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# Copyright (c) 2016, Legrandin <helderijs@gmail.com>
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__all__ = ['generate', 'construct', 'import_key',
           'RsaKey', 'oid']

import binascii
import struct

from Crypto import Random
from Crypto.IO import PKCS8, PEM
from Crypto.Util.py3compat import tobytes, bord, bchr, b, tostr
from Crypto.Util.asn1 import DerSequence

from Crypto.Math.Numbers import Integer
from Crypto.Math.Primality import (test_probable_prime,
                                   generate_probable_prime, COMPOSITE)

from Crypto.PublicKey import (_expand_subject_public_key_info,
                              _create_subject_public_key_info,
                              _extract_subject_public_key_info)


class RsaKey(object):
    r"""Class defining an actual RSA key.
    Do not instantiate directly.
    Use :func:`generate`, :func:`construct` or :func:`import_key` instead.

    :ivar n: RSA modulus
    :vartype n: integer

    :ivar e: RSA public exponent
    :vartype e: integer

    :ivar d: RSA private exponent
    :vartype d: integer

    :ivar p: First factor of the RSA modulus
    :vartype p: integer

    :ivar q: Second factor of the RSA modulus
    :vartype q: integer

    :ivar u: Chinese remainder component (:math:`p^{-1} \text{mod } q`)
    :vartype q: integer
    """

    def __init__(self, **kwargs):
        """Build an RSA key.

        :Keywords:
          n : integer
            The modulus.
          e : integer
            The public exponent.
          d : integer
            The private exponent. Only required for private keys.
          p : integer
            The first factor of the modulus. Only required for private keys.
          q : integer
            The second factor of the modulus. Only required for private keys.
          u : integer
            The CRT coefficient (inverse of p modulo q). Only required for
            privta keys.
        """

        input_set = set(kwargs.keys())
        public_set = set(('n', 'e'))
        private_set = public_set | set(('p', 'q', 'd', 'u'))
        if input_set not in (private_set, public_set):
            raise ValueError("Some RSA components are missing")
        for component, value in kwargs.items():
            setattr(self, "_" + component, value)

    @property
    def n(self):
        return int(self._n)

    @property
    def e(self):
        return int(self._e)

    @property
    def d(self):
        if not self.has_private():
            raise AttributeError("No private exponent available for public keys")
        return int(self._d)

    @property
    def p(self):
        if not self.has_private():
            raise AttributeError("No CRT component 'p' available for public keys")
        return int(self._p)

    @property
    def q(self):
        if not self.has_private():
            raise AttributeError("No CRT component 'q' available for public keys")
        return int(self._q)

    @property
    def u(self):
        if not self.has_private():
            raise AttributeError("No CRT component 'u' available for public keys")
        return int(self._u)

    def size_in_bits(self):
        """Size of the RSA modulus in bits"""
        return self._n.size_in_bits()

    def size_in_bytes(self):
        """The minimal amount of bytes that can hold the RSA modulus"""
        return (self._n.size_in_bits() - 1) // 8 + 1

    def _encrypt(self, plaintext):
        if not 0 < plaintext < self._n:
            raise ValueError("Plaintext too large")
        return int(pow(Integer(plaintext), self._e, self._n))

    def _decrypt(self, ciphertext):
        if not 0 < ciphertext < self._n:
            raise ValueError("Ciphertext too large")
        if not self.has_private():
            raise TypeError("This is not a private key")

        # Blinded RSA decryption (to prevent timing attacks):
        # Step 1: Generate random secret blinding factor r,
        # such that 0 < r < n-1
        r = Integer.random_range(min_inclusive=1, max_exclusive=self._n)
        # Step 2: Compute c' = c * r**e mod n
        cp = Integer(ciphertext) * pow(r, self._e, self._n) % self._n
        # Step 3: Compute m' = c'**d mod n       (ordinary RSA decryption)
        m1 = pow(cp, self._d % (self._p - 1), self._p)
        m2 = pow(cp, self._d % (self._q - 1), self._q)
        h = m2 - m1
        while h < 0:
            h += self._q
        h = (h * self._u) % self._q
        mp = h * self._p + m1
        # Step 4: Compute m = m**(r-1) mod n
        result = (r.inverse(self._n) * mp) % self._n
        # Verify no faults occured
        if ciphertext != pow(result, self._e, self._n):
            raise ValueError("Fault detected in RSA decryption")
        return result

    def has_private(self):
        """Whether this is an RSA private key"""

        return hasattr(self, "_d")

    def can_encrypt(self):  # legacy
        return True

    def can_sign(self):     # legacy
        return True

    def publickey(self):
        """A matching RSA public key.

