#!/usr/bin/env python

"""
<Program Name>
  keys.py

<Author>
  Vladimir Diaz <vladimir.v.diaz@gmail.com>

<Started>
  October 4, 2013.

<Copyright>
  See LICENSE for licensing information.

<Purpose>
  The goal of this module is to centralize cryptographic key routines and their
  supported operations (e.g., creating and verifying signatures).  This module
  is designed to support multiple public-key algorithms, such as RSA, Ed25519,
  and ECDSA, and multiple cryptography libraries.  Which cryptography library
  to use is determined by the default, or user modified, values set in
  'settings.py'

  https://en.wikipedia.org/wiki/RSA_(algorithm)
  http://ed25519.cr.yp.to/
  https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm

  The (RSA, ECDSA and Ed25519)-related functions provided include
  generate_rsa_key(), generate_ed25519_key(), generate_ecdsa_key(),
  create_signature(), and verify_signature().  The cryptography libraries
  called by 'securesystemslib.keys.py' generate the actual keys and the
  functions listed above can be viewed as the easy-to-use public interface.

  Additional functions contained here include format_keyval_to_metadata() and
  format_metadata_to_key().  These last two functions produce or use keys
  compatible with the key structures listed in Metadata files.  The key
  generation functions return a dictionary containing all the information needed
  of keys, such as public & private keys, and a keyID.  create_signature()
  and verify_signature() are supplemental functions needed for generating
  signatures and verifying them.

  Key IDs are used as identifiers for keys (e.g., RSA key).  They are the
  hexadecimal representation of the hash of the key object (specifically, the
  key object containing only the public key).  Review the '_get_keyid()'
  function of this module to see precisely how keyids are generated.  One may
  get the keyid of a key object by simply accessing the dictionary's 'keyid'
  key (i.e., rsakey['keyid']).
 """

# Required for hexadecimal conversions.  Signatures and public/private keys are
# hexlified.
import binascii

import logging

from securesystemslib import ecdsa_keys
from securesystemslib import ed25519_keys
from securesystemslib import exceptions
from securesystemslib import formats
from securesystemslib import rsa_keys
from securesystemslib import settings
from securesystemslib import util
from securesystemslib.hash import digest


# The hash algorithm to use in the generation of keyids.
_KEY_ID_HASH_ALGORITHM = 'sha256'

# Recommended RSA key sizes:
# http://www.emc.com/emc-plus/rsa-labs/historical/twirl-and-rsa-key-size.htm#table1
# According to the document above, revised May 6, 2003, RSA keys of
# size 3072 provide security through 2031 and beyond.
_DEFAULT_RSA_KEY_BITS = 3072


RSA_SIGNATURE_SCHEMES = [
  'rsassa-pss-md5',
  'rsassa-pss-sha1',
  'rsassa-pss-sha224',
  'rsassa-pss-sha256',
  'rsassa-pss-sha384',
  'rsassa-pss-sha512',
  'rsa-pkcs1v15-md5',
  'rsa-pkcs1v15-sha1',
  'rsa-pkcs1v15-sha224',
  'rsa-pkcs1v15-sha256',
  'rsa-pkcs1v15-sha384',
  'rsa-pkcs1v15-sha512',
]

logger = logging.getLogger(__name__)


def generate_rsa_key(bits=_DEFAULT_RSA_KEY_BITS, scheme='rsassa-pss-sha256'):
  """
  <Purpose>
    Generate public and private RSA keys, with modulus length 'bits'.  In
    addition, a keyid identifier for the RSA key is generated.  The object
    returned conforms to 'securesystemslib.formats.RSAKEY_SCHEMA' and has the
    form:

    {'keytype': 'rsa',
     'scheme': 'rsassa-pss-sha256',
     'keyid': keyid,
     'keyval': {'public': '-----BEGIN RSA PUBLIC KEY----- ...',
                'private': '-----BEGIN RSA PRIVATE KEY----- ...'}}

    The public and private keys are strings in PEM format.

    Although the PyCA cryptography library and/or its crypto backend might set
    a minimum key size, generate() enforces a minimum key size of 2048 bits.
    If 'bits' is unspecified, a 3072-bit RSA key is generated, which is the key
    size recommended by securesystemslib.  These key size restrictions are only
    enforced for keys generated within securesystemslib.  RSA keys with sizes
    lower than what we recommended may still be imported (e.g., with
    import_rsakey_from_pem().

    >>> rsa_key = generate_rsa_key(bits=2048)
    >>> securesystemslib.formats.RSAKEY_SCHEMA.matches(rsa_key)
    True

    >>> public = rsa_key['keyval']['public']
    >>> private = rsa_key['keyval']['private']
    >>> securesystemslib.formats.PEMRSA_SCHEMA.matches(public)
    True
    >>> securesystemslib.formats.PEMRSA_SCHEMA.matches(private)
    True

  <Arguments>
    bits:
      The key size, or key length, of the RSA key.  'bits' must be 2048, or
      greater, and a multiple of 256.

    scheme:
      The signature scheme used by the key.  It must be one from the list
      `securesystemslib.keys.RSA_SIGNATURE_SCHEMES`.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'bits' is improperly or invalid
    (i.e., not an integer and not at least 2048).

    ValueError, if an exception occurs after calling the RSA key generation
    routine.  The 'ValueError' exception is raised by the key generation
    function of the cryptography library called.

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the RSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.RSAKEY_SCHEMA'.
  """

  # Does 'bits' have the correct format?  This check will ensure 'bits'
  # conforms to 'securesystemslib.formats.RSAKEYBITS_SCHEMA'.  'bits' must be
  # an integer object, with a minimum value of 2048.  Raise
  # 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.RSAKEYBITS_SCHEMA.check_match(bits)
  formats.RSA_SCHEME_SCHEMA.check_match(scheme)

  # Begin building the RSA key dictionary.
  rsakey_dict = {}
  keytype = 'rsa'
  public = None
  private = None

  # Generate the public and private RSA keys.  The pyca/cryptography module is
  # used to generate the actual key.  Raise 'ValueError' if 'bits' is less than
  # 1024, although a 2048-bit minimum is enforced by
  # securesystemslib.formats.RSAKEYBITS_SCHEMA.check_match().
  public, private = rsa_keys.generate_rsa_public_and_private(bits)

  # When loading in PEM keys, extract_pem() is called, which strips any
  # leading or trailing new line characters. Do the same here before generating
  # the keyid.
  public =  extract_pem(public, private_pem=False)
  private = extract_pem(private, private_pem=True)

  # Generate the keyid of the RSA key.  Note: The private key material is not
  # included in the generation of the 'keyid' identifier.  Convert any '\r\n'
  # (e.g., Windows) newline characters to '\n' so that a consistent keyid is
  # generated.
  key_value = {'public': public.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  # Build the 'rsakey_dict' dictionary.  Update 'key_value' with the RSA
  # private key prior to adding 'key_value' to 'rsakey_dict'.
  key_value['private'] = private

  rsakey_dict['keytype'] = keytype
  rsakey_dict['scheme'] = scheme
  rsakey_dict['keyid'] = keyid
  rsakey_dict['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS
  rsakey_dict['keyval'] = key_value

  return rsakey_dict





def generate_ecdsa_key(scheme='ecdsa-sha2-nistp256'):
  """
  <Purpose>
    Generate public and private ECDSA keys, with NIST P-256 + SHA256 (for
    hashing) being the default scheme.  In addition, a keyid identifier for the
    ECDSA key is generated.  The object returned conforms to
    'securesystemslib.formats.ECDSAKEY_SCHEMA' and has the form:

    {'keytype': 'ecdsa',
     'scheme', 'ecdsa-sha2-nistp256',
     'keyid': keyid,
     'keyval': {'public': '',
                'private': ''}}

    The public and private keys are strings in TODO format.

