_point_validity(
+    p192, \
+    0x6a223d00bd22c52833409a163e057e5b5da1def2a197dd15, \
+    0x7b482604199367f1f303f9ef627f922f97023e90eae08abf, \
+    True )
+
+  test_point_validity(
+    p192, \
+    0x6dccbde75c0948c98dab32ea0bc59fe125cf0fb1a3798eda, \
+    0x0001171a3e0fa60cf3096f4e116b556198de430e1fbd330c8835, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0xd266b39e1f491fc4acbbbc7d098430931cfa66d55015af12, \
+    0x193782eb909e391a3148b7764e6b234aa94e48d30a16dbb2, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0x9d6ddbcd439baa0c6b80a654091680e462a7d1d3f1ffeb43, \
+    0x6ad8efc4d133ccf167c44eb4691c80abffb9f82b932b8caa, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0x146479d944e6bda87e5b35818aa666a4c998a71f4e95edbc, \
+    0xa86d6fe62bc8fbd88139693f842635f687f132255858e7f6, \
+    False )
+
+  test_point_validity(
+    p192, \
+    0xe594d4a598046f3598243f50fd2c7bd7d380edb055802253, \
+    0x509014c0c4d6b536e3ca750ec09066af39b4c8616a53a923, \
+    False )
+
+  print_("Trying signature-verification tests from ECDSAVS.pdf B.2.4:")
+  print_("P-192:")
+  Msg = 0x84ce72aa8699df436059f052ac51b6398d2511e49631bcb7e71f89c499b9ee425dfbc13a5f6d408471b054f2655617cbbaf7937b7c80cd8865cf02c8487d30d2b0fbd8b2c4e102e16d828374bbc47b93852f212d5043c3ea720f086178ff798cc4f63f787b9c2e419efa033e7644ea7936f54462dc21a6c4580725f7f0e7d158
+  Qx = 0xd9dbfb332aa8e5ff091e8ce535857c37c73f6250ffb2e7ac
+  Qy = 0x282102e364feded3ad15ddf968f88d8321aa268dd483ebc4
+  R = 0x64dca58a20787c488d11d6dd96313f1b766f2d8efe122916
+  S = 0x1ecba28141e84ab4ecad92f56720e2cc83eb3d22dec72479
+  test_signature_validity( Msg, Qx, Qy, R, S, True )
+
+  Msg = 0x94bb5bacd5f8ea765810024db87f4224ad71362a3c28284b2b9f39fab86db12e8beb94aae899768229be8fdb6c4f12f28912bb604703a79ccff769c1607f5a91450f30ba0460d359d9126cbd6296be6d9c4bb96c0ee74cbb44197c207f6db326ab6f5a659113a9034e54be7b041ced9dcf6458d7fb9cbfb2744d999f7dfd63f4
+  Qx = 0x3e53ef8d3112af3285c0e74842090712cd324832d4277ae7
+  Qy = 0xcc75f8952d30aec2cbb719fc6aa9934590b5d0ff5a83adb7
+  R = 0x8285261607283ba18f335026130bab31840dcfd9c3e555af
+  S = 0x356d89e1b04541afc9704a45e9c535ce4a50929e33d7e06c
+  test_signature_validity( Msg, Qx, Qy, R, S, True )
+
+  Msg = 0xf6227a8eeb34afed1621dcc89a91d72ea212cb2f476839d9b4243c66877911b37b4ad6f4448792a7bbba76c63bdd63414b6facab7dc71c3396a73bd7ee14cdd41a659c61c99b779cecf07bc51ab391aa3252386242b9853ea7da67fd768d303f1b9b513d401565b6f1eb722dfdb96b519fe4f9bd5de67ae131e64b40e78c42dd
+  Qx = 0x16335dbe95f8e8254a4e04575d736befb258b8657f773cb7
+  Qy = 0x421b13379c59bc9dce38a1099ca79bbd06d647c7f6242336
+  R = 0x4141bd5d64ea36c5b0bd21ef28c02da216ed9d04522b1e91
+  S = 0x159a6aa852bcc579e821b7bb0994c0861fb08280c38daa09
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x16b5f93afd0d02246f662761ed8e0dd9504681ed02a253006eb36736b563097ba39f81c8e1bce7a16c1339e345efabbc6baa3efb0612948ae51103382a8ee8bc448e3ef71e9f6f7a9676694831d7f5dd0db5446f179bcb737d4a526367a447bfe2c857521c7f40b6d7d7e01a180d92431fb0bbd29c04a0c420a57b3ed26ccd8a
+  Qx = 0xfd14cdf1607f5efb7b1793037b15bdf4baa6f7c16341ab0b
+  Qy = 0x83fa0795cc6c4795b9016dac928fd6bac32f3229a96312c4
+  R = 0x8dfdb832951e0167c5d762a473c0416c5c15bc1195667dc1
+  S = 0x1720288a2dc13fa1ec78f763f8fe2ff7354a7e6fdde44520
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x08a2024b61b79d260e3bb43ef15659aec89e5b560199bc82cf7c65c77d39192e03b9a895d766655105edd9188242b91fbde4167f7862d4ddd61e5d4ab55196683d4f13ceb90d87aea6e07eb50a874e33086c4a7cb0273a8e1c4408f4b846bceae1ebaac1b2b2ea851a9b09de322efe34cebe601653efd6ddc876ce8c2f2072fb
+  Qx = 0x674f941dc1a1f8b763c9334d726172d527b90ca324db8828
+  Qy = 0x65adfa32e8b236cb33a3e84cf59bfb9417ae7e8ede57a7ff
+  R = 0x9508b9fdd7daf0d8126f9e2bc5a35e4c6d800b5b804d7796
+  S = 0x36f2bf6b21b987c77b53bb801b3435a577e3d493744bfab0
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x1843aba74b0789d4ac6b0b8923848023a644a7b70afa23b1191829bbe4397ce15b629bf21a8838298653ed0c19222b95fa4f7390d1b4c844d96e645537e0aae98afb5c0ac3bd0e4c37f8daaff25556c64e98c319c52687c904c4de7240a1cc55cd9756b7edaef184e6e23b385726e9ffcba8001b8f574987c1a3fedaaa83ca6d
+  Qx = 0x10ecca1aad7220b56a62008b35170bfd5e35885c4014a19f
+  Qy = 0x04eb61984c6c12ade3bc47f3c629ece7aa0a033b9948d686
+  R = 0x82bfa4e82c0dfe9274169b86694e76ce993fd83b5c60f325
+  S = 0xa97685676c59a65dbde002fe9d613431fb183e8006d05633
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x5a478f4084ddd1a7fea038aa9732a822106385797d02311aeef4d0264f824f698df7a48cfb6b578cf3da416bc0799425bb491be5b5ecc37995b85b03420a98f2c4dc5c31a69a379e9e322fbe706bbcaf0f77175e05cbb4fa162e0da82010a278461e3e974d137bc746d1880d6eb02aa95216014b37480d84b87f717bb13f76e1
+  Qx = 0x6636653cb5b894ca65c448277b29da3ad101c4c2300f7c04
+  Qy = 0xfdf1cbb3fc3fd6a4f890b59e554544175fa77dbdbeb656c1
+  R = 0xeac2ddecddfb79931a9c3d49c08de0645c783a24cb365e1c
+  S = 0x3549fee3cfa7e5f93bc47d92d8ba100e881a2a93c22f8d50
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0xc598774259a058fa65212ac57eaa4f52240e629ef4c310722088292d1d4af6c39b49ce06ba77e4247b20637174d0bd67c9723feb57b5ead232b47ea452d5d7a089f17c00b8b6767e434a5e16c231ba0efa718a340bf41d67ea2d295812ff1b9277daacb8bc27b50ea5e6443bcf95ef4e9f5468fe78485236313d53d1c68f6ba2
+  Qx = 0xa82bd718d01d354001148cd5f69b9ebf38ff6f21898f8aaa
+  Qy = 0xe67ceede07fc2ebfafd62462a51e4b6c6b3d5b537b7caf3e
+  R = 0x4d292486c620c3de20856e57d3bb72fcde4a73ad26376955
+  S = 0xa85289591a6081d5728825520e62ff1c64f94235c04c7f95
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0xca98ed9db081a07b7557f24ced6c7b9891269a95d2026747add9e9eb80638a961cf9c71a1b9f2c29744180bd4c3d3db60f2243c5c0b7cc8a8d40a3f9a7fc910250f2187136ee6413ffc67f1a25e1c4c204fa9635312252ac0e0481d89b6d53808f0c496ba87631803f6c572c1f61fa049737fdacce4adff757afed4f05beb658
+  Qx = 0x7d3b016b57758b160c4fca73d48df07ae3b6b30225126c2f
+  Qy = 0x4af3790d9775742bde46f8da876711be1b65244b2b39e7ec
+  R = 0x95f778f5f656511a5ab49a5d69ddd0929563c29cbc3a9e62
+  S = 0x75c87fc358c251b4c83d2dd979faad496b539f9f2ee7a289
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x31dd9a54c8338bea06b87eca813d555ad1850fac9742ef0bbe40dad400e10288acc9c11ea7dac79eb16378ebea9490e09536099f1b993e2653cd50240014c90a9c987f64545abc6a536b9bd2435eb5e911fdfde2f13be96ea36ad38df4ae9ea387b29cced599af777338af2794820c9cce43b51d2112380a35802ab7e396c97a
+  Qx = 0x9362f28c4ef96453d8a2f849f21e881cd7566887da8beb4a
+  Qy = 0xe64d26d8d74c48a024ae85d982ee74cd16046f4ee5333905
+  R = 0xf3923476a296c88287e8de914b0b324ad5a963319a4fe73b
+  S = 0xf0baeed7624ed00d15244d8ba2aede085517dbdec8ac65f5
+  test_signature_validity( Msg, Qx, Qy, R, S, True )
+
+  Msg = 0xb2b94e4432267c92f9fdb9dc6040c95ffa477652761290d3c7de312283f6450d89cc4aabe748554dfb6056b2d8e99c7aeaad9cdddebdee9dbc099839562d9064e68e7bb5f3a6bba0749ca9a538181fc785553a4000785d73cc207922f63e8ce1112768cb1de7b673aed83a1e4a74592f1268d8e2a4e9e63d414b5d442bd0456d
+  Qx = 0xcc6fc032a846aaac25533eb033522824f94e670fa997ecef
+  Qy = 0xe25463ef77a029eccda8b294fd63dd694e38d223d30862f1
+  R = 0x066b1d07f3a40e679b620eda7f550842a35c18b80c5ebe06
+  S = 0xa0b0fb201e8f2df65e2c4508ef303bdc90d934016f16b2dc
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x4366fcadf10d30d086911de30143da6f579527036937007b337f7282460eae5678b15cccda853193ea5fc4bc0a6b9d7a31128f27e1214988592827520b214eed5052f7775b750b0c6b15f145453ba3fee24a085d65287e10509eb5d5f602c440341376b95c24e5c4727d4b859bfe1483d20538acdd92c7997fa9c614f0f839d7
+  Qx = 0x955c908fe900a996f7e2089bee2f6376830f76a19135e753
+  Qy = 0xba0c42a91d3847de4a592a46dc3fdaf45a7cc709b90de520
+  R = 0x1f58ad77fc04c782815a1405b0925e72095d906cbf52a668
+  S = 0xf2e93758b3af75edf784f05a6761c9b9a6043c66b845b599
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x543f8af57d750e33aa8565e0cae92bfa7a1ff78833093421c2942cadf9986670a5ff3244c02a8225e790fbf30ea84c74720abf99cfd10d02d34377c3d3b41269bea763384f372bb786b5846f58932defa68023136cd571863b304886e95e52e7877f445b9364b3f06f3c28da12707673fecb4b8071de06b6e0a3c87da160cef3
+  Qx = 0x31f7fa05576d78a949b24812d4383107a9a45bb5fccdd835
+  Qy = 0x8dc0eb65994a90f02b5e19bd18b32d61150746c09107e76b
+  R = 0xbe26d59e4e883dde7c286614a767b31e49ad88789d3a78ff
+  S = 0x8762ca831c1ce42df77893c9b03119428e7a9b819b619068
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0xd2e8454143ce281e609a9d748014dcebb9d0bc53adb02443a6aac2ffe6cb009f387c346ecb051791404f79e902ee333ad65e5c8cb38dc0d1d39a8dc90add5023572720e5b94b190d43dd0d7873397504c0c7aef2727e628eb6a74411f2e400c65670716cb4a815dc91cbbfeb7cfe8c929e93184c938af2c078584da045e8f8d1
+  Qx = 0x66aa8edbbdb5cf8e28ceb51b5bda891cae2df84819fe25c0
+  Qy = 0x0c6bc2f69030a7ce58d4a00e3b3349844784a13b8936f8da
+  R = 0xa4661e69b1734f4a71b788410a464b71e7ffe42334484f23
+  S = 0x738421cf5e049159d69c57a915143e226cac8355e149afe9
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+  Msg = 0x6660717144040f3e2f95a4e25b08a7079c702a8b29babad5a19a87654bc5c5afa261512a11b998a4fb36b5d8fe8bd942792ff0324b108120de86d63f65855e5461184fc96a0a8ffd2ce6d5dfb0230cbbdd98f8543e361b3205f5da3d500fdc8bac6db377d75ebef3cb8f4d1ff738071ad0938917889250b41dd1d98896ca06fb
+  Qx = 0xbcfacf45139b6f5f690a4c35a5fffa498794136a2353fc77
+  Qy = 0x6f4a6c906316a6afc6d98fe1f0399d056f128fe0270b0f22
+  R = 0x9db679a3dafe48f7ccad122933acfe9da0970b71c94c21c1
+  S = 0x984c2db99827576c0a41a5da41e07d8cc768bc82f18c9da9
+  test_signature_validity( Msg, Qx, Qy, R, S, False )
+
+
+
+  print_("Testing the example code:")
+
+  # Building a public/private key pair from the NIST Curve P-192:
+
+  g = generator_192
+  n = g.order()
+
+  # (random.SystemRandom is supposed to provide
+  # crypto-quality random numbers, but as Debian recently
+  # illustrated, a systems programmer can accidentally
+  # demolish this security, so in serious applications
+  # further precautions are appropriate.)