        Returns:
            a new :class:`RsaKey` object
        """
        return RsaKey(n=self._n, e=self._e)

    def __eq__(self, other):
        if self.has_private() != other.has_private():
            return False
        if self.n != other.n or self.e != other.e:
            return False
        if not self.has_private():
            return True
        return (self.d == other.d and
                self.q == other.q and
                self.p == other.p and
                self.u == other.u)

    def __ne__(self, other):
        return not (self == other)

    def __getstate__(self):
        # RSA key is not pickable
        from pickle import PicklingError
        raise PicklingError

    def __repr__(self):
        if self.has_private():
            extra = ", d=%d, p=%d, q=%d, u=%d" % (int(self._d), int(self._p),
                                                  int(self._q), int(self._u))
        else:
            extra = ""
        return "RsaKey(n=%d, e=%d%s)" % (int(self._n), int(self._e), extra)

    def __str__(self):
        if self.has_private():
            key_type = "Private"
        else:
            key_type = "Public"
        return "%s RSA key at 0x%X" % (key_type, id(self))

    def export_key(self, format='PEM', passphrase=None, pkcs=1,
                   protection=None, randfunc=None):
        """Export this RSA key.

        Args:
          format (string):
            The format to use for wrapping the key:

            - *'PEM'*. (*Default*) Text encoding, done according to `RFC1421`_/`RFC1423`_.
            - *'DER'*. Binary encoding.
            - *'OpenSSH'*. Textual encoding, done according to OpenSSH specification.
              Only suitable for public keys (not private keys).

          passphrase (string):
            (*For private keys only*) The pass phrase used for protecting the output.

          pkcs (integer):
            (*For private keys only*) The ASN.1 structure to use for
            serializing the key. Note that even in case of PEM
            encoding, there is an inner ASN.1 DER structure.

            With ``pkcs=1`` (*default*), the private key is encoded in a
            simple `PKCS#1`_ structure (``RSAPrivateKey``).

            With ``pkcs=8``, the private key is encoded in a `PKCS#8`_ structure
            (``PrivateKeyInfo``).

            .. note::
                This parameter is ignored for a public key.
                For DER and PEM, an ASN.1 DER ``SubjectPublicKeyInfo``
                structure is always used.

          protection (string):
            (*For private keys only*)
            The encryption scheme to use for protecting the private key.

            If ``None`` (default), the behavior depends on :attr:`format`:

            - For *'DER'*, the *PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC*
              scheme is used. The following operations are performed:

                1. A 16 byte Triple DES key is derived from the passphrase
                   using :func:`Crypto.Protocol.KDF.PBKDF2` with 8 bytes salt,
                   and 1 000 iterations of :mod:`Crypto.Hash.HMAC`.
                2. The private key is encrypted using CBC.
                3. The encrypted key is encoded according to PKCS#8.

            - For *'PEM'*, the obsolete PEM encryption scheme is used.
              It is based on MD5 for key derivation, and Triple DES for encryption.

            Specifying a value for :attr:`protection` is only meaningful for PKCS#8
            (that is, ``pkcs=8``) and only if a pass phrase is present too.

            The supported schemes for PKCS#8 are listed in the
            :mod:`Crypto.IO.PKCS8` module (see :attr:`wrap_algo` parameter).

          randfunc (callable):
            A function that provides random bytes. Only used for PEM encoding.
            The default is :func:`Crypto.Random.get_random_bytes`.

        Returns:
          byte string: the encoded key

        Raises:
          ValueError:when the format is unknown or when you try to encrypt a private
            key with *DER* format and PKCS#1.