    >>> ecdsa_key = generate_ecdsa_key(scheme='ecdsa-sha2-nistp256')
    >>> securesystemslib.formats.ECDSAKEY_SCHEMA.matches(ecdsa_key)
    True

  <Arguments>
    scheme:
      The ECDSA signature scheme.  By default, ECDSA NIST P-256 is used, with
      SHA256 for hashing.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'scheme' is improperly
    formatted or invalid (i.e., not one of the supported ECDSA signature
    schemes).

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the ECDSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.ECDSAKEY_SCHEMA'.
  """

  # Does 'scheme' have the correct format?
  # This check will ensure 'scheme' is properly formatted and is a supported
  # ECDSA signature scheme.  Raise 'securesystemslib.exceptions.FormatError' if
  # the check fails.
  formats.ECDSA_SCHEME_SCHEMA.check_match(scheme)

  # Begin building the ECDSA key dictionary.
  ecdsa_key = {}
  keytype = 'ecdsa'
  public = None
  private = None

  # Generate the public and private ECDSA keys with one of the supported
  # libraries.
  public, private = ecdsa_keys.generate_public_and_private(scheme)

  # Generate the keyid of the Ed25519 key.  'key_value' corresponds to the
  # 'keyval' entry of the 'Ed25519KEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # Convert any '\r\n' (e.g., Windows) newline characters to '\n' so that a
  # consistent keyid is generated.
  key_value = {'public': public.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  # Build the 'ed25519_key' dictionary.  Update 'key_value' with the Ed25519
  # private key prior to adding 'key_value' to 'ed25519_key'.

  key_value['private'] = private

  ecdsa_key['keytype'] = keytype
  ecdsa_key['scheme'] = scheme
  ecdsa_key['keyid'] = keyid
  ecdsa_key['keyval'] = key_value

  # Add "keyid_hash_algorithms" so that equal ECDSA keys with different keyids
  # can be associated using supported keyid_hash_algorithms.
  ecdsa_key['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return ecdsa_key





def generate_ed25519_key(scheme='ed25519'):
  """
  <Purpose>
    Generate public and private ED25519 keys, both of length 32-bytes, although
    they are hexlified to 64 bytes.  In addition, a keyid identifier generated
    for the returned ED25519 object.  The object returned conforms to
    'securesystemslib.formats.ED25519KEY_SCHEMA' and has the form:

    {'keytype': 'ed25519',
     'scheme': 'ed25519',
     'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
     'keyval': {'public': '9ccf3f02b17f82febf5dd3bab878b767d8408...',
                'private': 'ab310eae0e229a0eceee3947b6e0205dfab3...'}}

    >>> ed25519_key = generate_ed25519_key()
    >>> securesystemslib.formats.ED25519KEY_SCHEMA.matches(ed25519_key)
    True
    >>> len(ed25519_key['keyval']['public'])
    64
    >>> len(ed25519_key['keyval']['private'])
    64

  <Arguments>
    scheme:
      The signature scheme used by the generated Ed25519 key.

  <Exceptions>
    None.

  <Side Effects>
    The ED25519 keys are generated by calling either the optimized pure Python
    implementation of ed25519, or the ed25519 routines provided by 'pynacl'.

  <Returns>
    A dictionary containing the ED25519 keys and other identifying information.
    Conforms to 'securesystemslib.formats.ED25519KEY_SCHEMA'.
  """

  # Are the arguments properly formatted?  If not, raise an
  # 'securesystemslib.exceptions.FormatError' exceptions.
  formats.ED25519_SIG_SCHEMA.check_match(scheme)

  # Begin building the Ed25519 key dictionary.
  ed25519_key = {}
  keytype = 'ed25519'
  public = None
  private = None

  # Generate the public and private Ed25519 key with the 'pynacl' library.
  # Unlike in the verification of Ed25519 signatures, do not fall back to the
  # optimized, pure python implementation provided by PyCA.  Ed25519 should
  # always be generated with a backend like libsodium to prevent side-channel
  # attacks.
  public, private = ed25519_keys.generate_public_and_private()

  # Generate the keyid of the Ed25519 key.  'key_value' corresponds to the
  # 'keyval' entry of the 'Ed25519KEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  key_value = {'public': binascii.hexlify(public).decode(),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  # Build the 'ed25519_key' dictionary.  Update 'key_value' with the Ed25519
  # private key prior to adding 'key_value' to 'ed25519_key'.
  key_value['private'] = binascii.hexlify(private).decode()

  ed25519_key['keytype'] = keytype
  ed25519_key['scheme'] = scheme
  ed25519_key['keyid'] = keyid
  ed25519_key['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS
  ed25519_key['keyval'] = key_value

  return ed25519_key





def format_keyval_to_metadata(keytype, scheme, key_value, private=False):
  """
  <Purpose>
    Return a dictionary conformant to 'securesystemslib.formats.KEY_SCHEMA'.
    If 'private' is True, include the private key.  The dictionary
    returned has the form:

    {'keytype': keytype,
     'scheme' : scheme,
     'keyval': {'public': '...',
                'private': '...'}}

    or if 'private' is False:

    {'keytype': keytype,
     'scheme': scheme,
     'keyval': {'public': '...',
                'private': ''}}

    >>> ed25519_key = generate_ed25519_key()
    >>> key_val = ed25519_key['keyval']
    >>> keytype = ed25519_key['keytype']
    >>> scheme = ed25519_key['scheme']
    >>> ed25519_metadata = \
    format_keyval_to_metadata(keytype, scheme, key_val, private=True)
    >>> securesystemslib.formats.KEY_SCHEMA.matches(ed25519_metadata)
    True

  <Arguments>
    key_type:
      The 'rsa' or 'ed25519' strings.

    scheme:
      The signature scheme used by the key.

    key_value:
      A dictionary containing a private and public keys.
      'key_value' is of the form:

      {'public': '...',
       'private': '...'}},

      conformant to 'securesystemslib.formats.KEYVAL_SCHEMA'.

    private:
      Indicates if the private key should be included in the dictionary
      returned.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'key_value' does not conform to
    'securesystemslib.formats.KEYVAL_SCHEMA', or if the private key is not
    present in 'key_value' if requested by the caller via 'private'.

  <Side Effects>
    None.

  <Returns>
    A 'securesystemslib.formats.KEY_SCHEMA' dictionary.
  """

  # Does 'keytype' have the correct format?
  # This check will ensure 'keytype' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.KEYTYPE_SCHEMA.check_match(keytype)

  # Does 'scheme' have the correct format?
  formats.SCHEME_SCHEMA.check_match(scheme)

  # Does 'key_value' have the correct format?
  formats.KEYVAL_SCHEMA.check_match(key_value)

  if private is True:
    # If the caller requests (via the 'private' argument) to include a private
    # key in the returned dictionary, ensure the private key is actually
    # present in 'key_val' (a private key is optional for 'KEYVAL_SCHEMA'
    # dicts).
    if 'private' not in key_value:
      raise exceptions.FormatError('The required private key'
        ' is missing from: ' + repr(key_value))

    else:
      return {'keytype': keytype, 'scheme': scheme, 'keyval': key_value}

  else:
    public_key_value = {'public': key_value['public']}

    return {'keytype': keytype,
            'scheme': scheme,
            'keyid_hash_algorithms': settings.HASH_ALGORITHMS,
            'keyval': public_key_value}





def format_metadata_to_key(key_metadata, default_keyid=None,
    keyid_hash_algorithms=None):
  """
  <Purpose>
    Construct a key dictionary (e.g., securesystemslib.formats.RSAKEY_SCHEMA)
    according to the keytype of 'key_metadata'.  The dict returned by this
    function has the exact format as the dict returned by one of the key
    generations functions, like generate_ed25519_key().  The dict returned
    has the form:

    {'keytype': keytype,
     'scheme': scheme,
     'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
     'keyval': {'public': '...',
                'private': '...'}}

    For example, RSA key dictionaries in RSAKEY_SCHEMA format should be used by
    modules storing a collection of keys, such as with keydb.py.  RSA keys as
    stored in metadata files use a different format, so this function should be
    called if an RSA key is extracted from one of these metadata files and need
    converting.  The key generation functions create an entirely new key and
    return it in the format appropriate for 'keydb.py'.