+
+  randrange = random.SystemRandom().randrange
+
+  secret = randrange( 1, n )
+  pubkey = Public_key( g, g * secret )
+  privkey = Private_key( pubkey, secret )
+
+  # Signing a hash value:
+
+  hash = randrange( 1, n )
+  signature = privkey.sign( hash, randrange( 1, n ) )
+
+  # Verifying a signature for a hash value:
+
+  if pubkey.verifies( hash, signature ):
+    print_("Demo verification succeeded.")
+  else:
+    raise TestFailure("*** Demo verification failed.")
+
+  if pubkey.verifies( hash-1, signature ):
+    raise TestFailure( "**** Demo verification failed to reject tampered hash.")
+  else:
+    print_("Demo verification correctly rejected tampered hash.")
+
+if __name__ == "__main__":
+  __main__()

bin/python/ecdsa/ellipticcurve.py

@@ -0,0 +1,293 @@
+#! /usr/bin/env python
+#
+# Implementation of elliptic curves, for cryptographic applications.
+#
+# This module doesn't provide any way to choose a random elliptic
+# curve, nor to verify that an elliptic curve was chosen randomly,
+# because one can simply use NIST's standard curves.
+#
+# Notes from X9.62-1998 (draft):
+#   Nomenclature:
+#     - Q is a public key.
+#     The "Elliptic Curve Domain Parameters" include:
+#     - q is the "field size", which in our case equals p.
+#     - p is a big prime.
+#     - G is a point of prime order (5.1.1.1).
+#     - n is the order of G (5.1.1.1).
+#   Public-key validation (5.2.2):
+#     - Verify that Q is not the point at infinity.
+#     - Verify that X_Q and Y_Q are in [0,p-1].
+#     - Verify that Q is on the curve.
+#     - Verify that nQ is the point at infinity.
+#   Signature generation (5.3):
+#     - Pick random k from [1,n-1].
+#   Signature checking (5.4.2):
+#     - Verify that r and s are in [1,n-1].
+#
+# Version of 2008.11.25.
+#
+# Revision history:
+#    2005.12.31 - Initial version.
+#    2008.11.25 - Change CurveFp.is_on to contains_point.
+#
+# Written in 2005 by Peter Pearson and placed in the public domain.
+
+from __future__ import division
+
+from .six import print_
+from . import numbertheory
+
+class CurveFp( object ):
+  """Elliptic Curve over the field of integers modulo a prime."""
+  def __init__( self, p, a, b ):
+    """The curve of points satisfying y^2 = x^3 + a*x + b (mod p)."""
+    self.__p = p
+    self.__a = a
+    self.__b = b
+
+  def p( self ):
+    return self.__p
+
+  def a( self ):
+    return self.__a
+
+  def b( self ):
+    return self.__b
+
+  def contains_point( self, x, y ):
+    """Is the point (x,y) on this curve?"""
+    return ( y * y - ( x * x * x + self.__a * x + self.__b ) ) % self.__p == 0
+
+
+
+class Point( object ):
+  """A point on an elliptic curve. Altering x and y is forbidding,
+     but they can be read by the x() and y() methods."""
+  def __init__( self, curve, x, y, order = None ):
+    """curve, x, y, order; order (optional) is the order of this point."""
+    self.__curve = curve
+    self.__x = x
+    self.__y = y
+    self.__order = order
+    # self.curve is allowed to be None only for INFINITY:
+    if self.__curve: assert self.__curve.contains_point( x, y )
+    if order: assert self * order == INFINITY
+
+  def __eq__( self, other ):
+    """Return True if the points are identical, False otherwise."""
+    if self.__curve == other.__curve \
+       and self.__x == other.__x \
+       and self.__y == other.__y:
+      return True
+    else:
+      return False
+
+  def __add__( self, other ):
+    """Add one point to another point."""
+
+    # X9.62 B.3:
+
+    if other == INFINITY: return self
+    if self == INFINITY: return other
+    assert self.__curve == other.__curve
+    if self.__x == other.__x:
+      if ( self.__y + other.__y ) % self.__curve.p() == 0:
+        return INFINITY
+      else:
+        return self.double()
+
+    p = self.__curve.p()
+
+    l = ( ( other.__y - self.__y ) * \
+          numbertheory.inverse_mod( other.__x - self.__x, p ) ) % p
+
+    x3 = ( l * l - self.__x - other.__x ) % p
+    y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
+
+    return Point( self.__curve, x3, y3 )
+
+  def __mul__( self, other ):
+    """Multiply a point by an integer."""
+
+    def leftmost_bit( x ):
+      assert x > 0
+      result = 1
+      while result <= x: result = 2 * result
+      return result // 2
+
+    e = other
+    if self.__order: e = e % self.__order
+    if e == 0: return INFINITY
+    if self == INFINITY: return INFINITY
+    assert e > 0
+
+    # From X9.62 D.3.2:
+
+    e3 = 3 * e
+    negative_self = Point( self.__curve, self.__x, -self.__y, self.__order )
+    i = leftmost_bit( e3 ) // 2
+    result = self
+    # print_("Multiplying %s by %d (e3 = %d):" % ( self, other, e3 ))
+    while i > 1:
+      result = result.double()
+      if ( e3 & i ) != 0 and ( e & i ) == 0: result = result + self
+      if ( e3 & i ) == 0 and ( e & i ) != 0: result = result + negative_self
+      # print_(". . . i = %d, result = %s" % ( i, result ))
+      i = i // 2
+
+    return result
+
+  def __rmul__( self, other ):
+    """Multiply a point by an integer."""
+
+    return self * other
+
+  def __str__( self ):
+    if self == INFINITY: return "infinity"
+    return "(%d,%d)" % ( self.__x, self.__y )
+
+  def double( self ):
+    """Return a new point that is twice the old."""
+
+    if self == INFINITY:
+      return INFINITY
+
+    # X9.62 B.3:
+
+    p = self.__curve.p()
+    a = self.__curve.a()
+
+    l = ( ( 3 * self.__x * self.__x + a ) * \
+          numbertheory.inverse_mod( 2 * self.__y, p ) ) % p
+
+    x3 = ( l * l - 2 * self.__x ) % p
+    y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
+
+    return Point( self.__curve, x3, y3 )
+
+  def x( self ):
+    return self.__x
+
+  def y( self ):
+    return self.__y
+
+  def curve( self ):
+    return self.__curve
+
+  def order( self ):
+    return self.__order
+
+
+# This one point is the Point At Infinity for all purposes:
+INFINITY = Point( None, None, None )
+
+def __main__():
+
+  class FailedTest(Exception): pass
+  def test_add( c, x1, y1, x2,  y2, x3, y3 ):
+    """We expect that on curve c, (x1,y1) + (x2, y2 ) = (x3, y3)."""
+    p1 = Point( c, x1, y1 )
+    p2 = Point( c, x2, y2 )
+    p3 = p1 + p2
+    print_("%s + %s = %s" % ( p1, p2, p3 ), end=' ')
+    if p3.x() != x3 or p3.y() != y3:
+      raise FailedTest("Failure: should give (%d,%d)." % ( x3, y3 ))
+    else:
+      print_(" Good.")
+
+  def test_double( c, x1, y1, x3, y3 ):
+    """We expect that on curve c, 2*(x1,y1) = (x3, y3)."""
+    p1 = Point( c, x1, y1 )
+    p3 = p1.double()
+    print_("%s doubled = %s" % ( p1, p3 ), end=' ')
+    if p3.x() != x3 or p3.y() != y3:
+      raise FailedTest("Failure: should give (%d,%d)." % ( x3, y3 ))
+    else:
+      print_(" Good.")
+
+  def test_double_infinity( c ):
+    """We expect that on curve c, 2*INFINITY = INFINITY."""
+    p1 = INFINITY
+    p3 = p1.double()
+    print_("%s doubled = %s" % ( p1, p3 ), end=' ')
+    if p3.x() != INFINITY.x() or p3.y() != INFINITY.y():
+      raise FailedTest("Failure: should give (%d,%d)." % ( INFINITY.x(), INFINITY.y() ))
+    else:
+      print_(" Good.")
+
+  def test_multiply( c, x1, y1, m, x3, y3 ):
+    """We expect that on curve c, m*(x1,y1) = (x3,y3)."""
+    p1 = Point( c, x1, y1 )
+    p3 = p1 * m
+    print_("%s * %d = %s" % ( p1, m, p3 ), end=' ')
+    if p3.x() != x3 or p3.y() != y3:
+      raise FailedTest("Failure: should give (%d,%d)." % ( x3, y3 ))
+    else:
+      print_(" Good.")
+
+
+  # A few tests from X9.62 B.3:
+
+  c = CurveFp( 23, 1, 1 )
+  test_add( c, 3, 10, 9, 7, 17, 20 )
+  test_double( c, 3, 10, 7, 12 )
+  test_add( c, 3, 10, 3, 10, 7, 12 )	# (Should just invoke double.)
+  test_multiply( c, 3, 10, 2, 7, 12 )
+
+  test_double_infinity(c)
+
+  # From X9.62 I.1 (p. 96):
+
+  g = Point( c, 13, 7, 7 )
+
+  check = INFINITY
+  for i in range( 7 + 1 ):
+    p = ( i % 7 ) * g
+    print_("%s * %d = %s, expected %s . . ." % ( g, i, p, check ), end=' ')
+    if p == check:
+      print_(" Good.")
+    else:
+      raise FailedTest("Bad.")
+    check = check + g
+
+  # NIST Curve P-192:
+  p = 6277101735386680763835789423207666416083908700390324961279
+  r = 6277101735386680763835789423176059013767194773182842284081
+  #s = 0x3045ae6fc8422f64ed579528d38120eae12196d5L
+  c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65
+  b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
+  Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
+  Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
+
+  c192 = CurveFp( p, -3, b )
+  p192 = Point( c192, Gx, Gy, r )
+
+  # Checking against some sample computations presented
+  # in X9.62:
+
+  d = 651056770906015076056810763456358567190100156695615665659
+  Q = d * p192
+  if Q.x() != 0x62B12D60690CDCF330BABAB6E69763B471F994DD702D16A5:
+    raise FailedTest("p192 * d came out wrong.")
+  else:
+    print_("p192 * d came out right.")
+
+  k = 6140507067065001063065065565667405560006161556565665656654
+  R = k * p192
+  if R.x() != 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD \
+     or R.y() != 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835:
+    raise FailedTest("k * p192 came out wrong.")
+  else:
+    print_("k * p192 came out right.")
+
+  u1 = 2563697409189434185194736134579731015366492496392189760599
+  u2 = 6266643813348617967186477710235785849136406323338782220568
+  temp = u1 * p192 + u2 * Q
+  if temp.x() != 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD \
+     or temp.y() != 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835:
+    raise FailedTest("u1 * p192 + u2 * Q came out wrong.")
+  else:
+    print_("u1 * p192 + u2 * Q came out right.")