        .. warning::
            If you don't provide a pass phrase, the private key will be
            exported in the clear!

        .. _RFC1421:    http://www.ietf.org/rfc/rfc1421.txt
        .. _RFC1423:    http://www.ietf.org/rfc/rfc1423.txt
        .. _`PKCS#1`:   http://www.ietf.org/rfc/rfc3447.txt
        .. _`PKCS#8`:   http://www.ietf.org/rfc/rfc5208.txt
        """

        if passphrase is not None:
            passphrase = tobytes(passphrase)

        if randfunc is None:
            randfunc = Random.get_random_bytes

        if format == 'OpenSSH':
            e_bytes, n_bytes = [x.to_bytes() for x in (self._e, self._n)]
            if bord(e_bytes[0]) & 0x80:
                e_bytes = bchr(0) + e_bytes
            if bord(n_bytes[0]) & 0x80:
                n_bytes = bchr(0) + n_bytes
            keyparts = [b('ssh-rsa'), e_bytes, n_bytes]
            keystring = b('').join([struct.pack(">I", len(kp)) + kp for kp in keyparts])
            return b('ssh-rsa ') + binascii.b2a_base64(keystring)[:-1]

        # DER format is always used, even in case of PEM, which simply
        # encodes it into BASE64.
        if self.has_private():
            binary_key = DerSequence([0,
                                      self.n,
                                      self.e,
                                      self.d,
                                      self.p,
                                      self.q,
                                      self.d % (self.p-1),
                                      self.d % (self.q-1),
                                      Integer(self.q).inverse(self.p)
                                      ]).encode()
            if pkcs == 1:
                key_type = 'RSA PRIVATE KEY'
                if format == 'DER' and passphrase:
                    raise ValueError("PKCS#1 private key cannot be encrypted")
            else:  # PKCS#8
                if format == 'PEM' and protection is None:
                    key_type = 'PRIVATE KEY'
                    binary_key = PKCS8.wrap(binary_key, oid, None)
                else:
                    key_type = 'ENCRYPTED PRIVATE KEY'
                    if not protection:
                        protection = 'PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC'
                    binary_key = PKCS8.wrap(binary_key, oid,
                                            passphrase, protection)
                    passphrase = None
        else:
            key_type = "PUBLIC KEY"
            binary_key = _create_subject_public_key_info(oid,
                                                         DerSequence([self.n,
                                                                      self.e])
                                                         )

        if format == 'DER':
            return binary_key
        if format == 'PEM':
            pem_str = PEM.encode(binary_key, key_type, passphrase, randfunc)
            return tobytes(pem_str)

        raise ValueError("Unknown key format '%s'. Cannot export the RSA key." % format)

    # Backward compatibility
    exportKey = export_key

    # Methods defined in PyCrypto that we don't support anymore
    def sign(self, M, K):
        raise NotImplementedError("Use module Crypto.Signature.pkcs1_15 instead")

    def verify(self, M, signature):
        raise NotImplementedError("Use module Crypto.Signature.pkcs1_15 instead")

    def encrypt(self, plaintext, K):
        raise NotImplementedError("Use module Crypto.Cipher.PKCS1_OAEP instead")

    def decrypt(self, ciphertext):
        raise NotImplementedError("Use module Crypto.Cipher.PKCS1_OAEP instead")

    def blind(self, M, B):
        raise NotImplementedError

    def unblind(self, M, B):
        raise NotImplementedError

    def size():
        raise NotImplementedError


def generate(bits, randfunc=None, e=65537):
    """Create a new RSA key pair.

    The algorithm closely follows NIST `FIPS 186-4`_ in its
    sections B.3.1 and B.3.3. The modulus is the product of
    two non-strong probable primes.
    Each prime passes a suitable number of Miller-Rabin tests
    with random bases and a single Lucas test.

    Args:
      bits (integer):
        Key length, or size (in bits) of the RSA modulus.
        It must be at least 1024, but **2048 is recommended.**
        The FIPS standard only defines 1024, 2048 and 3072.
      randfunc (callable):
        Function that returns random bytes.
        The default is :func:`Crypto.Random.get_random_bytes`.
      e (integer):
        Public RSA exponent. It must be an odd positive integer.
        It is typically a small number with very few ones in its
        binary representation.
        The FIPS standard requires the public exponent to be
        at least 65537 (the default).