    >>> ed25519_key = generate_ed25519_key()
    >>> key_val = ed25519_key['keyval']
    >>> keytype = ed25519_key['keytype']
    >>> scheme = ed25519_key['scheme']
    >>> ed25519_metadata = \
    format_keyval_to_metadata(keytype, scheme, key_val, private=True)
    >>> ed25519_key_2, junk = format_metadata_to_key(ed25519_metadata)
    >>> securesystemslib.formats.ED25519KEY_SCHEMA.matches(ed25519_key_2)
    True
    >>> ed25519_key == ed25519_key_2
    True

  <Arguments>
    key_metadata:
      The key dictionary as stored in Metadata files, conforming to
      'securesystemslib.formats.KEY_SCHEMA'.  It has the form:

      {'keytype': '...',
       'scheme': scheme,
       'keyval': {'public': '...',
                  'private': '...'}}
    default_keyid:
      A default keyid associated with the key metadata. If this is not
      provided, the keyid will be calculated by _get_keyid using the default
      hash algorithm. If provided, the default keyid can be any string.

    keyid_hash_algorithms:
      An optional list of hash algorithms to use when generating keyids.
      Defaults to securesystemslib.settings.HASH_ALGORITHMS.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'key_metadata' does not conform
    to 'securesystemslib.formats.KEY_SCHEMA'.

  <Side Effects>
    None.

  <Returns>
    In the case of an RSA key, a dictionary conformant to
    'securesystemslib.formats.RSAKEY_SCHEMA'.
  """

  # Does 'key_metadata' have the correct format?
  # This check will ensure 'key_metadata' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.KEY_SCHEMA.check_match(key_metadata)

  # Construct the dictionary to be returned.
  key_dict = {}
  keytype = key_metadata['keytype']
  scheme = key_metadata['scheme']
  key_value = key_metadata['keyval']

  # Convert 'key_value' to 'securesystemslib.formats.KEY_SCHEMA' and generate
  # its hash The hash is in hexdigest form.
  if default_keyid is None:
    default_keyid = _get_keyid(keytype, scheme, key_value)
  keyids = set()
  keyids.add(default_keyid)

  if keyid_hash_algorithms is None:
    keyid_hash_algorithms = settings.HASH_ALGORITHMS

  for hash_algorithm in keyid_hash_algorithms:
    keyid = _get_keyid(keytype, scheme, key_value, hash_algorithm)
    keyids.add(keyid)

  # All the required key values gathered.  Build 'key_dict'.
  # 'keyid_hash_algorithms'
  key_dict['keytype'] = keytype
  key_dict['scheme'] = scheme
  key_dict['keyid'] = default_keyid
  key_dict['keyid_hash_algorithms'] = keyid_hash_algorithms
  key_dict['keyval'] = key_value

  return key_dict, keyids



def _get_keyid(keytype, scheme, key_value, hash_algorithm = 'sha256'):
  """Return the keyid of 'key_value'."""

  # 'keyid' will be generated from an object conformant to KEY_SCHEMA,
  # which is the format Metadata files (e.g., root.json) store keys.
  # 'format_keyval_to_metadata()' returns the object needed by _get_keyid().
  key_meta = format_keyval_to_metadata(keytype, scheme, key_value, private=False)

  # Convert the key to JSON Canonical format, suitable for adding
  # to digest objects.
  key_update_data = formats.encode_canonical(key_meta)

  # Create a digest object and call update(), using the JSON
  # canonical format of 'rskey_meta' as the update data.
  digest_object = digest(hash_algorithm)
  digest_object.update(key_update_data.encode('utf-8'))

  # 'keyid' becomes the hexadecimal representation of the hash.
  keyid = digest_object.hexdigest()

  return keyid





def create_signature(key_dict, data):
  """
  <Purpose>
    Return a signature dictionary of the form:
    {'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
     'sig': '...'}.

    The signing process will use the private key in
    key_dict['keyval']['private'] and 'data' to generate the signature.

    The following signature schemes are supported:

    'RSASSA-PSS'
    RFC3447 - RSASSA-PSS
    http://www.ietf.org/rfc/rfc3447.

    'ed25519'
    ed25519 - high-speed high security signatures
    http://ed25519.cr.yp.to/

    Which signature to generate is determined by the key type of 'key_dict'
    and the available cryptography library specified in 'settings'.

    >>> ed25519_key = generate_ed25519_key()
    >>> data = 'The quick brown fox jumps over the lazy dog'
    >>> signature = create_signature(ed25519_key, data)
    >>> securesystemslib.formats.SIGNATURE_SCHEMA.matches(signature)
    True
    >>> len(signature['sig'])
    128
    >>> rsa_key = generate_rsa_key(2048)
    >>> signature = create_signature(rsa_key, data)
    >>> securesystemslib.formats.SIGNATURE_SCHEMA.matches(signature)
    True
    >>> ecdsa_key = generate_ecdsa_key()
    >>> signature = create_signature(ecdsa_key, data)
    >>> securesystemslib.formats.SIGNATURE_SCHEMA.matches(signature)
    True

  <Arguments>
    key_dict:
      A dictionary containing the keys.  An example RSA key dict has the
      form:

      {'keytype': 'rsa',
       'scheme': 'rsassa-pss-sha256',
       'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
       'keyval': {'public': '-----BEGIN RSA PUBLIC KEY----- ...',
                  'private': '-----BEGIN RSA PRIVATE KEY----- ...'}}

      The public and private keys are strings in PEM format.

    data:
      Data to be signed. This should be a bytes object; data should be
      encoded/serialized before it is passed here.  The same value can be be
      passed into securesystemslib.verify_signature() (along with the public
      key) to later verify the signature.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'key_dict' is improperly
    formatted.

    securesystemslib.exceptions.UnsupportedAlgorithmError, if 'key_dict'
    specifies an unsupported key type or signing scheme.

    securesystemslib.exceptions.CryptoError, if the signature cannot be
    generated.

    TypeError, if 'key_dict' contains an invalid keytype.

  <Side Effects>
    The cryptography library specified in 'settings' is called to perform the
    actual signing routine.