+
+if __name__ == "__main__":
+  __main__()

bin/python/ecdsa/keys.py

@@ -0,0 +1,283 @@
+import binascii
+
+from . import ecdsa
+from . import der
+from . import rfc6979
+from .curves import NIST192p, find_curve
+from .util import string_to_number, number_to_string, randrange
+from .util import sigencode_string, sigdecode_string
+from .util import oid_ecPublicKey, encoded_oid_ecPublicKey
+from .six import PY3, b
+from hashlib import sha1
+
+class BadSignatureError(Exception):
+    pass
+class BadDigestError(Exception):
+    pass
+
+class VerifyingKey:
+    def __init__(self, _error__please_use_generate=None):
+        if not _error__please_use_generate:
+            raise TypeError("Please use SigningKey.generate() to construct me")
+
+    @classmethod
+    def from_public_point(klass, point, curve=NIST192p, hashfunc=sha1):
+        self = klass(_error__please_use_generate=True)
+        self.curve = curve
+        self.default_hashfunc = hashfunc
+        self.pubkey = ecdsa.Public_key(curve.generator, point)
+        self.pubkey.order = curve.order
+        return self
+
+    @classmethod
+    def from_string(klass, string, curve=NIST192p, hashfunc=sha1,
+                    validate_point=True):
+        order = curve.order
+        assert len(string) == curve.verifying_key_length, \
+               (len(string), curve.verifying_key_length)
+        xs = string[:curve.baselen]
+        ys = string[curve.baselen:]
+        assert len(xs) == curve.baselen, (len(xs), curve.baselen)
+        assert len(ys) == curve.baselen, (len(ys), curve.baselen)
+        x = string_to_number(xs)
+        y = string_to_number(ys)
+        if validate_point:
+            assert ecdsa.point_is_valid(curve.generator, x, y)
+        from . import ellipticcurve
+        point = ellipticcurve.Point(curve.curve, x, y, order)
+        return klass.from_public_point(point, curve, hashfunc)
+
+    @classmethod
+    def from_pem(klass, string):
+        return klass.from_der(der.unpem(string))
+
+    @classmethod
+    def from_der(klass, string):
+        # [[oid_ecPublicKey,oid_curve], point_str_bitstring]
+        s1,empty = der.remove_sequence(string)
+        if empty != b(""):
+            raise der.UnexpectedDER("trailing junk after DER pubkey: %s" %
+                                    binascii.hexlify(empty))
+        s2,point_str_bitstring = der.remove_sequence(s1)
+        # s2 = oid_ecPublicKey,oid_curve
+        oid_pk, rest = der.remove_object(s2)
+        oid_curve, empty = der.remove_object(rest)
+        if empty != b(""):
+            raise der.UnexpectedDER("trailing junk after DER pubkey objects: %s" %
+                                    binascii.hexlify(empty))
+        assert oid_pk == oid_ecPublicKey, (oid_pk, oid_ecPublicKey)
+        curve = find_curve(oid_curve)
+        point_str, empty = der.remove_bitstring(point_str_bitstring)
+        if empty != b(""):
+            raise der.UnexpectedDER("trailing junk after pubkey pointstring: %s" %
+                                    binascii.hexlify(empty))
+        assert point_str.startswith(b("\x00\x04"))
+        return klass.from_string(point_str[2:], curve)
+
+    def to_string(self):
+        # VerifyingKey.from_string(vk.to_string()) == vk as long as the
+        # curves are the same: the curve itself is not included in the
+        # serialized form
+        order = self.pubkey.order
+        x_str = number_to_string(self.pubkey.point.x(), order)
+        y_str = number_to_string(self.pubkey.point.y(), order)
+        return x_str + y_str
+
+    def to_pem(self):
+        return der.topem(self.to_der(), "PUBLIC KEY")
+
+    def to_der(self):
+        order = self.pubkey.order
+        x_str = number_to_string(self.pubkey.point.x(), order)
+        y_str = number_to_string(self.pubkey.point.y(), order)
+        point_str = b("\x00\x04") + x_str + y_str
+        return der.encode_sequence(der.encode_sequence(encoded_oid_ecPublicKey,
+                                                       self.curve.encoded_oid),
+                                   der.encode_bitstring(point_str))
+
+    def verify(self, signature, data, hashfunc=None, sigdecode=sigdecode_string):
+        hashfunc = hashfunc or self.default_hashfunc
+        digest = hashfunc(data).digest()
+        return self.verify_digest(signature, digest, sigdecode)
+
+    def verify_digest(self, signature, digest, sigdecode=sigdecode_string):
+        if len(digest) > self.curve.baselen:
+            raise BadDigestError("this curve (%s) is too short "
+                                 "for your digest (%d)" % (self.curve.name,
+                                                           8*len(digest)))
+        number = string_to_number(digest)
+        r, s = sigdecode(signature, self.pubkey.order)
+        sig = ecdsa.Signature(r, s)
+        if self.pubkey.verifies(number, sig):
+            return True
+        raise BadSignatureError
+
+class SigningKey:
+    def __init__(self, _error__please_use_generate=None):
+        if not _error__please_use_generate:
+            raise TypeError("Please use SigningKey.generate() to construct me")
+
+    @classmethod
+    def generate(klass, curve=NIST192p, entropy=None, hashfunc=sha1):
+        secexp = randrange(curve.order, entropy)
+        return klass.from_secret_exponent(secexp, curve, hashfunc)
+
+    # to create a signing key from a short (arbitrary-length) seed, convert
+    # that seed into an integer with something like
+    # secexp=util.randrange_from_seed__X(seed, curve.order), and then pass
+    # that integer into SigningKey.from_secret_exponent(secexp, curve)
+
+    @classmethod
+    def from_secret_exponent(klass, secexp, curve=NIST192p, hashfunc=sha1):
+        self = klass(_error__please_use_generate=True)
+        self.curve = curve
+        self.default_hashfunc = hashfunc
+        self.baselen = curve.baselen
+        n = curve.order
+        assert 1 <= secexp < n
+        pubkey_point = curve.generator*secexp
+        pubkey = ecdsa.Public_key(curve.generator, pubkey_point)
+        pubkey.order = n
+        self.verifying_key = VerifyingKey.from_public_point(pubkey_point, curve,
+                                                            hashfunc)
+        self.privkey = ecdsa.Private_key(pubkey, secexp)
+        self.privkey.order = n
+        return self
+
+    @classmethod
+    def from_string(klass, string, curve=NIST192p, hashfunc=sha1):
+        assert len(string) == curve.baselen, (len(string), curve.baselen)
+        secexp = string_to_number(string)
+        return klass.from_secret_exponent(secexp, curve, hashfunc)
+
+    @classmethod
+    def from_pem(klass, string, hashfunc=sha1):
+        # the privkey pem file has two sections: "EC PARAMETERS" and "EC
+        # PRIVATE KEY". The first is redundant.
+        if PY3 and isinstance(string, str):
+            string = string.encode()
+        privkey_pem = string[string.index(b("-----BEGIN EC PRIVATE KEY-----")):]
+        return klass.from_der(der.unpem(privkey_pem), hashfunc)
+    @classmethod
+    def from_der(klass, string, hashfunc=sha1):
+        # SEQ([int(1), octetstring(privkey),cont[0], oid(secp224r1),
+        #      cont[1],bitstring])
+        s, empty = der.remove_sequence(string)
+        if empty != b(""):
+            raise der.UnexpectedDER("trailing junk after DER privkey: %s" %
+                                    binascii.hexlify(empty))
+        one, s = der.remove_integer(s)
+        if one != 1:
+            raise der.UnexpectedDER("expected '1' at start of DER privkey,"
+                                    " got %d" % one)
+        privkey_str, s = der.remove_octet_string(s)
+        tag, curve_oid_str, s = der.remove_constructed(s)
+        if tag != 0:
+            raise der.UnexpectedDER("expected tag 0 in DER privkey,"
+                                    " got %d" % tag)
+        curve_oid, empty = der.remove_object(curve_oid_str)
+        if empty != b(""):
+            raise der.UnexpectedDER("trailing junk after DER privkey "
+                                    "curve_oid: %s" % binascii.hexlify(empty))
+        curve = find_curve(curve_oid)
+
+        # we don't actually care about the following fields
+        #
+        #tag, pubkey_bitstring, s = der.remove_constructed(s)
+        #if tag != 1:
+        #    raise der.UnexpectedDER("expected tag 1 in DER privkey, got %d"
+        #                            % tag)
+        #pubkey_str = der.remove_bitstring(pubkey_bitstring)
+        #if empty != "":
+        #    raise der.UnexpectedDER("trailing junk after DER privkey "
+        #                            "pubkeystr: %s" % binascii.hexlify(empty))
+
+        # our from_string method likes fixed-length privkey strings
+        if len(privkey_str) < curve.baselen:
+            privkey_str = b("\x00")*(curve.baselen-len(privkey_str)) + privkey_str
+        return klass.from_string(privkey_str, curve, hashfunc)
+
+    def to_string(self):
+        secexp = self.privkey.secret_multiplier
+        s = number_to_string(secexp, self.privkey.order)
+        return s
+
+    def to_pem(self):
+        # TODO: "BEGIN ECPARAMETERS"
+        return der.topem(self.to_der(), "EC PRIVATE KEY")
+
+    def to_der(self):
+        # SEQ([int(1), octetstring(privkey),cont[0], oid(secp224r1),
+        #      cont[1],bitstring])
+        encoded_vk = b("\x00\x04") + self.get_verifying_key().to_string()
+        return der.encode_sequence(der.encode_integer(1),
+                                   der.encode_octet_string(self.to_string()),
+                                   der.encode_constructed(0, self.curve.encoded_oid),
+                                   der.encode_constructed(1, der.encode_bitstring(encoded_vk)),
+                                   )
+
+    def get_verifying_key(self):
+        return self.verifying_key
+
+    def sign_deterministic(self, data, hashfunc=None, sigencode=sigencode_string):
+        hashfunc = hashfunc or self.default_hashfunc
+        digest = hashfunc(data).digest()
+
+        return self.sign_digest_deterministic(digest, hashfunc=hashfunc, sigencode=sigencode)
+
+    def sign_digest_deterministic(self, digest, hashfunc=None, sigencode=sigencode_string):
+        """
+        Calculates 'k' from data itself, removing the need for strong
+        random generator and producing deterministic (reproducible) signatures.
+        See RFC 6979 for more details.
+        """
+        secexp = self.privkey.secret_multiplier
+        k = rfc6979.generate_k(
+            self.curve.generator.order(), secexp, hashfunc, digest)
+
+        return self.sign_digest(digest, sigencode=sigencode, k=k)
+
+    def sign(self, data, entropy=None, hashfunc=None, sigencode=sigencode_string, k=None):
+        """
+        hashfunc= should behave like hashlib.sha1 . The output length of the
+        hash (in bytes) must not be longer than the length of the curve order
+        (rounded up to the nearest byte), so using SHA256 with nist256p is
+        ok, but SHA256 with nist192p is not. (In the 2**-96ish unlikely event
+        of a hash output larger than the curve order, the hash will
+        effectively be wrapped mod n).
+
+        Use hashfunc=hashlib.sha1 to match openssl's -ecdsa-with-SHA1 mode,
+        or hashfunc=hashlib.sha256 for openssl-1.0.0's -ecdsa-with-SHA256.
+        """
+
+        hashfunc = hashfunc or self.default_hashfunc
+        h = hashfunc(data).digest()
+        return self.sign_digest(h, entropy, sigencode, k)
+
+    def sign_digest(self, digest, entropy=None, sigencode=sigencode_string, k=None):
+        if len(digest) > self.curve.baselen:
+            raise BadDigestError("this curve (%s) is too short "
+                                 "for your digest (%d)" % (self.curve.name,
+                                                           8*len(digest)))
+        number = string_to_number(digest)
+        r, s = self.sign_number(number, entropy, k)
+        return sigencode(r, s, self.privkey.order)
+
+    def sign_number(self, number, entropy=None, k=None):
+        # returns a pair of numbers
+        order = self.privkey.order
+        # privkey.sign() may raise RuntimeError in the amazingly unlikely
+        # (2**-192) event that r=0 or s=0, because that would leak the key.
+        # We could re-try with a different 'k', but we couldn't test that
+        # code, so I choose to allow the signature to fail instead.
+
+        # If k is set, it is used directly. In other cases
+        # it is generated using entropy function
+        if k is not None:
+            _k = k
+        else:
+            _k = randrange(order, entropy)
+
+        assert 1 <= _k < order
+        sig = self.privkey.sign(number, _k)
+        return sig.r, sig.s

bin/python/ecdsa/numbertheory.py

@@ -0,0 +1,613 @@
+#! /usr/bin/env python
+#
+# Provide some simple capabilities from number theory.
+#
+# Version of 2008.11.14.
+#
+# Written in 2005 and 2006 by Peter Pearson and placed in the public domain.
+# Revision history:
+#   2008.11.14: Use pow( base, exponent, modulus ) for modular_exp.
+#               Make gcd and lcm accept arbitrarly many arguments.
+
+from __future__ import division
+
+from .six import print_, integer_types
+from .six.moves import reduce
+
+import math
+
+
+class Error( Exception ):
+  """Base class for exceptions in this module."""
+  pass
+
+class SquareRootError( Error ):
+  pass
+
+class NegativeExponentError( Error ):
+  pass
+
+
+def modular_exp( base, exponent, modulus ):
+  "Raise base to exponent, reducing by modulus"
+  if exponent < 0:
+    raise NegativeExponentError( "Negative exponents (%d) not allowed" \
+                                 % exponent )
+  return pow( base, exponent, modulus )
+#   result = 1L
+#   x = exponent
+#   b = base + 0L
+#   while x > 0:
+#     if x % 2 > 0: result = (result * b) % modulus
+#     x = x // 2
+#     b = ( b * b ) % modulus
+#   return result
+
+
+def polynomial_reduce_mod( poly, polymod, p ):
+  """Reduce poly by polymod, integer arithmetic modulo p.
+
+  Polynomials are represented as lists of coefficients
+  of increasing powers of x."""
+
+  # This module has been tested only by extensive use
+  # in calculating modular square roots.
+
+  # Just to make this easy, require a monic polynomial:
+  assert polymod[-1] == 1
+
+  assert len( polymod ) > 1
+
+  while len( poly ) >= len( polymod ):
+    if poly[-1] != 0:
+      for i in range( 2, len( polymod ) + 1 ):
+        poly[-i] = ( poly[-i] - poly[-1] * polymod[-i] ) % p
+    poly = poly[0:-1]
+
+  return poly
+
+
+
+def polynomial_multiply_mod( m1, m2, polymod, p ):
+  """Polynomial multiplication modulo a polynomial over ints mod p.
+
+  Polynomials are represented as lists of coefficients
+  of increasing powers of x."""
+
+  # This is just a seat-of-the-pants implementation.
+
+  # This module has been tested only by extensive use
+  # in calculating modular square roots.
