Danger

This is a “Hazardous Materials” module. You should ONLY use it if you’re 100% absolutely sure that you know what you’re doing because this module is full of land mines, dragons, and dinosaurs with laser guns.

Key derivation functions

Key derivation functions derive bytes suitable for cryptographic operations from passwords or other data sources using a pseudo-random function (PRF). Different KDFs are suitable for different tasks such as:

  • Cryptographic key derivation

    Deriving a key suitable for use as input to an encryption algorithm. Typically this means taking a password and running it through an algorithm such as PBKDF2HMAC or HKDF. This process is typically known as key stretching.

  • Password storage

    When storing passwords you want to use an algorithm that is computationally intensive. Legitimate users will only need to compute it once (for example, taking the user’s password, running it through the KDF, then comparing it to the stored value), while attackers will need to do it billions of times. Ideal password storage KDFs will be demanding on both computational and memory resources.

Variable cost algorithms

PBKDF2

class cryptography.hazmat.primitives.kdf.pbkdf2.PBKDF2HMAC(algorithm, length, salt, iterations)[source]

New in version 0.2.

PBKDF2 (Password Based Key Derivation Function 2) is typically used for deriving a cryptographic key from a password. It may also be used for key storage, but an alternate key storage KDF such as Scrypt is generally considered a better solution.

This class conforms to the KeyDerivationFunction interface.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.pbkdf2 import PBKDF2HMAC
>>> # Salts should be randomly generated
>>> salt = os.urandom(16)
>>> # derive
>>> kdf = PBKDF2HMAC(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     iterations=390000,
... )
>>> key = kdf.derive(b"my great password")
>>> # verify
>>> kdf = PBKDF2HMAC(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     iterations=390000,
... )
>>> kdf.verify(b"my great password", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is (232 - 1) * algorithm.digest_size.

  • salt (bytes) – A salt. Secure values [1] are 128-bits (16 bytes) or longer and randomly generated.

  • iterations (int) – The number of iterations to perform of the hash function. This can be used to control the length of time the operation takes. Higher numbers help mitigate brute force attacks against derived keys. A more detailed description can be consulted for additional information.

Raises:

TypeError – This exception is raised if salt is not bytes.

derive(key_material)[source]
Parameters:

key_material (bytes-like) – The input key material. For PBKDF2 this should be a password.

Return bytes:

the derived key.

Raises:

This generates and returns a new key from the supplied password.

verify(key_material, expected_key)[source]
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match. This can be used for checking whether the password a user provides matches the stored derived key.

Scrypt

class cryptography.hazmat.primitives.kdf.scrypt.Scrypt(salt, length, n, r, p)[source]

New in version 1.6.

Scrypt is a KDF designed for password storage by Colin Percival to be resistant against hardware-assisted attackers by having a tunable memory cost. It is described in RFC 7914.

This class conforms to the KeyDerivationFunction interface.

>>> import os
>>> from cryptography.hazmat.primitives.kdf.scrypt import Scrypt
>>> salt = os.urandom(16)
>>> # derive
>>> kdf = Scrypt(
...     salt=salt,
...     length=32,
...     n=2**14,
...     r=8,
...     p=1,
... )
>>> key = kdf.derive(b"my great password")
>>> # verify
>>> kdf = Scrypt(
...     salt=salt,
...     length=32,
...     n=2**14,
...     r=8,
...     p=1,
... )
>>> kdf.verify(b"my great password", key)
Parameters:

  • salt (bytes) – A salt.

  • length (int) – The desired length of the derived key in bytes.

  • n (int) – CPU/Memory cost parameter. It must be larger than 1 and be a power of 2.

  • r (int) – Block size parameter.

  • p (int) – Parallelization parameter.

The computational and memory cost of Scrypt can be adjusted by manipulating the 3 parameters: n, r, and p. In general, the memory cost of Scrypt is affected by the values of both n and r, while n also determines the number of iterations performed. p increases the computational cost without affecting memory usage. A more in-depth explanation of the 3 parameters can be found here.