  <Returns>
    A signature dictionary conformant to
    'securesystemslib_format.SIGNATURE_SCHEMA'.
  """

  # Does 'key_dict' have the correct format?
  # This check will ensure 'key_dict' has the appropriate number of objects
  # and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  # The key type of 'key_dict' must be either 'rsa' or 'ed25519'.
  formats.ANYKEY_SCHEMA.check_match(key_dict)

  # Signing the 'data' object requires a private key. Signing schemes that are
  # currently supported are: 'ed25519', 'ecdsa-sha2-nistp256',
  # 'ecdsa-sha2-nistp384' and rsa schemes defined in
  # `securesystemslib.keys.RSA_SIGNATURE_SCHEMES`.
  # RSASSA-PSS and RSA-PKCS1v15 keys and signatures can be generated and
  # verified by rsa_keys.py, and Ed25519 keys by PyNaCl and PyCA's
  # optimized, pure python implementation of Ed25519.
  signature = {}
  keytype = key_dict['keytype']
  scheme = key_dict['scheme']
  public = key_dict['keyval']['public']
  private = key_dict['keyval']['private']
  keyid = key_dict['keyid']
  sig = None

  if keytype == 'rsa':
    if scheme in RSA_SIGNATURE_SCHEMES:
      private = private.replace('\r\n', '\n')
      sig, scheme = rsa_keys.create_rsa_signature(private, data, scheme)

    else:
      raise exceptions.UnsupportedAlgorithmError('Unsupported'
        ' RSA signature scheme specified: ' + repr(scheme))

  elif keytype == 'ed25519':
    public = binascii.unhexlify(public.encode('utf-8'))
    private = binascii.unhexlify(private.encode('utf-8'))
    sig, scheme = ed25519_keys.create_signature(public, private, data, scheme)

  # Continue to support keytypes of ecdsa-sha2-nistp256 and ecdsa-sha2-nistp384
  # for backwards compatibility with older securesystemslib releases
  elif keytype in ['ecdsa', 'ecdsa-sha2-nistp256', 'ecdsa-sha2-nistp384']:
    sig, scheme = ecdsa_keys.create_signature(public, private, data, scheme)

  # 'securesystemslib.formats.ANYKEY_SCHEMA' should have detected invalid key
  # types.  This is a defensive check against an invalid key type.
  else: # pragma: no cover
    raise TypeError('Invalid key type.')

  # Build the signature dictionary to be returned.
  # The hexadecimal representation of 'sig' is stored in the signature.
  signature['keyid'] = keyid
  signature['sig'] = binascii.hexlify(sig).decode()

  return signature





def verify_signature(key_dict, signature, data):
  """
  <Purpose>
    Determine whether the private key belonging to 'key_dict' produced
    'signature'.  verify_signature() will use the public key found in
    'key_dict', the 'sig' objects contained in 'signature', and 'data' to
    complete the verification.

    >>> ed25519_key = generate_ed25519_key()
    >>> data = 'The quick brown fox jumps over the lazy dog'
    >>> signature = create_signature(ed25519_key, data)
    >>> verify_signature(ed25519_key, signature, data)
    True
    >>> verify_signature(ed25519_key, signature, 'bad_data')
    False
    >>> rsa_key = generate_rsa_key()
    >>> signature = create_signature(rsa_key, data)
    >>> verify_signature(rsa_key, signature, data)
    True
    >>> verify_signature(rsa_key, signature, 'bad_data')
    False
    >>> ecdsa_key = generate_ecdsa_key()
    >>> signature = create_signature(ecdsa_key, data)
    >>> verify_signature(ecdsa_key, signature, data)
    True
    >>> verify_signature(ecdsa_key, signature, 'bad_data')
    False

  <Arguments>
    key_dict:
      A dictionary containing the keys and other identifying information.
      If 'key_dict' is an RSA key, it has the form:

      {'keytype': 'rsa',
       'scheme': 'rsassa-pss-sha256',
       'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
       'keyval': {'public': '-----BEGIN RSA PUBLIC KEY----- ...',
                  'private': '-----BEGIN RSA PRIVATE KEY----- ...'}}

      The public and private keys are strings in PEM format.

    signature:
      The signature dictionary produced by one of the key generation functions.
      'signature' has the form:

      {'keyid': 'f30a0870d026980100c0573bd557394f8c1bbd6...',
       'sig': sig}.

      Conformant to 'securesystemslib.formats.SIGNATURE_SCHEMA'.

    data:
      Data that the signature is expected to be over.  This should be a bytes
      object; data should be encoded/serialized before it is passed here.)
      This is the same value that can be passed into
      securesystemslib.create_signature() in order to create the signature.

  <Exceptions>
    securesystemslib.exceptions.FormatError, raised if either 'key_dict' or
    'signature' are improperly formatted.

    securesystemslib.exceptions.UnsupportedAlgorithmError, if 'key_dict' or
    'signature' specifies an unsupported algorithm.

    securesystemslib.exceptions.CryptoError, if the KEYID in the given
    'key_dict' does not match the KEYID in 'signature'.

  <Side Effects>
    The cryptography library specified in 'settings' called to do the actual
    verification.

  <Returns>
    Boolean.  True if the signature is valid, False otherwise.
  """

  # Does 'key_dict' have the correct format?
  # This check will ensure 'key_dict' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.ANYKEY_SCHEMA.check_match(key_dict)

  # Does 'signature' have the correct format?
  formats.SIGNATURE_SCHEMA.check_match(signature)

  # Verify that the KEYID in 'key_dict' matches the KEYID listed in the
  # 'signature'.
  if key_dict['keyid'] != signature['keyid']:
    raise exceptions.CryptoError('The KEYID ('
        ' ' + repr(key_dict['keyid']) + ' ) in the given key does not match'
        ' the KEYID ( ' + repr(signature['keyid']) + ' ) in the signature.')

  else:
    logger.debug('The KEYIDs of key_dict and the signature match.')

  # Using the public key belonging to 'key_dict'
  # (i.e., rsakey_dict['keyval']['public']), verify whether 'signature'
  # was produced by key_dict's corresponding private key
  # key_dict['keyval']['private'].
  sig = signature['sig']
  sig = binascii.unhexlify(sig.encode('utf-8'))
  public = key_dict['keyval']['public']
  keytype = key_dict['keytype']
  scheme = key_dict['scheme']
  valid_signature = False


  if keytype == 'rsa':
    if scheme in RSA_SIGNATURE_SCHEMES:
      valid_signature = rsa_keys.verify_rsa_signature(sig,
        scheme, public, data)

    else:
      raise exceptions.UnsupportedAlgorithmError('Unsupported'
          ' signature scheme is specified: ' + repr(scheme))

  elif keytype == 'ed25519':
    if scheme == 'ed25519':
      try:
        public = binascii.unhexlify(public.encode('utf-8'))
      except binascii.Error as e:
        raise exceptions.FormatError(
          f'Failed to parse key {public} as hex'
        ) from e
      valid_signature = ed25519_keys.verify_signature(public,
          scheme, sig, data)

    else:
      raise exceptions.UnsupportedAlgorithmError('Unsupported'
          ' signature scheme is specified: ' + repr(scheme))

  elif keytype in ['ecdsa', 'ecdsa-sha2-nistp256', 'ecdsa-sha2-nistp384']:
    if scheme in ['ecdsa-sha2-nistp256', 'ecdsa-sha2-nistp384']:
      valid_signature = ecdsa_keys.verify_signature(public, scheme, sig, data)

    else:
      raise exceptions.UnsupportedAlgorithmError('Unsupported'
          ' signature scheme is specified: ' + repr(scheme))

  # 'securesystemslib.formats.ANYKEY_SCHEMA' should have detected invalid key
  # types.  This is a defensive check against an invalid key type.
  else: # pragma: no cover
    raise TypeError('Unsupported key type.')

  return valid_signature





def import_rsakey_from_private_pem(pem, scheme='rsassa-pss-sha256', password=None):
  """
  <Purpose>
    Import the private RSA key stored in 'pem', and generate its public key
    (which will also be included in the returned rsakey object).  In addition,
    a keyid identifier for the RSA key is generated.  The object returned
    conforms to 'securesystemslib.formats.RSAKEY_SCHEMA' and has the form:

    {'keytype': 'rsa',
     'scheme': 'rsassa-pss-sha256',
     'keyid': keyid,
     'keyval': {'public': '-----BEGIN RSA PUBLIC KEY----- ...',
                'private': '-----BEGIN RSA PRIVATE KEY----- ...'}}

    The private key is a string in PEM format.