+
+  # Initialize the product to zero:
+
+  prod = ( len( m1 ) + len( m2 ) - 1 ) * [0]
+
+  # Add together all the cross-terms:
+
+  for i in range( len( m1 ) ):
+    for j in range( len( m2 ) ):
+      prod[i+j] = ( prod[i+j] + m1[i] * m2[j] ) % p
+
+  return polynomial_reduce_mod( prod, polymod, p )
+
+
+def polynomial_exp_mod( base, exponent, polymod, p ):
+  """Polynomial exponentiation modulo a polynomial over ints mod p.
+
+  Polynomials are represented as lists of coefficients
+  of increasing powers of x."""
+
+  # Based on the Handbook of Applied Cryptography, algorithm 2.227.
+
+  # This module has been tested only by extensive use
+  # in calculating modular square roots.
+
+  assert exponent < p
+
+  if exponent == 0: return [ 1 ]
+
+  G = base
+  k = exponent
+  if k%2 == 1: s = G
+  else:        s = [ 1 ]
+
+  while k > 1:
+    k = k // 2
+    G = polynomial_multiply_mod( G, G, polymod, p )
+    if k%2 == 1: s = polynomial_multiply_mod( G, s, polymod, p )
+
+  return s
+
+
+
+def jacobi( a, n ):
+  """Jacobi symbol"""
+
+  # Based on the Handbook of Applied Cryptography (HAC), algorithm 2.149.
+
+  # This function has been tested by comparison with a small
+  # table printed in HAC, and by extensive use in calculating
+  # modular square roots.
+
+  assert n >= 3
+  assert n%2 == 1
+  a = a % n
+  if a == 0: return 0
+  if a == 1: return 1
+  a1, e = a, 0
+  while a1%2 == 0:
+    a1, e = a1//2, e+1
+  if e%2 == 0 or n%8 == 1 or n%8 == 7: s = 1
+  else: s = -1
+  if a1 == 1: return s
+  if n%4 == 3 and a1%4 == 3: s = -s
+  return s * jacobi( n % a1, a1 )
+
+
+
+def square_root_mod_prime( a, p ):
+  """Modular square root of a, mod p, p prime."""
+
+  # Based on the Handbook of Applied Cryptography, algorithms 3.34 to 3.39.
+
+  # This module has been tested for all values in [0,p-1] for
+  # every prime p from 3 to 1229.
+
+  assert 0 <= a < p
+  assert 1 < p
+
+  if a == 0: return 0
+  if p == 2: return a
+
+  jac = jacobi( a, p )
+  if jac == -1: raise SquareRootError( "%d has no square root modulo %d" \
+                                       % ( a, p ) )
+
+  if p % 4 == 3: return modular_exp( a, (p+1)//4, p )
+
+  if p % 8 == 5:
+    d = modular_exp( a, (p-1)//4, p )
+    if d == 1: return modular_exp( a, (p+3)//8, p )
+    if d == p-1: return ( 2 * a * modular_exp( 4*a, (p-5)//8, p ) ) % p
+    raise RuntimeError("Shouldn't get here.")
+
+  for b in range( 2, p ):
+    if jacobi( b*b-4*a, p ) == -1:
+      f = ( a, -b, 1 )
+      ff = polynomial_exp_mod( ( 0, 1 ), (p+1)//2, f, p )
+      assert ff[1] == 0
+      return ff[0]
+  raise RuntimeError("No b found.")
+
+
+
+def inverse_mod( a, m ):
+  """Inverse of a mod m."""
+
+  if a < 0 or m <= a: a = a % m
+
+  # From Ferguson and Schneier, roughly:
+
+  c, d = a, m
+  uc, vc, ud, vd = 1, 0, 0, 1
+  while c != 0:
+    q, c, d = divmod( d, c ) + ( c, )
+    uc, vc, ud, vd = ud - q*uc, vd - q*vc, uc, vc
+
+  # At this point, d is the GCD, and ud*a+vd*m = d.
+  # If d == 1, this means that ud is a inverse.
+
+  assert d == 1
+  if ud > 0: return ud
+  else: return ud + m
+
+
+def gcd2(a, b):
+  """Greatest common divisor using Euclid's algorithm."""
+  while a:
+    a, b = b%a, a
+  return b
+
+
+def gcd( *a ):
+  """Greatest common divisor.
+
+  Usage: gcd( [ 2, 4, 6 ] )
+  or:    gcd( 2, 4, 6 )
+  """
+
+  if len( a ) > 1: return reduce( gcd2, a )
+  if hasattr( a[0], "__iter__" ): return reduce( gcd2, a[0] )
+  return a[0]
+
+
+def lcm2(a,b):
+  """Least common multiple of two integers."""
+
+  return (a*b)//gcd(a,b)
+
+
+def lcm( *a ):
+  """Least common multiple.
+
+  Usage: lcm( [ 3, 4, 5 ] )
+  or:    lcm( 3, 4, 5 )
+  """
+
+  if len( a ) > 1: return reduce( lcm2, a )
+  if hasattr( a[0], "__iter__" ): return reduce( lcm2, a[0] )
+  return a[0]
+
+
+
+def factorization( n ):
+  """Decompose n into a list of (prime,exponent) pairs."""
+
+  assert isinstance( n, integer_types )
+
+  if n < 2: return []
+
+  result = []
+  d = 2
+
+  # Test the small primes:
+
+  for d in smallprimes:
+    if d > n: break
+    q, r = divmod( n, d )
+    if r == 0:
+      count = 1
+      while d <= n:
+        n = q
+        q, r = divmod( n, d )
+        if r != 0: break
+        count = count + 1
+      result.append( ( d, count ) )
+
+  # If n is still greater than the last of our small primes,
+  # it may require further work:
+
+  if n > smallprimes[-1]:
+    if is_prime( n ):   # If what's left is prime, it's easy:
+      result.append( ( n, 1 ) )
+    else:               # Ugh. Search stupidly for a divisor:
+      d = smallprimes[-1]
+      while 1:
+        d = d + 2               # Try the next divisor.
+        q, r = divmod( n, d )
+        if q < d: break         # n < d*d means we're done, n = 1 or prime.
+        if r == 0:              # d divides n. How many times?
+          count = 1
+          n = q
+          while d <= n:                 # As long as d might still divide n,
+            q, r = divmod( n, d )       # see if it does.
+            if r != 0: break
+            n = q                       # It does. Reduce n, increase count.
+            count = count + 1
+          result.append( ( d, count ) )
+      if n > 1: result.append( ( n, 1 ) )
+
+  return result
+
+
+
+def phi( n ):
+  """Return the Euler totient function of n."""
+
+  assert isinstance( n, integer_types )
+
+  if n < 3: return 1
+
+  result = 1
+  ff = factorization( n )
+  for f in ff:
+    e = f[1]
+    if e > 1:
+      result = result * f[0] ** (e-1) * ( f[0] - 1 )
+    else:
+      result = result * ( f[0] - 1 )
+  return result
+
+
+def carmichael( n ):
+  """Return Carmichael function of n.
+
+  Carmichael(n) is the smallest integer x such that
+  m**x = 1 mod n for all m relatively prime to n.
+  """
+
+  return carmichael_of_factorized( factorization( n ) )
+
+
+def carmichael_of_factorized( f_list ):
+  """Return the Carmichael function of a number that is
+  represented as a list of (prime,exponent) pairs.
+  """
+
+  if len( f_list ) < 1: return 1
+
+  result = carmichael_of_ppower( f_list[0] )
+  for i in range( 1, len( f_list ) ):
+    result = lcm( result, carmichael_of_ppower( f_list[i] ) )
+
+  return result
+
+def carmichael_of_ppower( pp ):
+  """Carmichael function of the given power of the given prime.
+  """
+
+  p, a = pp
+  if p == 2 and a > 2: return 2**(a-2)
+  else: return (p-1) * p**(a-1)
+
+
+
+def order_mod( x, m ):
+  """Return the order of x in the multiplicative group mod m.
+  """
+
+  # Warning: this implementation is not very clever, and will
+  # take a long time if m is very large.
+
+  if m <= 1: return 0
+
+  assert gcd( x, m ) == 1
+
+  z = x
+  result = 1
+  while z != 1:
+    z = ( z * x ) % m
+    result = result + 1
+  return result
+
+
+def largest_factor_relatively_prime( a, b ):
+  """Return the largest factor of a relatively prime to b.
+  """
+
+  while 1:
+    d = gcd( a, b )
+    if d <= 1: break
+    b = d
+    while 1:
+      q, r = divmod( a, d )
+      if r > 0:
+        break
+      a = q
+  return a
+
+
+def kinda_order_mod( x, m ):
+  """Return the order of x in the multiplicative group mod m',
+  where m' is the largest factor of m relatively prime to x.
+  """
+
+  return order_mod( x, largest_factor_relatively_prime( m, x ) )
+
+
+def is_prime( n ):
+  """Return True if x is prime, False otherwise.
+
+  We use the Miller-Rabin test, as given in Menezes et al. p. 138.
+  This test is not exact: there are composite values n for which
+  it returns True.
+
+  In testing the odd numbers from 10000001 to 19999999,
+  about 66 composites got past the first test,
+  5 got past the second test, and none got past the third.
+  Since factors of 2, 3, 5, 7, and 11 were detected during
+  preliminary screening, the number of numbers tested by
+  Miller-Rabin was (19999999 - 10000001)*(2/3)*(4/5)*(6/7)
+  = 4.57 million.
+  """
+
+  # (This is used to study the risk of false positives:)
+  global miller_rabin_test_count
+
+  miller_rabin_test_count = 0
+
+  if n <= smallprimes[-1]:
+    if n in smallprimes: return True
+    else: return False
+
+  if gcd( n, 2*3*5*7*11 ) != 1: return False
+
+  # Choose a number of iterations sufficient to reduce the
+  # probability of accepting a composite below 2**-80
+  # (from Menezes et al. Table 4.4):
+
+  t = 40
+  n_bits = 1 + int( math.log( n, 2 ) )
+  for k, tt in ( ( 100, 27 ),
+                 ( 150, 18 ),
+                 ( 200, 15 ),
+                 ( 250, 12 ),
+                 ( 300,  9 ),
+                 ( 350,  8 ),
+                 ( 400,  7 ),
+                 ( 450,  6 ),
+                 ( 550,  5 ),
+                 ( 650,  4 ),
+                 ( 850,  3 ),
+                 ( 1300, 2 ),
+                 ):
+    if n_bits < k: break
+    t = tt
+
+  # Run the test t times:
+
+  s = 0
+  r = n - 1
+  while ( r % 2 ) == 0:
+    s = s + 1
+    r = r // 2
+  for i in range( t ):
+    a = smallprimes[ i ]
+    y = modular_exp( a, r, n )
+    if y != 1 and y != n-1:
+      j = 1
+      while j <= s - 1 and y != n - 1:
+        y = modular_exp( y, 2, n )
+        if y == 1:
+          miller_rabin_test_count = i + 1
+          return False
+        j = j + 1
+      if y != n-1:
+        miller_rabin_test_count = i + 1
+        return False
+  return True
+
+
+def next_prime( starting_value ):
+  "Return the smallest prime larger than the starting value."
+
+  if starting_value < 2: return 2
+  result = ( starting_value + 1 ) | 1
+  while not is_prime( result ): result = result + 2
+  return result
+
+
+smallprimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
+               43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
+               101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
+               151, 157, 163, 167, 173, 179, 181, 191, 193, 197,
+               199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
+               263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
+               317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
+               383, 389, 397, 401, 409, 419, 421, 431, 433, 439,
+               443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
+               503, 509, 521, 523, 541, 547, 557, 563, 569, 571,
+               577, 587, 593, 599, 601, 607, 613, 617, 619, 631,
+               641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
+               701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
+               769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
+               839, 853, 857, 859, 863, 877, 881, 883, 887, 907,
+               911, 919, 929, 937, 941, 947, 953, 967, 971, 977,
+               983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
+               1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093,
+               1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
+               1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229]
+
+miller_rabin_test_count = 0
+
+def __main__():
+
+  # Making sure locally defined exceptions work:
+  # p = modular_exp( 2, -2, 3 )
+  # p = square_root_mod_prime( 2, 3 )
+
+
+  print_("Testing gcd...")
+  assert gcd( 3*5*7, 3*5*11, 3*5*13 )     == 3*5
+  assert gcd( [ 3*5*7, 3*5*11, 3*5*13 ] ) == 3*5
+  assert gcd( 3 ) == 3
+
+  print_("Testing lcm...")
+  assert lcm( 3, 5*3, 7*3 )     == 3*5*7
+  assert lcm( [ 3, 5*3, 7*3 ] ) == 3*5*7
+  assert lcm( 3 ) == 3
+
+  print_("Testing next_prime...")