    Returns: an RSA key object (:class:`RsaKey`, with private key).

    .. _FIPS 186-4: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
    """

    if bits < 1024:
        raise ValueError("RSA modulus length must be >= 1024")
    if e % 2 == 0 or e < 3:
        raise ValueError("RSA public exponent must be a positive, odd integer larger than 2.")

    if randfunc is None:
        randfunc = Random.get_random_bytes

    d = n = Integer(1)
    e = Integer(e)

    while n.size_in_bits() != bits and d < (1 << (bits // 2)):
        # Generate the prime factors of n: p and q.
        # By construciton, their product is always
        # 2^{bits-1} < p*q < 2^bits.
        size_q = bits // 2
        size_p = bits - size_q

        min_p = min_q = (Integer(1) << (2 * size_q - 1)).sqrt()
        if size_q != size_p:
            min_p = (Integer(1) << (2 * size_p - 1)).sqrt()

        def filter_p(candidate):
            return candidate > min_p and (candidate - 1).gcd(e) == 1

        p = generate_probable_prime(exact_bits=size_p,
                                    randfunc=randfunc,
                                    prime_filter=filter_p)

        min_distance = Integer(1) << (bits // 2 - 100)

        def filter_q(candidate):
            return (candidate > min_q and
                    (candidate - 1).gcd(e) == 1 and
                    abs(candidate - p) > min_distance)

        q = generate_probable_prime(exact_bits=size_q,
                                    randfunc=randfunc,
                                    prime_filter=filter_q)

        n = p * q
        lcm = (p - 1).lcm(q - 1)
        d = e.inverse(lcm)

    if p > q:
        p, q = q, p

    u = p.inverse(q)

    return RsaKey(n=n, e=e, d=d, p=p, q=q, u=u)


def construct(rsa_components, consistency_check=True):
    r"""Construct an RSA key from a tuple of valid RSA components.

    The modulus **n** must be the product of two primes.
    The public exponent **e** must be odd and larger than 1.

    In case of a private key, the following equations must apply:

    .. math::

        \begin{align}
        p*q &= n \\
        e*d &\equiv 1 ( \text{mod lcm} [(p-1)(q-1)]) \\
        p*u &\equiv 1 ( \text{mod } q)
        \end{align}

    Args:
        rsa_components (tuple):
            A tuple of integers, with at least 2 and no
            more than 6 items. The items come in the following order:

            1. RSA modulus *n*.
            2. Public exponent *e*.
            3. Private exponent *d*.
               Only required if the key is private.
            4. First factor of *n* (*p*).
               Optional, but the other factor *q* must also be present.
            5. Second factor of *n* (*q*). Optional.
            6. CRT coefficient *q*, that is :math:`p^{-1} \text{mod }q`. Optional.

        consistency_check (boolean):
            If ``True``, the library will verify that the provided components
            fulfil the main RSA properties.

    Raises:
        ValueError: when the key being imported fails the most basic RSA validity checks.

    Returns: An RSA key object (:class:`RsaKey`).
    """

    class InputComps(object):
        pass

    input_comps = InputComps()
    for (comp, value) in zip(('n', 'e', 'd', 'p', 'q', 'u'), rsa_components):
        setattr(input_comps, comp, Integer(value))