    >>> rsa_key = generate_rsa_key()
    >>> scheme = rsa_key['scheme']
    >>> private = rsa_key['keyval']['private']
    >>> passphrase = 'secret'
    >>> encrypted_pem = create_rsa_encrypted_pem(private, passphrase)
    >>> rsa_key2 = import_rsakey_from_private_pem(encrypted_pem, scheme, passphrase)
    >>> securesystemslib.formats.RSAKEY_SCHEMA.matches(rsa_key)
    True
    >>> securesystemslib.formats.RSAKEY_SCHEMA.matches(rsa_key2)
    True

  <Arguments>
    pem:
      A string in PEM format.  The private key is extracted and returned in
      an rsakey object.

    scheme:
      The signature scheme used by the imported key.

    password: (optional)
      The password, or passphrase, to decrypt the private part of the RSA key
      if it is encrypted.  'password' is not used directly as the encryption
      key, a stronger encryption key is derived from it.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if the arguments are improperly
    formatted.

    securesystemslib.exceptions.UnsupportedAlgorithmError, if 'pem' specifies
    an unsupported key type.

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the RSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.RSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure 'pem' conforms to
  # 'securesystemslib.formats.PEMRSA_SCHEMA'.
  formats.PEMRSA_SCHEMA.check_match(pem)

  # Is 'scheme' properly formatted?
  formats.RSA_SCHEME_SCHEMA.check_match(scheme)

  if password is not None:
    formats.PASSWORD_SCHEMA.check_match(password)

  else:
    logger.debug('The password/passphrase is unset.  The PEM is expected'
      ' to be unencrypted.')

  # Begin building the RSA key dictionary.
  rsakey_dict = {}
  keytype = 'rsa'
  public = None
  private = None

  # Generate the public and private RSA keys.  The pyca/cryptography library
  # performs the actual crypto operations.
  public, private = \
    rsa_keys.create_rsa_public_and_private_from_pem(pem, password)

  public =  extract_pem(public, private_pem=False)
  private = extract_pem(private, private_pem=True)

  # Generate the keyid of the RSA key.  'key_value' corresponds to the
  # 'keyval' entry of the 'RSAKEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # Convert any '\r\n' (e.g., Windows) newline characters to '\n' so that a
  # consistent keyid is generated.
  key_value = {'public': public.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  # Build the 'rsakey_dict' dictionary.  Update 'key_value' with the RSA
  # private key prior to adding 'key_value' to 'rsakey_dict'.
  key_value['private'] = private

  rsakey_dict['keytype'] = keytype
  rsakey_dict['scheme'] = scheme
  rsakey_dict['keyid'] = keyid
  rsakey_dict['keyval'] = key_value

  return rsakey_dict





def import_rsakey_from_public_pem(pem, scheme='rsassa-pss-sha256'):
  """
  <Purpose>
    Generate an RSA key object from 'pem'.  In addition, a keyid identifier for
    the RSA key is generated.  The object returned conforms to
    'securesystemslib.formats.RSAKEY_SCHEMA' and has the form:

    {'keytype': 'rsa',
     'keyid': keyid,
     'keyval': {'public': '-----BEGIN PUBLIC KEY----- ...',
                'private': ''}}

    The public portion of the RSA key is a string in PEM format.

    >>> rsa_key = generate_rsa_key()
    >>> public = rsa_key['keyval']['public']
    >>> rsa_key['keyval']['private'] = ''
    >>> rsa_key2 = import_rsakey_from_public_pem(public)
    >>> securesystemslib.formats.RSAKEY_SCHEMA.matches(rsa_key)
    True
    >>> securesystemslib.formats.RSAKEY_SCHEMA.matches(rsa_key2)
    True

  <Arguments>
    pem:
      A string in PEM format (it should contain a public RSA key).

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    Only the public portion of the PEM is extracted.  Leading or trailing
    whitespace is not included in the PEM string stored in the rsakey object
    returned.

  <Returns>
    A dictionary containing the RSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.RSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure arguments has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMRSA_SCHEMA.check_match(pem)

  # Does 'scheme' have the correct format?
  formats.RSA_SCHEME_SCHEMA.check_match(scheme)

  # Ensure the PEM string has a public header and footer.  Although a simple
  # validation of 'pem' is performed here, a fully valid PEM string is needed
  # later to successfully verify signatures.  Performing stricter validation of
  # PEMs are left to the external libraries that use 'pem'.

  if is_pem_public(pem):
    public_pem = extract_pem(pem, private_pem=False)

  else:
    raise exceptions.FormatError('Invalid public pem: ' + repr(pem))

  # Begin building the RSA key dictionary.
  rsakey_dict = {}
  keytype = 'rsa'

  # Generate the keyid of the RSA key.  'key_value' corresponds to the
  # 'keyval' entry of the 'RSAKEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # Convert any '\r\n' (e.g., Windows) newline characters to '\n' so that a
  # consistent keyid is generated.
  key_value = {'public': public_pem.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  rsakey_dict['keytype'] = keytype
  rsakey_dict['scheme'] = scheme
  rsakey_dict['keyid'] = keyid
  rsakey_dict['keyval'] = key_value

  # Add "keyid_hash_algorithms" so that equal RSA keys with different keyids
  # can be associated using supported keyid_hash_algorithms.
  rsakey_dict['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return rsakey_dict





def import_rsakey_from_pem(pem, scheme='rsassa-pss-sha256'):
  """
  <Purpose>
    Import either a public or private PEM.  In contrast to the other explicit
    import functions (import_rsakey_from_public_pem and
    import_rsakey_from_private_pem), this function is useful for when it is not
    known whether 'pem' is private or public.

  <Arguments>
    pem:
      A string in PEM format.

    scheme:
      The signature scheme used by the imported key.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the RSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.RSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure arguments has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMRSA_SCHEMA.check_match(pem)

  # Is 'scheme' properly formatted?
  formats.RSA_SCHEME_SCHEMA.check_match(scheme)

  public_pem = ''

  # Ensure the PEM string has a public or private header and footer.  Although
  # a simple validation of 'pem' is performed here, a fully valid PEM string is
  # needed later to successfully verify signatures.  Performing stricter
  # validation of PEMs are left to the external libraries that use 'pem'.
  if is_pem_public(pem):
    public_pem = extract_pem(pem, private_pem=False)

  elif is_pem_private(pem):
    # Return an rsakey object (RSAKEY_SCHEMA) with the private key included.
    return import_rsakey_from_private_pem(pem, scheme, password=None)

  else:
    raise exceptions.FormatError('PEM contains neither a'
      ' public nor private key: ' + repr(pem))

  # Begin building the RSA key dictionary.
  rsakey_dict = {}
  keytype = 'rsa'

  # Generate the keyid of the RSA key.  'key_value' corresponds to the 'keyval'
  # entry of the 'RSAKEY_SCHEMA' dictionary.  The private key information is
  # not included in the generation of the 'keyid' identifier.  If a PEM is
  # found to contain a private key, the generated rsakey object should be
  # returned above.  The following key object is for the case of a PEM with
  # only a public key.  Convert any '\r\n' (e.g., Windows) newline characters
  # to '\n' so that a consistent keyid is generated.
  key_value = {'public': public_pem.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  rsakey_dict['keytype'] = keytype
  rsakey_dict['scheme'] = scheme
  rsakey_dict['keyid'] = keyid
  rsakey_dict['keyval'] = key_value

  # Add "keyid_hash_algorithms" so that equal RSA keys with
  # different keyids can be associated using supported keyid_hash_algorithms.
  rsakey_dict['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return rsakey_dict




def extract_pem(pem, private_pem=False):
  """
  <Purpose>
    Extract only the portion of the pem that includes the header and footer,
    with any leading and trailing characters removed.  The string returned has
    the following form:

    '-----BEGIN PUBLIC KEY----- ... -----END PUBLIC KEY-----'

    or

    '-----BEGIN RSA PRIVATE KEY----- ... -----END RSA PRIVATE KEY-----'

    Note: This function assumes "pem" is a valid pem in the following format:
    pem header + key material + key footer.  Crypto libraries (e.g., pyca's
    cryptography) that parse the pem returned by this function are expected to
    fully validate the pem.