+  bigprimes = ( 999671,
+                999683,
+                999721,
+                999727,
+                999749,
+                999763,
+                999769,
+                999773,
+                999809,
+                999853,
+                999863,
+                999883,
+                999907,
+                999917,
+                999931,
+                999953,
+                999959,
+                999961,
+                999979,
+                999983 )
+
+  for i in range( len( bigprimes ) - 1 ):
+    assert next_prime( bigprimes[i] ) == bigprimes[ i+1 ]
+
+  error_tally = 0
+
+  # Test the square_root_mod_prime function:
+
+  for p in smallprimes:
+    print_("Testing square_root_mod_prime for modulus p = %d." % p)
+    squares = []
+
+    for root in range( 0, 1+p//2 ):
+      sq = ( root * root ) % p
+      squares.append( sq )
+      calculated = square_root_mod_prime( sq, p )
+      if ( calculated * calculated ) % p != sq:
+        error_tally = error_tally + 1
+        print_("Failed to find %d as sqrt( %d ) mod %d. Said %d." % \
+              ( root, sq, p, calculated ))
+
+    for nonsquare in range( 0, p ):
+      if nonsquare not in squares:
+        try:
+          calculated = square_root_mod_prime( nonsquare, p )
+        except SquareRootError:
+          pass
+        else:
+          error_tally = error_tally + 1
+          print_("Failed to report no root for sqrt( %d ) mod %d." % \
+                ( nonsquare, p ))
+
+  # Test the jacobi function:
+  for m in range( 3, 400, 2 ):
+    print_("Testing jacobi for modulus m = %d." % m)
+    if is_prime( m ):
+      squares = []
+      for root in range( 1, m ):
+        if jacobi( root * root, m ) != 1:
+          error_tally = error_tally + 1
+          print_("jacobi( %d * %d, %d ) != 1" % ( root, root, m ))
+        squares.append( root * root % m )
+      for i in range( 1, m ):
+        if not i in squares:
+          if jacobi( i, m ) != -1:
+            error_tally = error_tally + 1
+            print_("jacobi( %d, %d ) != -1" % ( i, m ))
+    else:       # m is not prime.
+      f = factorization( m )
+      for a in range( 1, m ):
+        c = 1
+        for i in f:
+          c = c * jacobi( a, i[0] ) ** i[1]
+        if c != jacobi( a, m ):
+          error_tally = error_tally + 1
+          print_("%d != jacobi( %d, %d )" % ( c, a, m ))
+
+
+# Test the inverse_mod function:
+  print_("Testing inverse_mod . . .")
+  import random
+  n_tests = 0
+  for i in range( 100 ):
+    m = random.randint( 20, 10000 )
+    for j in range( 100 ):
+      a = random.randint( 1, m-1 )
+      if gcd( a, m ) == 1:
+        n_tests = n_tests + 1
+        inv = inverse_mod( a, m )
+        if inv <= 0 or inv >= m or ( a * inv ) % m != 1:
+          error_tally = error_tally + 1
+          print_("%d = inverse_mod( %d, %d ) is wrong." % ( inv, a, m ))
+  assert n_tests > 1000
+  print_(n_tests, " tests of inverse_mod completed.")
+
+  class FailedTest(Exception): pass
+  print_(error_tally, "errors detected.")
+  if error_tally != 0:
+    raise FailedTest("%d errors detected" % error_tally)
+
+if __name__ == '__main__':
+  __main__()

bin/python/ecdsa/rfc6979.py

@@ -0,0 +1,103 @@
+'''
+RFC 6979:
+    Deterministic Usage of the Digital Signature Algorithm (DSA) and
+    Elliptic Curve Digital Signature Algorithm (ECDSA)
+
+    http://tools.ietf.org/html/rfc6979
+
+Many thanks to Coda Hale for his implementation in Go language:
+    https://github.com/codahale/rfc6979
+'''
+
+import hmac
+from binascii import hexlify
+from .util import number_to_string, number_to_string_crop
+from .six import b
+
+try:
+    bin(0)
+except NameError:
+    binmap = {"0": "0000", "1": "0001", "2": "0010", "3": "0011",
+              "4": "0100", "5": "0101", "6": "0110", "7": "0111",
+              "8": "1000", "9": "1001", "a": "1010", "b": "1011",
+              "c": "1100", "d": "1101", "e": "1110", "f": "1111"}
+    def bin(value): # for python2.5
+        v = "".join(binmap[x] for x in "%x"%abs(value)).lstrip("0")
+        if value < 0:
+            return "-0b" + v
+        return "0b" + v
+
+def bit_length(num):
+    # http://docs.python.org/dev/library/stdtypes.html#int.bit_length
+    s = bin(num)  # binary representation:  bin(-37) --> '-0b100101'
+    s = s.lstrip('-0b')  # remove leading zeros and minus sign
+    return len(s)  # len('100101') --> 6
+
+def bits2int(data, qlen):
+    x = int(hexlify(data), 16)
+    l = len(data) * 8
+
+    if l > qlen:
+        return x >> (l-qlen)
+    return x
+
+def bits2octets(data, order):
+    z1 = bits2int(data, bit_length(order))
+    z2 = z1 - order
+
+    if z2 < 0:
+        z2 = z1
+
+    return number_to_string_crop(z2, order)
+
+# https://tools.ietf.org/html/rfc6979#section-3.2
+def generate_k(order, secexp, hash_func, data):
+    '''
+        generator - order of the DSA generator used in the signature
+        secexp - secure exponent (private key) in numeric form
+        hash_func - reference to the same hash function used for generating hash
+        data - hash in binary form of the signing data
+    '''
+
+    qlen = bit_length(order)
+    holen = hash_func().digest_size
+    rolen = (qlen + 7) / 8
+    bx = number_to_string(secexp, order) + bits2octets(data, order)
+
+    # Step B
+    v = b('\x01') * holen
+
+    # Step C
+    k = b('\x00') * holen
+
+    # Step D
+
+    k = hmac.new(k, v+b('\x00')+bx, hash_func).digest()
+
+    # Step E
+    v = hmac.new(k, v, hash_func).digest()
+
+    # Step F
+    k = hmac.new(k, v+b('\x01')+bx, hash_func).digest()
+
+    # Step G
+    v = hmac.new(k, v, hash_func).digest()
+
+    # Step H
+    while True:
+        # Step H1
+        t = b('')
+
+        # Step H2
+        while len(t) < rolen:
+            v = hmac.new(k, v, hash_func).digest()
+            t += v
+
+        # Step H3
+        secret = bits2int(t, qlen)
+
+        if secret >= 1 and secret < order:
+            return secret
+
+        k = hmac.new(k, v+b('\x00'), hash_func).digest()
+        v = hmac.new(k, v, hash_func).digest()

bin/python/ecdsa/six.py

@@ -0,0 +1,394 @@
+"""Utilities for writing code that runs on Python 2 and 3"""
+
+# Copyright (c) 2010-2012 Benjamin Peterson
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy of
+# this software and associated documentation files (the "Software"), to deal in
+# the Software without restriction, including without limitation the rights to
+# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+# the Software, and to permit persons to whom the Software is furnished to do so,
+# subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+import operator
+import sys
+import types
+
+__author__ = "Benjamin Peterson <benjamin@python.org>"
+__version__ = "1.2.0"
+
+
+# True if we are running on Python 3.
+PY3 = sys.version_info[0] == 3
+
+if PY3:
+    string_types = str,
+    integer_types = int,
+    class_types = type,
+    text_type = str
+    binary_type = bytes
+
+    MAXSIZE = sys.maxsize
+else:
+    string_types = basestring,
+    integer_types = (int, long)
+    class_types = (type, types.ClassType)
+    text_type = unicode
+    binary_type = str
+
+    if sys.platform.startswith("java"):
+        # Jython always uses 32 bits.
+        MAXSIZE = int((1 << 31) - 1)
+    else:
+        # It's possible to have sizeof(long) != sizeof(Py_ssize_t).
+        class X(object):
+            def __len__(self):
+                return 1 << 31
+        try:
+            len(X())
+        except OverflowError:
+            # 32-bit
+            MAXSIZE = int((1 << 31) - 1)
+        else:
+            # 64-bit
+            MAXSIZE = int((1 << 63) - 1)
+            del X
+
+
+def _add_doc(func, doc):
+    """Add documentation to a function."""
+    func.__doc__ = doc
+
+
+def _import_module(name):
+    """Import module, returning the module after the last dot."""
+    __import__(name)
+    return sys.modules[name]
+
+
+class _LazyDescr(object):
+
+    def __init__(self, name):
+        self.name = name
+
+    def __get__(self, obj, tp):
+        result = self._resolve()
+        setattr(obj, self.name, result)
+        # This is a bit ugly, but it avoids running this again.
+        delattr(tp, self.name)
+        return result
+
+
+class MovedModule(_LazyDescr):
+
+    def __init__(self, name, old, new=None):
+        super(MovedModule, self).__init__(name)
+        if PY3:
+            if new is None:
+                new = name
+            self.mod = new
+        else:
+            self.mod = old
+
+    def _resolve(self):
+        return _import_module(self.mod)
+
+
+class MovedAttribute(_LazyDescr):
+
+    def __init__(self, name, old_mod, new_mod, old_attr=None, new_attr=None):
+        super(MovedAttribute, self).__init__(name)
+        if PY3:
+            if new_mod is None:
+                new_mod = name
+            self.mod = new_mod
+            if new_attr is None:
+                if old_attr is None:
+                    new_attr = name
+                else:
+                    new_attr = old_attr
+            self.attr = new_attr
+        else:
+            self.mod = old_mod
+            if old_attr is None:
+                old_attr = name
+            self.attr = old_attr
+
+    def _resolve(self):
+        module = _import_module(self.mod)
+        return getattr(module, self.attr)
+
+
+
+class _MovedItems(types.ModuleType):
+    """Lazy loading of moved objects"""
+
+
+_moved_attributes = [
+    MovedAttribute("cStringIO", "cStringIO", "io", "StringIO"),
+    MovedAttribute("filter", "itertools", "builtins", "ifilter", "filter"),
+    MovedAttribute("input", "__builtin__", "builtins", "raw_input", "input"),
+    MovedAttribute("map", "itertools", "builtins", "imap", "map"),
+    MovedAttribute("reload_module", "__builtin__", "imp", "reload"),
+    MovedAttribute("reduce", "__builtin__", "functools"),
+    MovedAttribute("StringIO", "StringIO", "io"),
+    MovedAttribute("xrange", "__builtin__", "builtins", "xrange", "range"),
+    MovedAttribute("zip", "itertools", "builtins", "izip", "zip"),
+
+    MovedModule("builtins", "__builtin__"),
+    MovedModule("configparser", "ConfigParser"),
+    MovedModule("copyreg", "copy_reg"),
+    MovedModule("http_cookiejar", "cookielib", "http.cookiejar"),
+    MovedModule("http_cookies", "Cookie", "http.cookies"),
+    MovedModule("html_entities", "htmlentitydefs", "html.entities"),
+    MovedModule("html_parser", "HTMLParser", "html.parser"),
+    MovedModule("http_client", "httplib", "http.client"),
+    MovedModule("email_mime_multipart", "email.MIMEMultipart", "email.mime.multipart"),
+    MovedModule("email_mime_text", "email.MIMEText", "email.mime.text"),
+    MovedModule("email_mime_base", "email.MIMEBase", "email.mime.base"),
+    MovedModule("BaseHTTPServer", "BaseHTTPServer", "http.server"),
+    MovedModule("CGIHTTPServer", "CGIHTTPServer", "http.server"),
+    MovedModule("SimpleHTTPServer", "SimpleHTTPServer", "http.server"),
+    MovedModule("cPickle", "cPickle", "pickle"),
+    MovedModule("queue", "Queue"),
+    MovedModule("reprlib", "repr"),
+    MovedModule("socketserver", "SocketServer"),
+    MovedModule("tkinter", "Tkinter"),
+    MovedModule("tkinter_dialog", "Dialog", "tkinter.dialog"),
+    MovedModule("tkinter_filedialog", "FileDialog", "tkinter.filedialog"),
+    MovedModule("tkinter_scrolledtext", "ScrolledText", "tkinter.scrolledtext"),
+    MovedModule("tkinter_simpledialog", "SimpleDialog", "tkinter.simpledialog"),
+    MovedModule("tkinter_tix", "Tix", "tkinter.tix"),
+    MovedModule("tkinter_constants", "Tkconstants", "tkinter.constants"),
+    MovedModule("tkinter_dnd", "Tkdnd", "tkinter.dnd"),
+    MovedModule("tkinter_colorchooser", "tkColorChooser",
+                "tkinter.colorchooser"),
+    MovedModule("tkinter_commondialog", "tkCommonDialog",
+                "tkinter.commondialog"),
+    MovedModule("tkinter_tkfiledialog", "tkFileDialog", "tkinter.filedialog"),
+    MovedModule("tkinter_font", "tkFont", "tkinter.font"),
+    MovedModule("tkinter_messagebox", "tkMessageBox", "tkinter.messagebox"),
+    MovedModule("tkinter_tksimpledialog", "tkSimpleDialog",
+                "tkinter.simpledialog"),
+    MovedModule("urllib_robotparser", "robotparser", "urllib.robotparser"),
+    MovedModule("winreg", "_winreg"),
+]
+for attr in _moved_attributes:
+    setattr(_MovedItems, attr.name, attr)
+del attr
+
+moves = sys.modules[__name__ + ".moves"] = _MovedItems("moves")
+
+
+def add_move(move):
+    """Add an item to six.moves."""
+    setattr(_MovedItems, move.name, move)
+
+
+def remove_move(name):
+    """Remove item from six.moves."""
