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.. hazmat:: Elliptic curve cryptography =========================== .. module:: cryptography.hazmat.primitives.asymmetric.ec .. function:: generate_private_key(curve) .. versionadded:: 0.5 Generate a new private key on ``curve``. :param curve: An instance of :class:`EllipticCurve`. :returns: A new instance of :class:`EllipticCurvePrivateKey`. .. function:: derive_private_key(private_value, curve) .. versionadded:: 1.6 Derive a private key from ``private_value`` on ``curve``. :param int private_value: The secret scalar value. :param curve: An instance of :class:`EllipticCurve`. :returns: A new instance of :class:`EllipticCurvePrivateKey`. Elliptic Curve Signature Algorithms ----------------------------------- .. class:: ECDSA(algorithm) .. versionadded:: 0.5 The ECDSA signature algorithm first standardized in NIST publication `FIPS 186-3`_, and later in `FIPS 186-4`_. Note that while elliptic curve keys can be used for both signing and key exchange, this is `bad cryptographic practice`_. Instead, users should generate separate signing and ECDH keys. :param algorithm: An instance of :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`. :param bool deterministic_signing: A boolean flag defaulting to ``False`` that specifies whether the signing procedure should be deterministic or not, as defined in :rfc:`6979`. This only impacts the signing process, verification is not affected (the verification process is the same for both deterministic and non-deterministic signed messages). .. versionadded:: 43.0.0 :raises cryptography.exceptions.UnsupportedAlgorithm: If ``deterministic_signing`` is set to ``True`` and the version of OpenSSL does not support ECDSA with deterministic signing. .. doctest:: >>> from cryptography.hazmat.primitives import hashes >>> from cryptography.hazmat.primitives.asymmetric import ec >>> private_key = ec.generate_private_key( ... ec.SECP384R1() ... ) >>> data = b"this is some data I'd like to sign" >>> signature = private_key.sign( ... data, ... ec.ECDSA(hashes.SHA256()) ... ) The ``signature`` is a ``bytes`` object, whose contents are DER encoded as described in :rfc:`3279`. This can be decoded using :func:`~cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature`. If your data is too large to be passed in a single call, you can hash it separately and pass that value using :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`. .. doctest:: >>> from cryptography.hazmat.primitives.asymmetric import utils >>> chosen_hash = hashes.SHA256() >>> hasher = hashes.Hash(chosen_hash) >>> hasher.update(b"data & ") >>> hasher.update(b"more data") >>> digest = hasher.finalize() >>> sig = private_key.sign( ... digest, ... ec.ECDSA(utils.Prehashed(chosen_hash)) ... ) Verification requires the public key, the DER-encoded signature itself, the signed data, and knowledge of the hashing algorithm that was used when producing the signature: >>> public_key = private_key.public_key() >>> public_key.verify(signature, data, ec.ECDSA(hashes.SHA256())) As above, the ``signature`` is a ``bytes`` object whose contents are DER encoded as described in :rfc:`3279`. It can be created from a raw ``(r,s)`` pair by using :func:`~cryptography.hazmat.primitives.asymmetric.utils.encode_dss_signature`. If the signature is not valid, an :class:`~cryptography.exceptions.InvalidSignature` exception will be raised. If your data is too large to be passed in a single call, you can hash it separately and pass that value using :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`. .. doctest:: >>> chosen_hash = hashes.SHA256() >>> hasher = hashes.Hash(chosen_hash) >>> hasher.update(b"data & ") >>> hasher.update(b"more data") >>> digest = hasher.finalize() >>> public_key.verify( ... sig, ... digest, ... ec.ECDSA(utils.Prehashed(chosen_hash)) ... ) .. note:: Although in this case the public key was derived from the private one, in a typical setting you will not possess the private key. The `Key loading`_ section explains how to load the public key from other sources. .. class:: EllipticCurvePrivateNumbers(private_value, public_numbers) .. versionadded:: 0.5 The collection of integers that make up an EC private key. .. attribute:: public_numbers :type: :class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers` The :class:`EllipticCurvePublicNumbers` which makes up the EC public key associated with this EC private key. .. attribute:: private_value :type: int The private value. .. method:: private_key() Convert a collection of numbers into a private key suitable for doing actual cryptographic operations. :returns: A new instance of :class:`EllipticCurvePrivateKey`. .. class:: EllipticCurvePublicNumbers(x, y, curve) .. warning:: The point represented by this object is not validated in any way until :meth:`EllipticCurvePublicNumbers.public_key` is called and may not represent a valid point on the curve. You should not attempt to perform any computations using the values from this class until you have either validated it yourself or called ``public_key()`` successfully. .. versionadded:: 0.5 The collection of integers that make up an EC public key. .. attribute:: curve :type: :class:`EllipticCurve` The elliptic curve for this key. .. attribute:: x :type: int The affine x component of the public point used for verifying. .. attribute:: y :type: int The affine y component of the public point used for verifying. .. method:: public_key() Convert a collection of numbers into a public key suitable for doing actual cryptographic operations. :raises ValueError: Raised if the point is invalid for the curve. :returns: A new instance of :class:`EllipticCurvePublicKey`. Elliptic Curve Key Exchange algorithm ------------------------------------- .. class:: ECDH() .. versionadded:: 1.1 The Elliptic Curve Diffie-Hellman Key Exchange algorithm standardized in NIST publication `800-56A`_. For most applications the ``shared_key`` should be passed to a key derivation function. This allows mixing of additional information into the key, derivation of multiple keys, and destroys any structure that may be present. Note that while elliptic curve keys can be used for both signing and key exchange, this is `bad cryptographic practice`_. Instead, users should generate separate signing and ECDH keys. .. warning:: This example does not give `forward secrecy`_ and is only provided as a demonstration of the basic Diffie-Hellman construction. For real world applications always use the ephemeral form described after this example. .. doctest:: >>> from cryptography.hazmat.primitives import hashes >>> from cryptography.hazmat.primitives.asymmetric import ec >>> from cryptography.hazmat.primitives.kdf.hkdf import HKDF >>> # Generate a private key for use in the exchange. >>> server_private_key = ec.generate_private_key( ... ec.SECP384R1() ... ) >>> # In a real handshake the peer is a remote client. For this >>> # example we'll generate another local private key though. >>> peer_private_key = ec.generate_private_key( ... ec.SECP384R1() ... ) >>> shared_key = server_private_key.exchange( ... ec.ECDH(), peer_private_key.public_key()) >>> # Perform key derivation. >>> derived_key = HKDF( ... algorithm=hashes.SHA256(), ... length=32, ... salt=None, ... info=b'handshake data', ... ).derive(shared_key) >>> # And now we can demonstrate that the handshake performed in the >>> # opposite direction gives the same final value >>> same_shared_key = peer_private_key.exchange( ... ec.ECDH(), server_private_key.public_key()) >>> # Perform key derivation. >>> same_derived_key = HKDF( ... algorithm=hashes.SHA256(), ... length=32, ... salt=None, ... info=b'handshake data', ... ).derive(same_shared_key) >>> derived_key == same_derived_key True ECDHE (or EECDH), the ephemeral form of this exchange, is **strongly preferred** over simple ECDH and provides `forward secrecy`_ when used. You must generate a new private key using :func:`generate_private_key` for each :meth:`~EllipticCurvePrivateKey.exchange` when performing an ECDHE key exchange. An example of the ephemeral form: .. doctest:: >>> from cryptography.hazmat.primitives import hashes >>> from cryptography.hazmat.primitives.asymmetric import ec >>> from cryptography.hazmat.primitives.kdf.hkdf import HKDF >>> # Generate a private key for use in the exchange. >>> private_key = ec.generate_private_key( ... ec.SECP384R1() ... ) >>> # In a real handshake the peer_public_key will be received from the >>> # other party. For this example we'll generate another private key >>> # and get a public key from that. >>> peer_public_key = ec.generate_private_key( ... ec.SECP384R1() ... ).public_key() >>> shared_key = private_key.exchange(ec.ECDH(), peer_public_key) >>> # Perform key derivation. >>> derived_key = HKDF( ... algorithm=hashes.SHA256(), ... length=32, ... salt=None, ... info=b'handshake data', ... ).derive(shared_key) >>> # For the next handshake we MUST generate another private key. >>> private_key_2 = ec.generate_private_key( ... ec.SECP384R1() ... ) >>> peer_public_key_2 = ec.generate_private_key( ... ec.SECP384R1() ... ).public_key() >>> shared_key_2 = private_key_2.exchange(ec.ECDH(), peer_public_key_2) >>> derived_key_2 = HKDF( ... algorithm=hashes.SHA256(), ... length=32, ... salt=None, ... info=b'handshake data', ... ).derive(shared_key_2) Elliptic Curves --------------- Elliptic curves provide equivalent security at much smaller key sizes than other asymmetric cryptography systems such as RSA or DSA. For many operations elliptic curves are also significantly faster; `elliptic curve diffie-hellman is faster than