  <Arguments>
    pem:
      A string in PEM format.

    private_pem:
      Boolean that indicates whether 'pem' is a private PEM.  Private PEMs
      are not shown in exception messages.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    Only the public and private portion of the PEM is extracted.  Leading or
    trailing whitespace is not included in the returned PEM string.

  <Returns>
    A PEM string (excluding leading and trailing newline characters).
    That is: pem header + key material + pem footer.

  """

  if private_pem:
    pem_header = '-----BEGIN RSA PRIVATE KEY-----'
    pem_footer = '-----END RSA PRIVATE KEY-----'

  else:
    pem_header = '-----BEGIN PUBLIC KEY-----'
    pem_footer = '-----END PUBLIC KEY-----'

  header_start = 0
  footer_start = 0

  # Raise error message if the expected header or footer is not found in 'pem'.
  try:
    header_start = pem.index(pem_header)

  except ValueError:
    # Be careful not to print private key material in exception message.
    if not private_pem:
      raise exceptions.FormatError('Required PEM'
        ' header ' + repr(pem_header) + '\n not found in PEM'
        ' string: ' + repr(pem))

    else:
      raise exceptions.FormatError('Required PEM'
        ' header ' + repr(pem_header) + '\n not found in private PEM string.')

  try:
    # Search for 'pem_footer' after the PEM header.
    footer_start = pem.index(pem_footer, header_start + len(pem_header))

  except ValueError:
    # Be careful not to print private key material in exception message.
    if not private_pem:
      raise exceptions.FormatError('Required PEM'
        ' footer ' + repr(pem_footer) + '\n not found in PEM'
        ' string ' + repr(pem))

    else:
      raise exceptions.FormatError('Required PEM'
        ' footer ' + repr(pem_footer) + '\n not found in private PEM string.')

  # Extract only the public portion of 'pem'.  Leading or trailing whitespace
  # is excluded.
  pem = pem[header_start:footer_start + len(pem_footer)]

  return pem





def encrypt_key(key_object, password):
  """
  <Purpose>
    Return a string containing 'key_object' in encrypted form. Encrypted
    strings may be safely saved to a file.  The corresponding decrypt_key()
    function can be applied to the encrypted string to restore the original key
    object.  'key_object' is a key (e.g., RSAKEY_SCHEMA, ED25519KEY_SCHEMA).
    This function relies on the rsa_keys.py module to perform the
    actual encryption.

    Encrypted keys use AES-256-CTR-Mode, and passwords are strengthened with
    PBKDF2-HMAC-SHA256 (100K iterations by default, but may be overriden in
    'securesystemslib.settings.PBKDF2_ITERATIONS' by the user).

    http://en.wikipedia.org/wiki/Advanced_Encryption_Standard
    http://en.wikipedia.org/wiki/CTR_mode#Counter_.28CTR.29
    https://en.wikipedia.org/wiki/PBKDF2

    >>> ed25519_key = generate_ed25519_key()
    >>> password = 'secret'
    >>> encrypted_key = encrypt_key(ed25519_key, password).encode('utf-8')
    >>> securesystemslib.formats.ENCRYPTEDKEY_SCHEMA.matches(encrypted_key)
    True

  <Arguments>
    key_object:
      A key (containing also the private key portion) of the form
      'securesystemslib.formats.ANYKEY_SCHEMA'

    password:
      The password, or passphrase, to encrypt the private part of the RSA
      key.  'password' is not used directly as the encryption key, a stronger
      encryption key is derived from it.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if the arguments are improperly
    formatted.

    securesystemslib.exceptions.CryptoError, if 'key_object' cannot be
    encrypted.

  <Side Effects>
    None.

  <Returns>
    An encrypted string of the form:
    'securesystemslib.formats.ENCRYPTEDKEY_SCHEMA'.
  """

  # Does 'key_object' have the correct format?
  # This check will ensure 'key_object' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.ANYKEY_SCHEMA.check_match(key_object)

  # Does 'password' have the correct format?
  formats.PASSWORD_SCHEMA.check_match(password)

  # Encrypted string of 'key_object'.  The encrypted string may be safely saved
  # to a file and stored offline.
  encrypted_key = None

  # Generate an encrypted string of 'key_object' using AES-256-CTR-Mode, where
  # 'password' is strengthened with PBKDF2-HMAC-SHA256.
  encrypted_key = rsa_keys.encrypt_key(key_object, password)

  return encrypted_key





def decrypt_key(encrypted_key, passphrase):
  """
  <Purpose>
    Return a string containing 'encrypted_key' in non-encrypted form.  The
    decrypt_key() function can be applied to the encrypted string to restore
    the original key object, a key (e.g., RSAKEY_SCHEMA, ED25519KEY_SCHEMA).
    This function calls rsa_keys.py to perform the actual decryption.

    Encrypted keys use AES-256-CTR-Mode and passwords are strengthened with
    PBKDF2-HMAC-SHA256 (100K iterations be default, but may be overriden in
    'settings.py' by the user).

    http://en.wikipedia.org/wiki/Advanced_Encryption_Standard
    http://en.wikipedia.org/wiki/CTR_mode#Counter_.28CTR.29
    https://en.wikipedia.org/wiki/PBKDF2

    >>> ed25519_key = generate_ed25519_key()
    >>> password = 'secret'
    >>> encrypted_key = encrypt_key(ed25519_key, password)
    >>> decrypted_key = decrypt_key(encrypted_key.encode('utf-8'), password)
    >>> securesystemslib.formats.ANYKEY_SCHEMA.matches(decrypted_key)
    True
    >>> decrypted_key == ed25519_key
    True

  <Arguments>
    encrypted_key:
      An encrypted key (additional data is also included, such as salt, number
      of password iterations used for the derived encryption key, etc) of the
      form 'securesystemslib.formats.ENCRYPTEDKEY_SCHEMA'.  'encrypted_key'
      should have been generated with encrypt_key().

    password:
      The password, or passphrase, to decrypt 'encrypted_key'.  'password' is
      not used directly as the encryption key, a stronger encryption key is
      derived from it.  The supported general-purpose module takes care of
      re-deriving the encryption key.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if the arguments are improperly
    formatted.

    securesystemslib.exceptions.CryptoError, if 'encrypted_key' cannot be
    decrypted.

  <Side Effects>
    None.