+    try:
+        delattr(_MovedItems, name)
+    except AttributeError:
+        try:
+            del moves.__dict__[name]
+        except KeyError:
+            raise AttributeError("no such move, %r" % (name,))
+
+
+if PY3:
+    _meth_func = "__func__"
+    _meth_self = "__self__"
+
+    _func_code = "__code__"
+    _func_defaults = "__defaults__"
+
+    _iterkeys = "keys"
+    _itervalues = "values"
+    _iteritems = "items"
+else:
+    _meth_func = "im_func"
+    _meth_self = "im_self"
+
+    _func_code = "func_code"
+    _func_defaults = "func_defaults"
+
+    _iterkeys = "iterkeys"
+    _itervalues = "itervalues"
+    _iteritems = "iteritems"
+
+
+try:
+    advance_iterator = next
+except NameError:
+    def advance_iterator(it):
+        return it.next()
+next = advance_iterator
+
+
+try:
+    callable = callable
+except NameError:
+    def callable(obj):
+        return any("__call__" in klass.__dict__ for klass in type(obj).__mro__)
+
+
+if PY3:
+    def get_unbound_function(unbound):
+        return unbound
+
+    Iterator = object
+else:
+    def get_unbound_function(unbound):
+        return unbound.im_func
+
+    class Iterator(object):
+
+        def next(self):
+            return type(self).__next__(self)
+
+    callable = callable
+_add_doc(get_unbound_function,
+         """Get the function out of a possibly unbound function""")
+
+
+get_method_function = operator.attrgetter(_meth_func)
+get_method_self = operator.attrgetter(_meth_self)
+get_function_code = operator.attrgetter(_func_code)
+get_function_defaults = operator.attrgetter(_func_defaults)
+
+
+def iterkeys(d):
+    """Return an iterator over the keys of a dictionary."""
+    return iter(getattr(d, _iterkeys)())
+
+def itervalues(d):
+    """Return an iterator over the values of a dictionary."""
+    return iter(getattr(d, _itervalues)())
+
+def iteritems(d):
+    """Return an iterator over the (key, value) pairs of a dictionary."""
+    return iter(getattr(d, _iteritems)())
+
+
+if PY3:
+    def b(s):
+        return s.encode("latin-1")
+    def u(s):
+        return s
+    if sys.version_info[1] <= 1:
+        def int2byte(i):
+            return bytes((i,))
+    else:
+        # This is about 2x faster than the implementation above on 3.2+
+        int2byte = operator.methodcaller("to_bytes", 1, "big")
+    import io
+    StringIO = io.StringIO
+    BytesIO = io.BytesIO
+else:
+    def b(s):
+        return s
+    def u(s):
+        if isinstance(s, unicode):
+            return s
+        return unicode(s, "unicode_escape")
+    int2byte = chr
+    import StringIO
+    StringIO = BytesIO = StringIO.StringIO
+_add_doc(b, """Byte literal""")
+_add_doc(u, """Text literal""")
+
+
+if PY3:
+    import builtins
+    exec_ = getattr(builtins, "exec")
+
+
+    def reraise(tp, value, tb=None):
+        if value.__traceback__ is not tb:
+            raise value.with_traceback(tb)
+        raise value
+
+
+    print_ = getattr(builtins, "print")
+    del builtins
+
+else:
+    def exec_(_code_, _globs_=None, _locs_=None):
+        """Execute code in a namespace."""
+        if _globs_ is None:
+            frame = sys._getframe(1)
+            _globs_ = frame.f_globals
+            if _locs_ is None:
+                _locs_ = frame.f_locals
+            del frame
+        elif _locs_ is None:
+            _locs_ = _globs_
+        exec("""exec _code_ in _globs_, _locs_""")
+
+
+    exec_("""def reraise(tp, value, tb=None):
+    raise tp, value, tb
+""")
+
+
+    def print_(*args, **kwargs):
+        """The new-style print function."""
+        fp = kwargs.pop("file", sys.stdout)
+        if fp is None:
+            return
+        def write(data):
+            if not isinstance(data, basestring):
+                data = str(data)
+            fp.write(data)
+        want_unicode = False
+        sep = kwargs.pop("sep", None)
+        if sep is not None:
+            if isinstance(sep, unicode):
+                want_unicode = True
+            elif not isinstance(sep, str):
+                raise TypeError("sep must be None or a string")
+        end = kwargs.pop("end", None)
+        if end is not None:
+            if isinstance(end, unicode):
+                want_unicode = True
+            elif not isinstance(end, str):
+                raise TypeError("end must be None or a string")
+        if kwargs:
+            raise TypeError("invalid keyword arguments to print()")
+        if not want_unicode:
+            for arg in args:
+                if isinstance(arg, unicode):
+                    want_unicode = True
+                    break
+        if want_unicode:
+            newline = unicode("\n")
+            space = unicode(" ")
+        else:
+            newline = "\n"
+            space = " "
+        if sep is None:
+            sep = space
+        if end is None:
+            end = newline
+        for i, arg in enumerate(args):
+            if i:
+                write(sep)
+            write(arg)
+        write(end)
+
+_add_doc(reraise, """Reraise an exception.""")
+
+
+def with_metaclass(meta, base=object):
+    """Create a base class with a metaclass."""
+    return meta("NewBase", (base,), {})

bin/python/ecdsa/test_pyecdsa.py

@@ -0,0 +1,663 @@
+from __future__ import with_statement, division
+
+import unittest
+import os
+import time
+import shutil
+import subprocess
+from binascii import hexlify, unhexlify
+from hashlib import sha1, sha256, sha512
+
+from .six import b, print_, binary_type
+from .keys import SigningKey, VerifyingKey
+from .keys import BadSignatureError
+from . import util
+from .util import sigencode_der, sigencode_strings
+from .util import sigdecode_der, sigdecode_strings
+from .curves import Curve, UnknownCurveError
+from .curves import NIST192p, NIST224p, NIST256p, NIST384p, NIST521p, SECP256k1
+from .ellipticcurve import Point
+from . import der
+from . import rfc6979
+
+class SubprocessError(Exception):
+    pass
+
+def run_openssl(cmd):
+    OPENSSL = "openssl"
+    p = subprocess.Popen([OPENSSL] + cmd.split(),
+                         stdout=subprocess.PIPE,
+                         stderr=subprocess.STDOUT)
+    stdout, ignored = p.communicate()
+    if p.returncode != 0:
+        raise SubprocessError("cmd '%s %s' failed: rc=%s, stdout/err was %s" %
+                              (OPENSSL, cmd, p.returncode, stdout))
+    return stdout.decode()
+
+BENCH = False
+
+class ECDSA(unittest.TestCase):
+    def test_basic(self):
+        priv = SigningKey.generate()
+        pub = priv.get_verifying_key()
+
+        data = b("blahblah")
+        sig = priv.sign(data)
+
+        self.assertTrue(pub.verify(sig, data))
+        self.assertRaises(BadSignatureError, pub.verify, sig, data+b("bad"))
+
+        pub2 = VerifyingKey.from_string(pub.to_string())
+        self.assertTrue(pub2.verify(sig, data))
+
+    def test_deterministic(self):
+        data = b("blahblah")
+        secexp = int("9d0219792467d7d37b4d43298a7d0c05", 16)
+
+        priv = SigningKey.from_secret_exponent(secexp, SECP256k1, sha256)
+        pub = priv.get_verifying_key()
+
+        k = rfc6979.generate_k(
+            SECP256k1.generator.order(), secexp, sha256, sha256(data).digest())
+
+        sig1 = priv.sign(data, k=k)
+        self.assertTrue(pub.verify(sig1, data))
+
+        sig2 = priv.sign(data, k=k)
+        self.assertTrue(pub.verify(sig2, data))
+
+        sig3 = priv.sign_deterministic(data, sha256)
+        self.assertTrue(pub.verify(sig3, data))
+
+        self.assertEqual(sig1, sig2)
+        self.assertEqual(sig1, sig3)
+
+    def test_bad_usage(self):
+        # sk=SigningKey() is wrong
+        self.assertRaises(TypeError, SigningKey)
+        self.assertRaises(TypeError, VerifyingKey)
+
+    def test_lengths(self):
+        default = NIST192p
+        priv = SigningKey.generate()
+        pub = priv.get_verifying_key()
+        self.assertEqual(len(pub.to_string()), default.verifying_key_length)
+        sig = priv.sign(b("data"))
+        self.assertEqual(len(sig), default.signature_length)
+        if BENCH:
+            print_()
+        for curve in (NIST192p, NIST224p, NIST256p, NIST384p, NIST521p):
+            start = time.time()
+            priv = SigningKey.generate(curve=curve)
+            pub1 = priv.get_verifying_key()
+            keygen_time = time.time() - start
+            pub2 = VerifyingKey.from_string(pub1.to_string(), curve)
+            self.assertEqual(pub1.to_string(), pub2.to_string())
+            self.assertEqual(len(pub1.to_string()),
+                                 curve.verifying_key_length)
+            start = time.time()
+            sig = priv.sign(b("data"))
+            sign_time = time.time() - start
+            self.assertEqual(len(sig), curve.signature_length)
+            if BENCH:
+                start = time.time()
+                pub1.verify(sig, b("data"))
+                verify_time = time.time() - start
+                print_("%s: siglen=%d, keygen=%0.3fs, sign=%0.3f, verify=%0.3f" \
+                      % (curve.name, curve.signature_length,
+                         keygen_time, sign_time, verify_time))
+
+    def test_serialize(self):
+        seed = b("secret")
+        curve = NIST192p
+        secexp1 = util.randrange_from_seed__trytryagain(seed, curve.order)
+        secexp2 = util.randrange_from_seed__trytryagain(seed, curve.order)
+        self.assertEqual(secexp1, secexp2)
+        priv1 = SigningKey.from_secret_exponent(secexp1, curve)
+        priv2 = SigningKey.from_secret_exponent(secexp2, curve)
+        self.assertEqual(hexlify(priv1.to_string()),
+                             hexlify(priv2.to_string()))
+        self.assertEqual(priv1.to_pem(), priv2.to_pem())
+        pub1 = priv1.get_verifying_key()
+        pub2 = priv2.get_verifying_key()
+        data = b("data")
+        sig1 = priv1.sign(data)
+        sig2 = priv2.sign(data)
+        self.assertTrue(pub1.verify(sig1, data))
+        self.assertTrue(pub2.verify(sig1, data))
+        self.assertTrue(pub1.verify(sig2, data))
+        self.assertTrue(pub2.verify(sig2, data))
+        self.assertEqual(hexlify(pub1.to_string()),
+                             hexlify(pub2.to_string()))
+
+    def test_nonrandom(self):
+        s = b("all the entropy in the entire world, compressed into one line")
+        def not_much_entropy(numbytes):
+            return s[:numbytes]
+        # we control the entropy source, these two keys should be identical:
+        priv1 = SigningKey.generate(entropy=not_much_entropy)
+        priv2 = SigningKey.generate(entropy=not_much_entropy)
+        self.assertEqual(hexlify(priv1.get_verifying_key().to_string()),
+                             hexlify(priv2.get_verifying_key().to_string()))
+        # likewise, signatures should be identical. Obviously you'd never
+        # want to do this with keys you care about, because the secrecy of
+        # the private key depends upon using different random numbers for
+        # each signature
+        sig1 = priv1.sign(b("data"), entropy=not_much_entropy)
+        sig2 = priv2.sign(b("data"), entropy=not_much_entropy)
+        self.assertEqual(hexlify(sig1), hexlify(sig2))
+
+    def assertTruePrivkeysEqual(self, priv1, priv2):
+        self.assertEqual(priv1.privkey.secret_multiplier,
+                             priv2.privkey.secret_multiplier)
+        self.assertEqual(priv1.privkey.public_key.generator,
+                             priv2.privkey.public_key.generator)
+
+    def failIfPrivkeysEqual(self, priv1, priv2):
+        self.failIfEqual(priv1.privkey.secret_multiplier,
+                         priv2.privkey.secret_multiplier)
+
+    def test_privkey_creation(self):
+        s = b("all the entropy in the entire world, compressed into one line")
+        def not_much_entropy(numbytes):
+            return s[:numbytes]
+        priv1 = SigningKey.generate()
+        self.assertEqual(priv1.baselen, NIST192p.baselen)
+
+        priv1 = SigningKey.generate(curve=NIST224p)
+        self.assertEqual(priv1.baselen, NIST224p.baselen)
+
+        priv1 = SigningKey.generate(entropy=not_much_entropy)
+        self.assertEqual(priv1.baselen, NIST192p.baselen)
+        priv2 = SigningKey.generate(entropy=not_much_entropy)
+        self.assertEqual(priv2.baselen, NIST192p.baselen)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        priv1 = SigningKey.from_secret_exponent(secexp=3)
+        self.assertEqual(priv1.baselen, NIST192p.baselen)
+        priv2 = SigningKey.from_secret_exponent(secexp=3)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        priv1 = SigningKey.from_secret_exponent(secexp=4, curve=NIST224p)
+        self.assertEqual(priv1.baselen, NIST224p.baselen)
+
+    def test_privkey_strings(self):
+        priv1 = SigningKey.generate()
+        s1 = priv1.to_string()
+        self.assertEqual(type(s1), binary_type)
+        self.assertEqual(len(s1), NIST192p.baselen)
+        priv2 = SigningKey.from_string(s1)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        s1 = priv1.to_pem()
+        self.assertEqual(type(s1), binary_type)
+        self.assertTrue(s1.startswith(b("-----BEGIN EC PRIVATE KEY-----")))
+        self.assertTrue(s1.strip().endswith(b("-----END EC PRIVATE KEY-----")))
+        priv2 = SigningKey.from_pem(s1)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        s1 = priv1.to_der()
+        self.assertEqual(type(s1), binary_type)
+        priv2 = SigningKey.from_der(s1)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        priv1 = SigningKey.generate(curve=NIST256p)
+        s1 = priv1.to_pem()
+        self.assertEqual(type(s1), binary_type)
+        self.assertTrue(s1.startswith(b("-----BEGIN EC PRIVATE KEY-----")))