diffie-hellman`_. .. note:: Curves with a size of `less than 224 bits`_ should not be used. You should strongly consider using curves of at least 224 :term:`bits`. Generally the NIST prime field ("P") curves are significantly faster than the other types suggested by NIST at both signing and verifying with ECDSA. Prime fields also `minimize the number of security concerns for elliptic-curve cryptography`_. However, there is `some concern`_ that both the prime field and binary field ("B") NIST curves may have been weakened during their generation. Currently `cryptography` only supports NIST curves, none of which are considered "safe" by the `SafeCurves`_ project run by Daniel J. Bernstein and Tanja Lange. All named curves are instances of :class:`EllipticCurve`. .. class:: SECP256R1 .. versionadded:: 0.5 SECG curve ``secp256r1``. Also called NIST P-256. .. class:: SECP384R1 .. versionadded:: 0.5 SECG curve ``secp384r1``. Also called NIST P-384. .. class:: SECP521R1 .. versionadded:: 0.5 SECG curve ``secp521r1``. Also called NIST P-521. .. class:: SECP224R1 .. versionadded:: 0.5 SECG curve ``secp224r1``. Also called NIST P-224. .. class:: SECP192R1 .. versionadded:: 0.5 SECG curve ``secp192r1``. Also called NIST P-192. .. class:: SECP256K1 .. versionadded:: 0.9 SECG curve ``secp256k1``. .. class:: BrainpoolP256R1 .. versionadded:: 2.2 Brainpool curve specified in :rfc:`5639`. These curves are discouraged for new systems. .. class:: BrainpoolP384R1 .. versionadded:: 2.2 Brainpool curve specified in :rfc:`5639`. These curves are discouraged for new systems. .. class:: BrainpoolP512R1 .. versionadded:: 2.2 Brainpool curve specified in :rfc:`5639`. These curves are discouraged for new systems. .. class:: SECT571K1 .. versionadded:: 0.5 SECG curve ``sect571k1``. Also called NIST K-571. These binary curves are discouraged for new systems. .. class:: SECT409K1 .. versionadded:: 0.5 SECG curve ``sect409k1``. Also called NIST K-409. These binary curves are discouraged for new systems. .. class:: SECT283K1 .. versionadded:: 0.5 SECG curve ``sect283k1``. Also called NIST K-283. These binary curves are discouraged for new systems. .. class:: SECT233K1 .. versionadded:: 0.5 SECG curve ``sect233k1``. Also called NIST K-233. These binary curves are discouraged for new systems. .. class:: SECT163K1 .. versionadded:: 0.5 SECG curve ``sect163k1``. Also called NIST K-163. These binary curves are discouraged for new systems. .. class:: SECT571R1 .. versionadded:: 0.5 SECG curve ``sect571r1``. Also called NIST B-571. These binary curves are discouraged for new systems. .. class:: SECT409R1 .. versionadded:: 0.5 SECG curve ``sect409r1``. Also called NIST B-409. These binary curves are discouraged for new systems. .. class:: SECT283R1 .. versionadded:: 0.5 SECG curve ``sect283r1``. Also called NIST B-283. These binary curves are discouraged for new systems. .. class:: SECT233R1 .. versionadded:: 0.5 SECG curve ``sect233r1``. Also called NIST B-233. These binary curves are discouraged for new systems. .. class:: SECT163R2 .. versionadded:: 0.5 SECG curve ``sect163r2``. Also called NIST B-163. These binary curves are discouraged for new systems. Key Interfaces ~~~~~~~~~~~~~~ .. class:: EllipticCurve .. versionadded:: 0.5 A named elliptic curve. .. attribute:: name :type: str The name of the curve. Usually the name used for the ASN.1 OID such as ``secp256k1``. .. attribute:: key_size :type: int Size (in :term:`bits`) of a secret scalar for the curve (as generated by :func:`generate_private_key`). .. class:: EllipticCurveSignatureAlgorithm .. versionadded:: 0.5 .. versionchanged:: 1.6 :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed` can now be used as an ``algorithm``. A signature algorithm for use with elliptic curve keys. .. attribute:: algorithm :type: :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm` or :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed` The digest algorithm to be used with the signature scheme. .. class:: EllipticCurvePrivateKey .. versionadded:: 0.5 An elliptic curve private key for use with an algorithm such as `ECDSA`_. .. method:: exchange(algorithm, peer_public_key) .. versionadded:: 1.1 Performs a key exchange operation using the provided algorithm with the peer's public key. For most applications the ``shared_key`` should be passed to a key derivation function. This allows mixing of additional information into the key, derivation of multiple keys, and destroys any structure that may be present. :param algorithm: The key exchange algorithm, currently only :class:`~cryptography.hazmat.primitives.asymmetric.ec.ECDH` is supported. :param EllipticCurvePublicKey peer_public_key: The public key for the peer. :returns bytes: A shared key. .. method:: public_key() :return: :class:`EllipticCurvePublicKey` The EllipticCurvePublicKey object