  <Returns>
    A key object of the form: 'securesystemslib.formats.ANYKEY_SCHEMA' (e.g.,
    RSAKEY_SCHEMA, ED25519KEY_SCHEMA).
  """

  # Does 'encrypted_key' have the correct format?
  # This check ensures 'encrypted_key' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.ENCRYPTEDKEY_SCHEMA.check_match(encrypted_key)

  # Does 'passphrase' have the correct format?
  formats.PASSWORD_SCHEMA.check_match(passphrase)

  # Store and return the decrypted key object.
  key_object = None

  # Decrypt 'encrypted_key' so that the original key object is restored.
  # encrypt_key() generates an encrypted string of the key object using
  # AES-256-CTR-Mode, where 'password' is strengthened with PBKDF2-HMAC-SHA256.
  key_object = rsa_keys.decrypt_key(encrypted_key, passphrase)

  # The corresponding encrypt_key() encrypts and stores key objects in
  # non-metadata format (i.e., original format of key object argument to
  # encrypt_key()) prior to returning.

  return key_object





def create_rsa_encrypted_pem(private_key, passphrase):
  """
  <Purpose>
    Return a string in PEM format (TraditionalOpenSSL), where the private part
    of the RSA key is encrypted using the best available encryption for a given
    key's backend. This is a curated (by cryptography.io) encryption choice and
    the algorithm may change over time.

    c.f. cryptography.io/en/latest/hazmat/primitives/asymmetric/serialization/
        #cryptography.hazmat.primitives.serialization.BestAvailableEncryption

  >>> rsa_key = generate_rsa_key()
  >>> private = rsa_key['keyval']['private']
  >>> passphrase = 'secret'
  >>> encrypted_pem = create_rsa_encrypted_pem(private, passphrase)
  >>> securesystemslib.formats.PEMRSA_SCHEMA.matches(encrypted_pem)
  True

  <Arguments>
    private_key:
      The private key string in PEM format.

    passphrase:
      The passphrase, or password, to encrypt the private part of the RSA key.
      'passphrase' is not used directly as the encryption key, a stronger
      encryption key is derived from it.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if the arguments are improperly
    formatted.

    securesystemslib.exceptions.CryptoError, if an RSA key in encrypted PEM
    format cannot be created.

    TypeError, 'private_key' is unset.

  <Side Effects>
    None.

  <Returns>
    A string in PEM format, where the private RSA key is encrypted.
    Conforms to 'securesystemslib.formats.PEMRSA_SCHEMA'.
  """

  # Does 'private_key' have the correct format?
  # This check will ensure 'private_key' has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMRSA_SCHEMA.check_match(private_key)

  # Does 'passphrase' have the correct format?
  formats.PASSWORD_SCHEMA.check_match(passphrase)

  encrypted_pem = None

  # Generate the public and private RSA keys. A 2048-bit minimum is enforced by
  # create_rsa_encrypted_pem() via a
  # securesystemslib.formats.RSAKEYBITS_SCHEMA.check_match().
  encrypted_pem = rsa_keys.create_rsa_encrypted_pem(private_key, passphrase)

  return encrypted_pem




def is_pem_public(pem):
  """
  <Purpose>
    Checks if a passed PEM formatted string is a PUBLIC key, by looking for the
    following pattern:

    '-----BEGIN PUBLIC KEY----- ... -----END PUBLIC KEY-----'

    >>> rsa_key = generate_rsa_key()
    >>> public = rsa_key['keyval']['public']
    >>> private = rsa_key['keyval']['private']
    >>> is_pem_public(public)
    True
    >>> is_pem_public(private)
    False

  <Arguments>
    pem:
      A string in PEM format.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    None

  <Returns>
    True if 'pem' is public and false otherwise.
  """

  # Do the arguments have the correct format?
  # This check will ensure arguments have the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMRSA_SCHEMA.check_match(pem)

  pem_header = '-----BEGIN PUBLIC KEY-----'
  pem_footer = '-----END PUBLIC KEY-----'

  try:
    header_start = pem.index(pem_header)
    pem.index(pem_footer, header_start + len(pem_header))

  except ValueError:
    return False

  return True




def is_pem_private(pem, keytype='rsa'):
  """
  <Purpose>
    Checks if a passed PEM formatted string is a PRIVATE key, by looking for
    the following patterns:

    '-----BEGIN RSA PRIVATE KEY----- ... -----END RSA PRIVATE KEY-----'
    '-----BEGIN EC PRIVATE KEY----- ... -----END EC PRIVATE KEY-----'

    >>> rsa_key = generate_rsa_key()
    >>> private = rsa_key['keyval']['private']
    >>> public = rsa_key['keyval']['public']
    >>> is_pem_private(private)
    True
    >>> is_pem_private(public)
    False

  <Arguments>
    pem:
      A string in PEM format.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if any of the arguments are
    improperly formatted.

  <Side Effects>
    None

  <Returns>
    True if 'pem' is private and false otherwise.
  """

  # Do the arguments have the correct format?
  # This check will ensure arguments have the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMRSA_SCHEMA.check_match(pem)
  formats.NAME_SCHEMA.check_match(keytype)

  if keytype == 'rsa':
    pem_header = '-----BEGIN RSA PRIVATE KEY-----'
    pem_footer = '-----END RSA PRIVATE KEY-----'

  elif keytype == 'ec':
    pem_header = '-----BEGIN EC PRIVATE KEY-----'
    pem_footer = '-----END EC PRIVATE KEY-----'

  else:
    raise exceptions.FormatError('Unsupported key'
      ' type: ' + repr(keytype) + '.  Supported keytypes: ["rsa", "ec"]')

  try:
    header_start = pem.index(pem_header)
    pem.index(pem_footer, header_start + len(pem_header))

  except ValueError:
    return False

  return True





def import_ed25519key_from_private_json(json_str, password=None):
  if password is not None:
    # This check will not fail, because a mal-formatted passed password fails
    # above and an entered password will always be a string (see get_password)
    # However, we include it in case PASSWORD_SCHEMA or get_password changes.
    formats.PASSWORD_SCHEMA.check_match(password)

    # Decrypt the loaded key file, calling the 'cryptography' library to
    # generate the derived encryption key from 'password'.  Raise
    # 'securesystemslib.exceptions.CryptoError' if the decryption fails.
    key_object = decrypt_key(json_str.decode('utf-8'), password)

  else:
    logger.debug('No password was given. Attempting to import an'
        ' unencrypted file.')
    try:
      key_object = util.load_json_string(json_str.decode('utf-8'))
    # If the JSON could not be decoded, it is very likely, but not necessarily,
    # due to a non-empty password.
    except exceptions.Error:
      raise exceptions.CryptoError('Malformed Ed25519 key JSON, '
                                   'possibly due to encryption, '
                                   'but no password provided?')

  # Raise an exception if an unexpected key type is imported.
  if key_object['keytype'] != 'ed25519':
    message = 'Invalid key type loaded: ' + repr(key_object['keytype'])
    raise exceptions.FormatError(message)

  # Add "keyid_hash_algorithms" so that equal ed25519 keys with
  # different keyids can be associated using supported keyid_hash_algorithms.
  key_object['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return key_object





def import_ecdsakey_from_private_pem(pem, scheme='ecdsa-sha2-nistp256', password=None):
  """
  <Purpose>
    Import the private ECDSA key stored in 'pem', and generate its public key
    (which will also be included in the returned ECDSA key object).  In addition,
    a keyid identifier for the ECDSA key is generated.  The object returned
    conforms to:

    {'keytype': 'ecdsa',
     'scheme': 'ecdsa-sha2-nistp256',
     'keyid': keyid,
     'keyval': {'public': '-----BEGIN PUBLIC KEY----- ... -----END PUBLIC KEY-----',
                'private': '-----BEGIN EC PRIVATE KEY----- ... -----END EC PRIVATE KEY-----'}}

    The private key is a string in PEM format.

    >>> ecdsa_key = generate_ecdsa_key()
    >>> private_pem = ecdsa_key['keyval']['private']
    >>> ecdsa_key = import_ecdsakey_from_private_pem(private_pem)
    >>> securesystemslib.formats.ECDSAKEY_SCHEMA.matches(ecdsa_key)
    True

  <Arguments>
    pem:
      A string in PEM format.  The private key is extracted and returned in
      an ecdsakey object.

    scheme:
      The signature scheme used by the imported key.

    password: (optional)
      The password, or passphrase, to decrypt the private part of the ECDSA
      key if it is encrypted.  'password' is not used directly as the encryption
      key, a stronger encryption key is derived from it.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if the arguments are improperly
    formatted.

    securesystemslib.exceptions.UnsupportedAlgorithmError, if 'pem' specifies
    an unsupported key type.