    n = input_comps.n
    e = input_comps.e
    if not hasattr(input_comps, 'd'):
        key = RsaKey(n=n, e=e)
    else:
        d = input_comps.d
        if hasattr(input_comps, 'q'):
            p = input_comps.p
            q = input_comps.q
        else:
            # Compute factors p and q from the private exponent d.
            # We assume that n has no more than two factors.
            # See 8.2.2(i) in Handbook of Applied Cryptography.
            ktot = d * e - 1
            # The quantity d*e-1 is a multiple of phi(n), even,
            # and can be represented as t*2^s.
            t = ktot
            while t % 2 == 0:
                t //= 2
            # Cycle through all multiplicative inverses in Zn.
            # The algorithm is non-deterministic, but there is a 50% chance
            # any candidate a leads to successful factoring.
            # See "Digitalized Signatures and Public Key Functions as Intractable
            # as Factorization", M. Rabin, 1979
            spotted = False
            a = Integer(2)
            while not spotted and a < 100:
                k = Integer(t)
                # Cycle through all values a^{t*2^i}=a^k
                while k < ktot:
                    cand = pow(a, k, n)
                    # Check if a^k is a non-trivial root of unity (mod n)
                    if cand != 1 and cand != (n - 1) and pow(cand, 2, n) == 1:
                        # We have found a number such that (cand-1)(cand+1)=0 (mod n).
                        # Either of the terms divides n.
                        p = Integer(n).gcd(cand + 1)
                        spotted = True
                        break
                    k *= 2
                # This value was not any good... let's try another!
                a += 2
            if not spotted:
                raise ValueError("Unable to compute factors p and q from exponent d.")
            # Found !
            assert ((n % p) == 0)
            q = n // p

        if hasattr(input_comps, 'u'):
            u = input_comps.u
        else:
            u = p.inverse(q)

        # Build key object
        key = RsaKey(n=n, e=e, d=d, p=p, q=q, u=u)

    # Verify consistency of the key
    if consistency_check:

        # Modulus and public exponent must be coprime
        if e <= 1 or e >= n:
            raise ValueError("Invalid RSA public exponent")
        if Integer(n).gcd(e) != 1:
            raise ValueError("RSA public exponent is not coprime to modulus")

        # For RSA, modulus must be odd
        if not n & 1:
            raise ValueError("RSA modulus is not odd")

        if key.has_private():
            # Modulus and private exponent must be coprime
            if d <= 1 or d >= n:
                raise ValueError("Invalid RSA private exponent")
            if Integer(n).gcd(d) != 1:
                raise ValueError("RSA private exponent is not coprime to modulus")
            # Modulus must be product of 2 primes
            if p * q != n:
                raise ValueError("RSA factors do not match modulus")
            if test_probable_prime(p) == COMPOSITE:
                raise ValueError("RSA factor p is composite")
            if test_probable_prime(q) == COMPOSITE:
                raise ValueError("RSA factor q is composite")
            # See Carmichael theorem
            phi = (p - 1) * (q - 1)
            lcm = phi // (p - 1).gcd(q - 1)
            if (e * d % int(lcm)) != 1:
                raise ValueError("Invalid RSA condition")
            if hasattr(key, 'u'):
                # CRT coefficient
                if u <= 1 or u >= q:
                    raise ValueError("Invalid RSA component u")
                if (p * u % q) != 1:
                    raise ValueError("Invalid RSA component u with p")

    return key


def _import_pkcs1_private(encoded, *kwargs):
    # RSAPrivateKey ::= SEQUENCE {
    #           version Version,
    #           modulus INTEGER, -- n
    #           publicExponent INTEGER, -- e
    #           privateExponent INTEGER, -- d
    #           prime1 INTEGER, -- p
    #           prime2 INTEGER, -- q
    #           exponent1 INTEGER, -- d mod (p-1)
    #           exponent2 INTEGER, -- d mod (q-1)
    #           coefficient INTEGER -- (inverse of q) mod p
    # }
    #
    # Version ::= INTEGER
    der = DerSequence().decode(encoded, nr_elements=9, only_ints_expected=True)
    if der[0] != 0:
        raise ValueError("No PKCS#1 encoding of an RSA private key")
    return construct(der[1:6] + [Integer(der[4]).inverse(der[5])])


def _import_pkcs1_public(encoded, *kwargs):
    # RSAPublicKey ::= SEQUENCE {
    #           modulus INTEGER, -- n
    #           publicExponent INTEGER -- e
    # }
    der = DerSequence().decode(encoded, nr_elements=2, only_ints_expected=True)
    return construct(der)


def _import_subjectPublicKeyInfo(encoded, *kwargs):

    algoid, encoded_key, params = _expand_subject_public_key_info(encoded)
    if algoid != oid or params is not None:
        raise ValueError("No RSA subjectPublicKeyInfo")
    return _import_pkcs1_public(encoded_key)


def _import_x509_cert(encoded, *kwargs):

    sp_info = _extract_subject_public_key_info(encoded)
    return _import_subjectPublicKeyInfo(sp_info)


def _import_pkcs8(encoded, passphrase):
    k = PKCS8.unwrap(encoded, passphrase)
    if k[0] != oid:
        raise ValueError("No PKCS#8 encoded RSA key")
    return _import_keyDER(k[1], passphrase)


def _import_keyDER(extern_key, passphrase):
    """Import an RSA key (public or private half), encoded in DER form."""