+        self.assertTrue(s1.strip().endswith(b("-----END EC PRIVATE KEY-----")))
+        priv2 = SigningKey.from_pem(s1)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+        s1 = priv1.to_der()
+        self.assertEqual(type(s1), binary_type)
+        priv2 = SigningKey.from_der(s1)
+        self.assertTruePrivkeysEqual(priv1, priv2)
+
+    def assertTruePubkeysEqual(self, pub1, pub2):
+        self.assertEqual(pub1.pubkey.point, pub2.pubkey.point)
+        self.assertEqual(pub1.pubkey.generator, pub2.pubkey.generator)
+        self.assertEqual(pub1.curve, pub2.curve)
+
+    def test_pubkey_strings(self):
+        priv1 = SigningKey.generate()
+        pub1 = priv1.get_verifying_key()
+        s1 = pub1.to_string()
+        self.assertEqual(type(s1), binary_type)
+        self.assertEqual(len(s1), NIST192p.verifying_key_length)
+        pub2 = VerifyingKey.from_string(s1)
+        self.assertTruePubkeysEqual(pub1, pub2)
+
+        priv1 = SigningKey.generate(curve=NIST256p)
+        pub1 = priv1.get_verifying_key()
+        s1 = pub1.to_string()
+        self.assertEqual(type(s1), binary_type)
+        self.assertEqual(len(s1), NIST256p.verifying_key_length)
+        pub2 = VerifyingKey.from_string(s1, curve=NIST256p)
+        self.assertTruePubkeysEqual(pub1, pub2)
+
+        pub1_der = pub1.to_der()
+        self.assertEqual(type(pub1_der), binary_type)
+        pub2 = VerifyingKey.from_der(pub1_der)
+        self.assertTruePubkeysEqual(pub1, pub2)
+
+        self.assertRaises(der.UnexpectedDER,
+                              VerifyingKey.from_der, pub1_der+b("junk"))
+        badpub = VerifyingKey.from_der(pub1_der)
+        class FakeGenerator:
+            def order(self): return 123456789
+        badcurve = Curve("unknown", None, None, FakeGenerator(), (1,2,3,4,5,6))
+        badpub.curve = badcurve
+        badder = badpub.to_der()
+        self.assertRaises(UnknownCurveError, VerifyingKey.from_der, badder)
+
+        pem = pub1.to_pem()
+        self.assertEqual(type(pem), binary_type)
+        self.assertTrue(pem.startswith(b("-----BEGIN PUBLIC KEY-----")), pem)
+        self.assertTrue(pem.strip().endswith(b("-----END PUBLIC KEY-----")), pem)
+        pub2 = VerifyingKey.from_pem(pem)
+        self.assertTruePubkeysEqual(pub1, pub2)
+
+    def test_signature_strings(self):
+        priv1 = SigningKey.generate()
+        pub1 = priv1.get_verifying_key()
+        data = b("data")
+
+        sig = priv1.sign(data)
+        self.assertEqual(type(sig), binary_type)
+        self.assertEqual(len(sig), NIST192p.signature_length)
+        self.assertTrue(pub1.verify(sig, data))
+
+        sig = priv1.sign(data, sigencode=sigencode_strings)
+        self.assertEqual(type(sig), tuple)
+        self.assertEqual(len(sig), 2)
+        self.assertEqual(type(sig[0]), binary_type)
+        self.assertEqual(type(sig[1]), binary_type)
+        self.assertEqual(len(sig[0]), NIST192p.baselen)
+        self.assertEqual(len(sig[1]), NIST192p.baselen)
+        self.assertTrue(pub1.verify(sig, data, sigdecode=sigdecode_strings))
+
+        sig_der = priv1.sign(data, sigencode=sigencode_der)
+        self.assertEqual(type(sig_der), binary_type)
+        self.assertTrue(pub1.verify(sig_der, data, sigdecode=sigdecode_der))
+
+    def test_hashfunc(self):
+        sk = SigningKey.generate(curve=NIST256p, hashfunc=sha256)
+        data = b("security level is 128 bits")
+        sig = sk.sign(data)
+        vk = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
+                                      curve=NIST256p, hashfunc=sha256)
+        self.assertTrue(vk.verify(sig, data))
+
+        sk2 = SigningKey.generate(curve=NIST256p)
+        sig2 = sk2.sign(data, hashfunc=sha256)
+        vk2 = VerifyingKey.from_string(sk2.get_verifying_key().to_string(),
+                                       curve=NIST256p, hashfunc=sha256)
+        self.assertTrue(vk2.verify(sig2, data))
+
+        vk3 = VerifyingKey.from_string(sk.get_verifying_key().to_string(),
+                                       curve=NIST256p)
+        self.assertTrue(vk3.verify(sig, data, hashfunc=sha256))
+
+
+class OpenSSL(unittest.TestCase):
+    # test interoperability with OpenSSL tools. Note that openssl's ECDSA
+    # sign/verify arguments changed between 0.9.8 and 1.0.0: the early
+    # versions require "-ecdsa-with-SHA1", the later versions want just
+    # "-SHA1" (or to leave out that argument entirely, which means the
+    # signature will use some default digest algorithm, probably determined
+    # by the key, probably always SHA1).
+    #
+    # openssl ecparam -name secp224r1 -genkey -out privkey.pem
+    # openssl ec -in privkey.pem -text -noout # get the priv/pub keys
+    # openssl dgst -ecdsa-with-SHA1 -sign privkey.pem -out data.sig data.txt
+    # openssl asn1parse -in data.sig -inform DER
+    #  data.sig is 64 bytes, probably 56b plus ASN1 overhead
+    # openssl dgst -ecdsa-with-SHA1 -prverify privkey.pem -signature data.sig data.txt ; echo $?
+    # openssl ec -in privkey.pem -pubout -out pubkey.pem
+    # openssl ec -in privkey.pem -pubout -outform DER -out pubkey.der
+
+    def get_openssl_messagedigest_arg(self):
+        v = run_openssl("version")
+        # e.g. "OpenSSL 1.0.0 29 Mar 2010", or "OpenSSL 1.0.0a 1 Jun 2010",
+        # or "OpenSSL 0.9.8o 01 Jun 2010"
+        vs = v.split()[1].split(".")
+        if vs >= ["1","0","0"]:
+            return "-SHA1"
+        else:
+            return "-ecdsa-with-SHA1"
+
+    # sk: 1:OpenSSL->python  2:python->OpenSSL
+    # vk: 3:OpenSSL->python  4:python->OpenSSL
+    # sig: 5:OpenSSL->python 6:python->OpenSSL
+
+    def test_from_openssl_nist192p(self):
+        return self.do_test_from_openssl(NIST192p)
+    def test_from_openssl_nist224p(self):
+        return self.do_test_from_openssl(NIST224p)
+    def test_from_openssl_nist256p(self):
+        return self.do_test_from_openssl(NIST256p)
+    def test_from_openssl_nist384p(self):
+        return self.do_test_from_openssl(NIST384p)
+    def test_from_openssl_nist521p(self):
+        return self.do_test_from_openssl(NIST521p)
+    def test_from_openssl_secp256k1(self):
+        return self.do_test_from_openssl(SECP256k1)
+
+    def do_test_from_openssl(self, curve):
+        curvename = curve.openssl_name
+        assert curvename
+        # OpenSSL: create sk, vk, sign.
+        # Python: read vk(3), checksig(5), read sk(1), sign, check
+        mdarg = self.get_openssl_messagedigest_arg()
+        if os.path.isdir("t"):
+            shutil.rmtree("t")
+        os.mkdir("t")
+        run_openssl("ecparam -name %s -genkey -out t/privkey.pem" % curvename)
+        run_openssl("ec -in t/privkey.pem -pubout -out t/pubkey.pem")
+        data = b("data")
+        with open("t/data.txt","wb") as e: e.write(data)
+        run_openssl("dgst %s -sign t/privkey.pem -out t/data.sig t/data.txt" % mdarg)
+        run_openssl("dgst %s -verify t/pubkey.pem -signature t/data.sig t/data.txt" % mdarg)
+        with open("t/pubkey.pem","rb") as e: pubkey_pem = e.read()
+        vk = VerifyingKey.from_pem(pubkey_pem) # 3
+        with open("t/data.sig","rb") as e: sig_der = e.read()
+        self.assertTrue(vk.verify(sig_der, data, # 5
+                                  hashfunc=sha1, sigdecode=sigdecode_der))
+
+        with open("t/privkey.pem") as e: fp = e.read()
+        sk = SigningKey.from_pem(fp) # 1
+        sig = sk.sign(data)
+        self.assertTrue(vk.verify(sig, data))
+
+    def test_to_openssl_nist192p(self):
+        self.do_test_to_openssl(NIST192p)
+    def test_to_openssl_nist224p(self):
+        self.do_test_to_openssl(NIST224p)
+    def test_to_openssl_nist256p(self):
+        self.do_test_to_openssl(NIST256p)
+    def test_to_openssl_nist384p(self):
+        self.do_test_to_openssl(NIST384p)
+    def test_to_openssl_nist521p(self):
+        self.do_test_to_openssl(NIST521p)
+    def test_to_openssl_secp256k1(self):
+        self.do_test_to_openssl(SECP256k1)
+
+    def do_test_to_openssl(self, curve):
+        curvename = curve.openssl_name
+        assert curvename
+        # Python: create sk, vk, sign.
+        # OpenSSL: read vk(4), checksig(6), read sk(2), sign, check
+        mdarg = self.get_openssl_messagedigest_arg()
+        if os.path.isdir("t"):
+            shutil.rmtree("t")
+        os.mkdir("t")
+        sk = SigningKey.generate(curve=curve)
+        vk = sk.get_verifying_key()
+        data = b("data")
+        with open("t/pubkey.der","wb") as e: e.write(vk.to_der()) # 4
+        with open("t/pubkey.pem","wb") as e: e.write(vk.to_pem()) # 4
+        sig_der = sk.sign(data, hashfunc=sha1, sigencode=sigencode_der)
+
+        with open("t/data.sig","wb") as e: e.write(sig_der) # 6
+        with open("t/data.txt","wb") as e: e.write(data)
+        with open("t/baddata.txt","wb") as e: e.write(data+b("corrupt"))
+
+        self.assertRaises(SubprocessError, run_openssl,
+                              "dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/baddata.txt" % mdarg)
+        run_openssl("dgst %s -verify t/pubkey.der -keyform DER -signature t/data.sig t/data.txt" % mdarg)
+
+        with open("t/privkey.pem","wb") as e: e.write(sk.to_pem()) # 2
+        run_openssl("dgst %s -sign t/privkey.pem -out t/data.sig2 t/data.txt" % mdarg)
+        run_openssl("dgst %s -verify t/pubkey.pem -signature t/data.sig2 t/data.txt" % mdarg)
+
+class DER(unittest.TestCase):
+    def test_oids(self):
+        oid_ecPublicKey = der.encode_oid(1, 2, 840, 10045, 2, 1)
+        self.assertEqual(hexlify(oid_ecPublicKey), b("06072a8648ce3d0201"))
+        self.assertEqual(hexlify(NIST224p.encoded_oid), b("06052b81040021"))
+        self.assertEqual(hexlify(NIST256p.encoded_oid),
+                             b("06082a8648ce3d030107"))
+        x = oid_ecPublicKey + b("more")
+        x1, rest = der.remove_object(x)
+        self.assertEqual(x1, (1, 2, 840, 10045, 2, 1))
+        self.assertEqual(rest, b("more"))
+
+    def test_integer(self):
+        self.assertEqual(der.encode_integer(0), b("\x02\x01\x00"))
+        self.assertEqual(der.encode_integer(1), b("\x02\x01\x01"))
+        self.assertEqual(der.encode_integer(127), b("\x02\x01\x7f"))
+        self.assertEqual(der.encode_integer(128), b("\x02\x02\x00\x80"))
+        self.assertEqual(der.encode_integer(256), b("\x02\x02\x01\x00"))
+        #self.assertEqual(der.encode_integer(-1), b("\x02\x01\xff"))
+
+        def s(n): return der.remove_integer(der.encode_integer(n) + b("junk"))
+        self.assertEqual(s(0), (0, b("junk")))
+        self.assertEqual(s(1), (1, b("junk")))
+        self.assertEqual(s(127), (127, b("junk")))
+        self.assertEqual(s(128), (128, b("junk")))
+        self.assertEqual(s(256), (256, b("junk")))
+        self.assertEqual(s(1234567890123456789012345678901234567890),
+                             (1234567890123456789012345678901234567890,b("junk")))
+
+    def test_number(self):
+        self.assertEqual(der.encode_number(0), b("\x00"))
+        self.assertEqual(der.encode_number(127), b("\x7f"))
+        self.assertEqual(der.encode_number(128), b("\x81\x00"))
+        self.assertEqual(der.encode_number(3*128+7), b("\x83\x07"))
+        #self.assertEqual(der.read_number("\x81\x9b"+"more"), (155, 2))
+        #self.assertEqual(der.encode_number(155), b("\x81\x9b"))
+        for n in (0, 1, 2, 127, 128, 3*128+7, 840, 10045): #, 155):
+            x = der.encode_number(n) + b("more")
+            n1, llen = der.read_number(x)
+            self.assertEqual(n1, n)
+            self.assertEqual(x[llen:], b("more"))
+
+    def test_length(self):
+        self.assertEqual(der.encode_length(0), b("\x00"))
+        self.assertEqual(der.encode_length(127), b("\x7f"))
+        self.assertEqual(der.encode_length(128), b("\x81\x80"))
+        self.assertEqual(der.encode_length(255), b("\x81\xff"))
+        self.assertEqual(der.encode_length(256), b("\x82\x01\x00"))
+        self.assertEqual(der.encode_length(3*256+7), b("\x82\x03\x07"))
+        self.assertEqual(der.read_length(b("\x81\x9b")+b("more")), (155, 2))
+        self.assertEqual(der.encode_length(155), b("\x81\x9b"))
+        for n in (0, 1, 2, 127, 128, 255, 256, 3*256+7, 155):
+            x = der.encode_length(n) + b("more")
+            n1, llen = der.read_length(x)
+            self.assertEqual(n1, n)
+            self.assertEqual(x[llen:], b("more"))
+
+    def test_sequence(self):
+        x = der.encode_sequence(b("ABC"), b("DEF")) + b("GHI")
+        self.assertEqual(x, b("\x30\x06ABCDEFGHI"))
+        x1, rest = der.remove_sequence(x)
+        self.assertEqual(x1, b("ABCDEF"))
+        self.assertEqual(rest, b("GHI"))
+
+    def test_constructed(self):
+        x = der.encode_constructed(0, NIST224p.encoded_oid)
+        self.assertEqual(hexlify(x), b("a007") + b("06052b81040021"))
+        x = der.encode_constructed(1, unhexlify(b("0102030a0b0c")))
+        self.assertEqual(hexlify(x), b("a106") + b("0102030a0b0c"))
+
+class Util(unittest.TestCase):
+    def test_trytryagain(self):
+        tta = util.randrange_from_seed__trytryagain
+        for i in range(1000):
+            seed = "seed-%d" % i
+            for order in (2**8-2, 2**8-1, 2**8, 2**8+1, 2**8+2,
+                          2**16-1, 2**16+1):
+                n = tta(seed, order)
+                self.assertTrue(1 <= n < order, (1, n, order))
+        # this trytryagain *does* provide long-term stability
+        self.assertEqual(("%x"%(tta("seed", NIST224p.order))).encode(),
+                             b("6fa59d73bf0446ae8743cf748fc5ac11d5585a90356417e97155c3bc"))
+
+    def test_randrange(self):
+        # util.randrange does not provide long-term stability: we might
+        # change the algorithm in the future.