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the ECDSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.ECDSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure 'pem' conforms to
  # 'securesystemslib.formats.ECDSARSA_SCHEMA'.
  formats.PEMECDSA_SCHEMA.check_match(pem)

  # Is 'scheme' properly formatted?
  formats.ECDSA_SCHEME_SCHEMA.check_match(scheme)

  if password is not None:
    formats.PASSWORD_SCHEMA.check_match(password)

  else:
    logger.debug('The password/passphrase is unset.  The PEM is expected'
      ' to be unencrypted.')

  # Begin building the ECDSA key dictionary.
  ecdsakey_dict = {}
  keytype = 'ecdsa'
  public = None
  private = None

  public, private = \
      ecdsa_keys.create_ecdsa_public_and_private_from_pem(pem, password)

  # Generate the keyid of the ECDSA key.  'key_value' corresponds to the
  # 'keyval' entry of the 'ECDSAKEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # Convert any '\r\n' (e.g., Windows) newline characters to '\n' so that a
  # consistent keyid is generated.
  key_value = {'public': public.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  # Build the 'ecdsakey_dict' dictionary.  Update 'key_value' with the ECDSA
  # private key prior to adding 'key_value' to 'ecdsakey_dict'.
  key_value['private'] = private

  ecdsakey_dict['keytype'] = keytype
  ecdsakey_dict['scheme'] = scheme
  ecdsakey_dict['keyid'] = keyid
  ecdsakey_dict['keyval'] = key_value

  # Add "keyid_hash_algorithms" so equal ECDSA keys with
  # different keyids can be associated using supported keyid_hash_algorithms
  ecdsakey_dict['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return ecdsakey_dict





def import_ecdsakey_from_public_pem(pem, scheme='ecdsa-sha2-nistp256'):
  """
  <Purpose>
    Generate an ECDSA key object from 'pem'.  In addition, a keyid identifier
    for the ECDSA key is generated.  The object returned conforms to
    'securesystemslib.formats.ECDSAKEY_SCHEMA' and has the form:

    {'keytype': 'ecdsa',
     'scheme': 'ecdsa-sha2-nistp256',
     'keyid': keyid,
     'keyval': {'public': '-----BEGIN PUBLIC KEY----- ...',
                'private': ''}}

    The public portion of the ECDSA key is a string in PEM format.

    >>> ecdsa_key = generate_ecdsa_key()
    >>> public = ecdsa_key['keyval']['public']
    >>> ecdsa_key['keyval']['private'] = ''
    >>> scheme = ecdsa_key['scheme']
    >>> ecdsa_key2 = import_ecdsakey_from_public_pem(public, scheme)
    >>> securesystemslib.formats.ECDSAKEY_SCHEMA.matches(ecdsa_key)
    True
    >>> securesystemslib.formats.ECDSAKEY_SCHEMA.matches(ecdsa_key2)
    True

  <Arguments>
    pem:
      A string in PEM format (it should contain a public ECDSA key).

    scheme:
      The signature scheme used by the imported key.

  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    Only the public portion of the PEM is extracted.  Leading or trailing
    whitespace is not included in the PEM string stored in the rsakey object
    returned.

  <Returns>
    A dictionary containing the ECDSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.ECDSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure arguments has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMECDSA_SCHEMA.check_match(pem)

  # Is 'scheme' properly formatted?
  formats.ECDSA_SCHEME_SCHEMA.check_match(scheme)

  # Ensure the PEM string has a public header and footer.  Although a simple
  # validation of 'pem' is performed here, a fully valid PEM string is needed
  # later to successfully verify signatures.  Performing stricter validation of
  # PEMs are left to the external libraries that use 'pem'.

  if is_pem_public(pem):
    public_pem = extract_pem(pem, private_pem=False)

  else:
    raise exceptions.FormatError('Invalid public'
        ' pem: ' + repr(pem))

  # Begin building the ECDSA key dictionary.
  ecdsakey_dict = {}
  keytype = 'ecdsa'

  # Generate the keyid of the ECDSA key.  'key_value' corresponds to the
  # 'keyval' entry of the 'ECDSAKEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # Convert any '\r\n' (e.g., Windows) newline characters to '\n' so that a
  # consistent keyid is generated.
  key_value = {'public': public_pem.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  ecdsakey_dict['keytype'] = keytype
  ecdsakey_dict['scheme'] = scheme
  ecdsakey_dict['keyid'] = keyid
  ecdsakey_dict['keyval'] = key_value

  # Add "keyid_hash_algorithms" so that equal ECDSA keys with different keyids
  # can be associated using supported keyid_hash_algorithms.
  ecdsakey_dict['keyid_hash_algorithms'] = settings.HASH_ALGORITHMS

  return ecdsakey_dict





def import_ecdsakey_from_pem(pem, scheme='ecdsa-sha2-nistp256'):
  """
  <Purpose>
    Import either a public or private ECDSA PEM.  In contrast to the other
    explicit import functions (import_ecdsakey_from_public_pem and
    import_ecdsakey_from_private_pem), this function is useful for when it is
    not known whether 'pem' is private or public.

  <Arguments>
    pem:
      A string in PEM format.

    scheme:
      The signature scheme used by the imported key.
  <Exceptions>
    securesystemslib.exceptions.FormatError, if 'pem' is improperly formatted.

  <Side Effects>
    None.

  <Returns>
    A dictionary containing the ECDSA keys and other identifying information.
    Conforms to 'securesystemslib.formats.ECDSAKEY_SCHEMA'.
  """

  # Does 'pem' have the correct format?
  # This check will ensure arguments has the appropriate number
  # of objects and object types, and that all dict keys are properly named.
  # Raise 'securesystemslib.exceptions.FormatError' if the check fails.
  formats.PEMECDSA_SCHEMA.check_match(pem)

  # Is 'scheme' properly formatted?
  formats.ECDSA_SCHEME_SCHEMA.check_match(scheme)

  public_pem = ''

  # Ensure the PEM string has a public or private header and footer.  Although
  # a simple validation of 'pem' is performed here, a fully valid PEM string is
  # needed later to successfully verify signatures.  Performing stricter
  # validation of PEMs are left to the external libraries that use 'pem'.
  if is_pem_public(pem):
    public_pem = extract_pem(pem, private_pem=False)

  elif is_pem_private(pem, 'ec'):
    # Return an ecdsakey object (ECDSAKEY_SCHEMA) with the private key included.
    return import_ecdsakey_from_private_pem(pem, password=None)

  else:
    raise exceptions.FormatError('PEM contains neither a public'
      ' nor private key: ' + repr(pem))

  # Begin building the ECDSA key dictionary.
  ecdsakey_dict = {}
  keytype = 'ecdsa'

  # Generate the keyid of the ECDSA key.  'key_value' corresponds to the
  # 'keyval' entry of the 'ECDSAKEY_SCHEMA' dictionary.  The private key
  # information is not included in the generation of the 'keyid' identifier.
  # If a PEM is found to contain a private key, the generated rsakey object
  # should be returned above.  The following key object is for the case of a
  # PEM with only a public key.  Convert any '\r\n' (e.g., Windows) newline
  # characters to '\n' so that a consistent keyid is generated.
  key_value = {'public': public_pem.replace('\r\n', '\n'),
               'private': ''}
  keyid = _get_keyid(keytype, scheme, key_value)

  ecdsakey_dict['keytype'] = keytype
  ecdsakey_dict['scheme'] = scheme
  ecdsakey_dict['keyid'] = keyid
  ecdsakey_dict['keyval'] = key_value

  return ecdsakey_dict



if __name__ == '__main__':
  # The interactive sessions of the documentation strings can
  # be tested by running 'keys.py' as a standalone module:
  # $ python keys.py
  import doctest
  doctest.testmod()