    decodings = (_import_pkcs1_private,
                 _import_pkcs1_public,
                 _import_subjectPublicKeyInfo,
                 _import_x509_cert,
                 _import_pkcs8)

    for decoding in decodings:
        try:
            return decoding(extern_key, passphrase)
        except ValueError:
            pass

    raise ValueError("RSA key format is not supported")


def import_key(extern_key, passphrase=None):
    """Import an RSA key (public or private half), encoded in standard
    form.

    Args:
      extern_key (string or byte string):
        The RSA key to import.

        The following formats are supported for an RSA **public key**:

        - X.509 certificate (binary or PEM format)
        - X.509 ``subjectPublicKeyInfo`` DER SEQUENCE (binary or PEM
          encoding)
        - `PKCS#1`_ ``RSAPublicKey`` DER SEQUENCE (binary or PEM encoding)
        - OpenSSH (textual public key only)

        The following formats are supported for an RSA **private key**:

        - PKCS#1 ``RSAPrivateKey`` DER SEQUENCE (binary or PEM encoding)
        - `PKCS#8`_ ``PrivateKeyInfo`` or ``EncryptedPrivateKeyInfo``
          DER SEQUENCE (binary or PEM encoding)
        - OpenSSH (textual public key only)

        For details about the PEM encoding, see `RFC1421`_/`RFC1423`_.

        The private key may be encrypted by means of a certain pass phrase
        either at the PEM level or at the PKCS#8 level.

      passphrase (string):
        In case of an encrypted private key, this is the pass phrase from
        which the decryption key is derived.

    Returns: An RSA key object (:class:`RsaKey`).

    Raises:
      ValueError/IndexError/TypeError:
        When the given key cannot be parsed (possibly because the pass
        phrase is wrong).

    .. _RFC1421: http://www.ietf.org/rfc/rfc1421.txt
    .. _RFC1423: http://www.ietf.org/rfc/rfc1423.txt
    .. _`PKCS#1`: http://www.ietf.org/rfc/rfc3447.txt
    .. _`PKCS#8`: http://www.ietf.org/rfc/rfc5208.txt
    """

    extern_key = tobytes(extern_key)
    if passphrase is not None:
        passphrase = tobytes(passphrase)

    if extern_key.startswith(b('-----')):
        # This is probably a PEM encoded key.
        (der, marker, enc_flag) = PEM.decode(tostr(extern_key), passphrase)
        if enc_flag:
            passphrase = None
        return _import_keyDER(der, passphrase)

    if extern_key.startswith(b('ssh-rsa ')):
            # This is probably an OpenSSH key
            keystring = binascii.a2b_base64(extern_key.split(b(' '))[1])
            keyparts = []
            while len(keystring) > 4:
                l = struct.unpack(">I", keystring[:4])[0]
                keyparts.append(keystring[4:4 + l])
                keystring = keystring[4 + l:]
            e = Integer.from_bytes(keyparts[1])
            n = Integer.from_bytes(keyparts[2])
            return construct([n, e])

    if bord(extern_key[0]) == 0x30:
            # This is probably a DER encoded key
            return _import_keyDER(extern_key, passphrase)

    raise ValueError("RSA key format is not supported")

# Backward compatibility
importKey = import_key

#: `Object ID`_ for the RSA encryption algorithm. This OID often indicates
#: a generic RSA key, even when such key will be actually used for digital
#: signatures.
#:
#: .. _`Object ID`: http://www.alvestrand.no/objectid/1.2.840.113549.1.1.1.html
oid = "1.2.840.113549.1.1.1"