+        for i in range(1000):
+            entropy = util.PRNG("seed-%d" % i)
+            for order in (2**8-2, 2**8-1, 2**8,
+                          2**16-1, 2**16+1,
+                          ):
+                # that oddball 2**16+1 takes half our runtime
+                n = util.randrange(order, entropy=entropy)
+                self.assertTrue(1 <= n < order, (1, n, order))
+
+    def OFF_test_prove_uniformity(self):
+        order = 2**8-2
+        counts = dict([(i, 0) for i in range(1, order)])
+        assert 0 not in counts
+        assert order not in counts
+        for i in range(1000000):
+            seed = "seed-%d" % i
+            n = util.randrange_from_seed__trytryagain(seed, order)
+            counts[n] += 1
+        # this technique should use the full range
+        self.assertTrue(counts[order-1])
+        for i in range(1, order):
+            print_("%3d: %s" % (i, "*"*(counts[i]//100)))
+
+class RFC6979(unittest.TestCase):
+    # https://tools.ietf.org/html/rfc6979#appendix-A.1
+    def _do(self, generator, secexp, hsh, hash_func, expected):
+        actual = rfc6979.generate_k(generator.order(), secexp, hash_func, hsh)
+        self.assertEqual(expected, actual)
+
+    def test_SECP256k1(self):
+        '''RFC doesn't contain test vectors for SECP256k1 used in bitcoin.
+        This vector has been computed by Golang reference implementation instead.'''
+        self._do(
+            generator = SECP256k1.generator,
+            secexp = int("9d0219792467d7d37b4d43298a7d0c05", 16),
+            hsh = sha256(b("sample")).digest(),
+            hash_func = sha256,
+            expected = int("8fa1f95d514760e498f28957b824ee6ec39ed64826ff4fecc2b5739ec45b91cd", 16))
+
+    def test_SECP256k1_2(self):
+        self._do(
+            generator=SECP256k1.generator,
+            secexp=int("cca9fbcc1b41e5a95d369eaa6ddcff73b61a4efaa279cfc6567e8daa39cbaf50", 16),
+            hsh=sha256(b("sample")).digest(),
+            hash_func=sha256,
+            expected=int("2df40ca70e639d89528a6b670d9d48d9165fdc0febc0974056bdce192b8e16a3", 16))
+
+    def test_SECP256k1_3(self):
+        self._do(
+            generator=SECP256k1.generator,
+            secexp=0x1,
+            hsh=sha256(b("Satoshi Nakamoto")).digest(),
+            hash_func=sha256,
+            expected=0x8F8A276C19F4149656B280621E358CCE24F5F52542772691EE69063B74F15D15)
+
+    def test_SECP256k1_4(self):
+        self._do(
+            generator=SECP256k1.generator,
+            secexp=0x1,
+            hsh=sha256(b("All those moments will be lost in time, like tears in rain. Time to die...")).digest(),
+            hash_func=sha256,
+            expected=0x38AA22D72376B4DBC472E06C3BA403EE0A394DA63FC58D88686C611ABA98D6B3)
+
+    def test_SECP256k1_5(self):
+        self._do(
+            generator=SECP256k1.generator,
+            secexp=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140,
+            hsh=sha256(b("Satoshi Nakamoto")).digest(),
+            hash_func=sha256,
+            expected=0x33A19B60E25FB6F4435AF53A3D42D493644827367E6453928554F43E49AA6F90)
+
+    def test_SECP256k1_6(self):
+        self._do(
+            generator=SECP256k1.generator,
+            secexp=0xf8b8af8ce3c7cca5e300d33939540c10d45ce001b8f252bfbc57ba0342904181,
+            hsh=sha256(b("Alan Turing")).digest(),
+            hash_func=sha256,
+            expected=0x525A82B70E67874398067543FD84C83D30C175FDC45FDEEE082FE13B1D7CFDF1)
+
+    def test_1(self):
+        # Basic example of the RFC, it also tests 'try-try-again' from Step H of rfc6979
+        self._do(
+            generator = Point(None, 0, 0, int("4000000000000000000020108A2E0CC0D99F8A5EF", 16)),
+            secexp = int("09A4D6792295A7F730FC3F2B49CBC0F62E862272F", 16),
+            hsh = unhexlify(b("AF2BDBE1AA9B6EC1E2ADE1D694F41FC71A831D0268E9891562113D8A62ADD1BF")),
+            hash_func = sha256,
+            expected = int("23AF4074C90A02B3FE61D286D5C87F425E6BDD81B", 16))
+
+    def test_2(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha1(b("sample")).digest(),
+            hash_func = sha1,
+            expected = int("37D7CA00D2C7B0E5E412AC03BD44BA837FDD5B28CD3B0021", 16))
+
+    def test_3(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha256(b("sample")).digest(),
+            hash_func = sha256,
+            expected = int("32B1B6D7D42A05CB449065727A84804FB1A3E34D8F261496", 16))
+
+    def test_4(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha512(b("sample")).digest(),
+            hash_func = sha512,
+            expected = int("A2AC7AB055E4F20692D49209544C203A7D1F2C0BFBC75DB1", 16))
+
+    def test_5(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha1(b("test")).digest(),
+            hash_func = sha1,
+            expected = int("D9CF9C3D3297D3260773A1DA7418DB5537AB8DD93DE7FA25", 16))
+
+    def test_6(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha256(b("test")).digest(),
+            hash_func = sha256,
+            expected = int("5C4CE89CF56D9E7C77C8585339B006B97B5F0680B4306C6C", 16))
+
+    def test_7(self):
+        self._do(
+            generator=NIST192p.generator,
+            secexp = int("6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4", 16),
+            hsh = sha512(b("test")).digest(),
+            hash_func = sha512,
+            expected = int("0758753A5254759C7CFBAD2E2D9B0792EEE44136C9480527", 16))
+
+    def test_8(self):
+        self._do(
+            generator=NIST521p.generator,
+            secexp = int("0FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75CAA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83538", 16),
+            hsh = sha1(b("sample")).digest(),
+            hash_func = sha1,
+            expected = int("089C071B419E1C2820962321787258469511958E80582E95D8378E0C2CCDB3CB42BEDE42F50E3FA3C71F5A76724281D31D9C89F0F91FC1BE4918DB1C03A5838D0F9", 16))
+
+    def test_9(self):
+        self._do(
+            generator=NIST521p.generator,
+            secexp = int("0FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75CAA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83538", 16),
+            hsh = sha256(b("sample")).digest(),
+            hash_func = sha256,
+            expected = int("0EDF38AFCAAECAB4383358B34D67C9F2216C8382AAEA44A3DAD5FDC9C32575761793FEF24EB0FC276DFC4F6E3EC476752F043CF01415387470BCBD8678ED2C7E1A0", 16))
+
+    def test_10(self):
+        self._do(
+            generator=NIST521p.generator,
+            secexp = int("0FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75CAA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83538", 16),
+            hsh = sha512(b("test")).digest(),
+            hash_func = sha512,
+            expected = int("16200813020EC986863BEDFC1B121F605C1215645018AEA1A7B215A564DE9EB1B38A67AA1128B80CE391C4FB71187654AAA3431027BFC7F395766CA988C964DC56D", 16))
+
+def __main__():
+    unittest.main()
+if __name__ == "__main__":
+    __main__()

bin/python/ecdsa/util.py

@@ -0,0 +1,247 @@
+from __future__ import division
+
+import os
+import math
+import binascii
+from hashlib import sha256
+from . import der
+from .curves import orderlen
+from .six import PY3, int2byte, b, next
+
+# 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)
+
+def randrange(order, entropy=None):
+    """Return a random integer k such that 1 <= k < order, uniformly
+    distributed across that range. For simplicity, this only behaves well if
+    'order' is fairly close (but below) a power of 256. The try-try-again
+    algorithm we use takes longer and longer time (on average) to complete as
+    'order' falls, rising to a maximum of avg=512 loops for the worst-case
+    (256**k)+1 . All of the standard curves behave well. There is a cutoff at
+    10k loops (which raises RuntimeError) to prevent an infinite loop when
+    something is really broken like the entropy function not working.
+
+    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.
+    """
+    # we could handle arbitrary orders (even 256**k+1) better if we created
+    # candidates bit-wise instead of byte-wise, which would reduce the
+    # worst-case behavior to avg=2 loops, but that would be more complex. The
+    # change would be to round the order up to a power of 256, subtract one
+    # (to get 0xffff..), use that to get a byte-long mask for the top byte,
+    # generate the len-1 entropy bytes, generate one extra byte and mask off
+    # the top bits, then combine it with the rest. Requires jumping back and
+    # forth between strings and integers a lot.
+
+    if entropy is None:
+        entropy = os.urandom
+    assert order > 1
+    bytes = orderlen(order)
+    dont_try_forever = 10000 # gives about 2**-60 failures for worst case
+    while dont_try_forever > 0:
+        dont_try_forever -= 1
+        candidate = string_to_number(entropy(bytes)) + 1
+        if 1 <= candidate < order:
+            return candidate
+        continue
+    raise RuntimeError("randrange() tried hard but gave up, either something"
+                       " is very wrong or you got realllly unlucky. Order was"
+                       " %x" % order)
+
+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 PY3:
+            return bytes(a)
+        else:
+            return "".join(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)
+
+# these methods are useful for the sigencode= argument to SK.sign() and the
+# sigdecode= argument to VK.verify(), and control how the signature is packed
+# or unpacked.
+
+def sigencode_strings(r, s, order):
+    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):
+    # 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):
+    return der.encode_sequence(der.encode_integer(r), der.encode_integer(s))
+
+# canonical versions of sigencode methods
+# these enforce low S values, by negating the value (modulo the order) if above order/2
+# see CECKey::Sign() https://github.com/bitcoin/bitcoin/blob/master/src/key.cpp#L214
+def sigencode_strings_canonize(r, s, order):
+    if s > order / 2:
+        s = order - s
+    return sigencode_strings(r, s, order)
+
+def sigencode_string_canonize(r, s, order):
+    if s > order / 2:
+        s = order - s
+    return sigencode_string(r, s, order)
+
+def sigencode_der_canonize(r, s, order):
+    if s > order / 2:
+        s = order - s
+    return sigencode_der(r, s, order)
+
+
+def sigdecode_string(signature, order):
+    l = orderlen(order)
+    assert len(signature) == 2*l, (len(signature), 2*l)
+    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):
+    (r_str, s_str) = rs_strings
+    l = orderlen(order)
+    assert len(r_str) == l, (len(r_str), l)
+    assert len(s_str) == l, (len(s_str), l)
+    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):
+    #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
+