for this private key. .. method:: sign(data, signature_algorithm) .. versionadded:: 1.5 Sign one block of data which can be verified later by others using the public key. :param data: The message string to sign. :type data: :term:`bytes-like` :param signature_algorithm: An instance of :class:`EllipticCurveSignatureAlgorithm`, such as :class:`ECDSA`. :return bytes: The signature as a ``bytes`` object, whose contents are DER encoded as described in :rfc:`3279`. This can be decoded using :func:`~cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature`, which returns the decoded tuple ``(r, s)``. .. attribute:: curve :type: :class:`EllipticCurve` The EllipticCurve that this key is on. .. attribute:: key_size .. versionadded:: 1.9 :type: int Size (in :term:`bits`) of a secret scalar for the curve (as generated by :func:`generate_private_key`). .. method:: private_numbers() Create a :class:`EllipticCurvePrivateNumbers` object. :returns: An :class:`EllipticCurvePrivateNumbers` instance. .. method:: private_bytes(encoding, format, encryption_algorithm) Allows serialization of the key to bytes. Encoding ( :attr:`~cryptography.hazmat.primitives.serialization.Encoding.PEM` or :attr:`~cryptography.hazmat.primitives.serialization.Encoding.DER`), format ( :attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL`, :attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.OpenSSH` or :attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8`) and encryption algorithm (such as :class:`~cryptography.hazmat.primitives.serialization.BestAvailableEncryption` or :class:`~cryptography.hazmat.primitives.serialization.NoEncryption`) are chosen to define the exact serialization. :param encoding: A value from the :class:`~cryptography.hazmat.primitives.serialization.Encoding` enum. :param format: A value from the :class:`~cryptography.hazmat.primitives.serialization.PrivateFormat` enum. :param encryption_algorithm: An instance of an object conforming to the :class:`~cryptography.hazmat.primitives.serialization.KeySerializationEncryption` interface. :return bytes: Serialized key. .. class:: EllipticCurvePublicKey .. versionadded:: 0.5 An elliptic curve public key. .. attribute:: curve :type: :class:`EllipticCurve` The elliptic curve for this key. .. method:: public_numbers() Create a :class:`EllipticCurvePublicNumbers` object. :returns: An :class:`EllipticCurvePublicNumbers` instance. .. method:: public_bytes(encoding, format) Allows serialization of the key data to bytes. When encoding the public key the encodings ( :attr:`~cryptography.hazmat.primitives.serialization.Encoding.PEM`, :attr:`~cryptography.hazmat.primitives.serialization.Encoding.DER`) and format ( :attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.SubjectPublicKeyInfo`) are chosen to define the exact serialization. When encoding the point the encoding :attr:`~cryptography.hazmat.primitives.serialization.Encoding.X962` should be used with the formats ( :attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.UncompressedPoint` or :attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.CompressedPoint` ). :param encoding: A value from the :class:`~cryptography.hazmat.primitives.serialization.Encoding` enum. :param format: A value from the :class:`~cryptography.hazmat.primitives.serialization.PublicFormat` enum. :return bytes: Serialized data. .. method:: verify(signature, data, signature_algorithm) .. versionadded:: 1.5 Verify one block of data was signed by the private key associated with this public key. :param signature: The DER-encoded signature to verify. A raw signature may be DER-encoded by splitting it into the ``r`` and ``s`` components and passing them into :func:`~cryptography.hazmat.primitives.asymmetric.utils.encode_dss_signature`. :type signature: :term:`bytes-like` :param data: The message string that was signed. :type data: :term:`bytes-like` :param signature_algorithm: An instance of :class:`EllipticCurveSignatureAlgorithm`. :returns: None :raises cryptography.exceptions.InvalidSignature: If the signature does not validate. .. attribute:: key_size .. versionadded:: 1.9 :type: int Size (in :term:`bits`) of a secret scalar for the curve (as generated by :func:`generate_private_key`). .. classmethod:: from_encoded_point(curve, data) .. versionadded:: 2.5 Decodes a byte string as described in `SEC 1 v2.0`_ section 2.3.3 and returns an :class:`EllipticCurvePublicKey`. This class method supports compressed points. :param curve: An :class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve` instance. :param bytes data: The serialized point byte string. :returns: An :class:`EllipticCurvePublicKey` instance. :raises ValueError: Raised when an invalid point is supplied. :raises TypeError: Raised when curve is not an :class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve`. Serialization ~~~~~~~~~~~~~ This sample demonstrates how to generate a private key and serialize it. .. doctest:: >>> from cryptography.hazmat.primitives import serialization >>> from cryptography.hazmat.primitives.asymmetric import ec >>> private_key = ec.generate_private_key(ec.SECP384R1()) >>> serialized_private = private_key.private_bytes( ... encoding=serialization.Encoding.PEM, ... format=serialization.PrivateFormat.PKCS8, ... encryption_algorithm=serialization.BestAvailableEncryption(b'testpassword') ... ) >>> serialized_private.splitlines()[0] b'-----BEGIN ENCRYPTED PRIVATE KEY-----' You can also serialize the key without a password, by relying on :class:`~cryptography.hazmat.primitives.serialization.NoEncryption`. The public key is serialized as follows: .. doctest:: >>> public_key = private_key.public_key() >>> serialized_public = public_key.public_bytes( ... encoding=serialization.Encoding.PEM, ... format=serialization.PublicFormat.SubjectPublicKeyInfo ... ) >>> serialized_public.splitlines()[0] b'-----BEGIN PUBLIC KEY-----' This is the part that you would normally share with the rest of the world. Key loading ~~~~~~~~~~~ This extends the sample in the previous section, assuming that the variables ``serialized_private`` and ``serialized_public`` contain the respective keys in PEM format. .. doctest:: >>> loaded_public_key = serialization.load_pem_public_key( ... serialized_public, ... ) >>> loaded_private_key = serialization.load_pem_private_key( ... serialized_private, ... # or password=None, if in plain text ... password=b'testpassword', ... ) Elliptic Curve Object Identifiers ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. class:: EllipticCurveOID .. versionadded:: 2.4 .. attribute:: SECP192R1 Corresponds to the dotted string ``"1.2.840.10045.3.1.1"``. .. attribute:: SECP224R1 Corresponds to the dotted string ``"1.3.132.0.33"``. .. attribute:: SECP256K1 Corresponds to the dotted string ``"1.3.132.0.10"``. .. attribute:: SECP256R1 Corresponds to the dotted string ``"1.2.840.10045.3.1.7"``. .. attribute:: SECP384R1 Corresponds to the dotted string ``"1.3.132.0.34"``. .. attribute:: SECP521R1 Corresponds to the dotted string ``"1.3.132.0.35"``. .. attribute:: BRAINPOOLP256R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.7"``. .. attribute:: BRAINPOOLP384R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.11"``. .. attribute:: BRAINPOOLP512R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.13"``. .. attribute:: SECT163K1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.1"``. .. attribute:: SECT163R2 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.15"``. .. attribute:: SECT233K1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.26"``. .. attribute:: SECT233R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.27"``. .. attribute:: SECT283K1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.16"``. .. attribute:: SECT283R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.17"``. .. attribute:: SECT409K1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.36"``. .. attribute:: SECT409R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.37"``. .. attribute:: SECT571K1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.38"``. .. attribute:: SECT571R1 .. versionadded:: 2.5 Corresponds to the dotted string ``"1.3.132.0.39"``. .. function:: get_curve_for_oid(oid) .. versionadded:: 2.6 A function that takes an :class:`~cryptography.x509.ObjectIdentifier` and returns the associated elliptic curve class. :param oid: An instance of :class:`~cryptography.x509.ObjectIdentifier`. :returns: The matching elliptic curve class. The returned class conforms to the :class:`EllipticCurve` interface. :raises LookupError: Raised if no elliptic curve is found that matches the provided object identifier. .. _`FIPS 186-3`: https://csrc.nist.gov/files/pubs/fips/186-3/final/docs/fips_186-3.pdf .. _`FIPS 186-4`: https://csrc.nist.gov/pubs/fips/186-4/final .. _`800-56A`: https://csrc.nist.gov/pubs/sp/800/56/a/r3/final .. _`some concern`: https://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters .. _`less than 224 bits`: https://www.cosic.esat.kuleuven.be/ecrypt/ecrypt2/documents/D.SPA.20.pdf .. _`elliptic curve diffie-hellman is faster than diffie-hellman`: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1100&context=cseconfwork .. _`minimize the number of security concerns for elliptic-curve cryptography`: https://cr.yp.to/ecdh/curve25519-20060209.pdf .. _`SafeCurves`: https://safecurves.cr.yp.to/ .. _`ECDSA`: https://en.wikipedia.org/wiki/ECDSA .. _`forward secrecy`: https://en.wikipedia.org/wiki/Forward_secrecy .. _`SEC 1 v2.0`: https://www.secg.org/sec1-v2.pdf .. _`bad cryptographic practice`: https://crypto.stackexchange.com/a/3313
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