RFC 7914 recommends values of r=8 and p=1 while scaling n to a number appropriate for your system. The scrypt paper suggests a minimum value of n=2**14 for interactive logins (t < 100ms), or n=2**20 for more sensitive files (t < 5s).

Raises:

  • cryptography.exceptions.UnsupportedAlgorithm – If Scrypt is not supported by the OpenSSL version cryptography is using.

  • TypeError – This exception is raised if salt is not bytes.

  • ValueError – This exception is raised if n is less than 2, if n is not a power of 2, if r is less than 1 or if p is less than 1.

derive(key_material)[source]
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

the derived key.

Raises:

This generates and returns a new key from the supplied password.

verify(key_material, expected_key)[source]
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match. This can be used for checking whether the password a user provides matches the stored derived key.

Fixed cost algorithms

ConcatKDF

class cryptography.hazmat.primitives.kdf.concatkdf.ConcatKDFHash(algorithm, length, otherinfo)

New in version 1.0.

ConcatKDFHash (Concatenation Key Derivation Function) is defined by the NIST Special Publication NIST SP 800-56Ar2 document, to be used to derive keys for use after a Key Exchange negotiation operation.

Warning

ConcatKDFHash should not be used for password storage.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHash
>>> otherinfo = b"concatkdf-example"
>>> ckdf = ConcatKDFHash(
...     algorithm=hashes.SHA256(),
...     length=32,
...     otherinfo=otherinfo,
... )
>>> key = ckdf.derive(b"input key")
>>> ckdf = ConcatKDFHash(
...     algorithm=hashes.SHA256(),
...     length=32,
...     otherinfo=otherinfo,
... )
>>> ckdf.verify(b"input key", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is hashlen * (2^32 -1).

  • otherinfo (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

Raises:

TypeError – This exception is raised if otherinfo is not bytes.

derive(key_material)
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

class cryptography.hazmat.primitives.kdf.concatkdf.ConcatKDFHMAC(algorithm, length, salt, otherinfo)

New in version 1.0.

Similar to ConcatKFDHash but uses an HMAC function instead.

Warning

ConcatKDFHMAC should not be used for password storage.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.concatkdf import ConcatKDFHMAC
>>> salt = os.urandom(16)
>>> otherinfo = b"concatkdf-example"
>>> ckdf = ConcatKDFHMAC(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     otherinfo=otherinfo,
... )
>>> key = ckdf.derive(b"input key")
>>> ckdf = ConcatKDFHMAC(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     otherinfo=otherinfo,
... )
>>> ckdf.verify(b"input key", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is hashlen * (2^32 -1).

  • salt (bytes) – A salt. Randomizes the KDF’s output. Optional, but highly recommended. Ideally as many bits of entropy as the security level of the hash: often that means cryptographically random and as long as the hash output. Does not have to be secret, but may cause stronger security guarantees if secret; If None is explicitly passed a default salt of algorithm.block_size null bytes will be used.

  • otherinfo (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

Raises:

TypeError – This exception is raised if salt or otherinfo is not bytes.

derive(key_material)
Parameters:

key_material (bytes) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

HKDF

class cryptography.hazmat.primitives.kdf.hkdf.HKDF(algorithm, length, salt, info)

New in version 0.2.

HKDF (HMAC-based Extract-and-Expand Key Derivation Function) is suitable for deriving keys of a fixed size used for other cryptographic operations.

Warning

HKDF should not be used for password storage.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.hkdf import HKDF
>>> salt = os.urandom(16)
>>> info = b"hkdf-example"
>>> hkdf = HKDF(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     info=info,
... )
>>> key = hkdf.derive(b"input key")
>>> hkdf = HKDF(
...     algorithm=hashes.SHA256(),
...     length=32,
...     salt=salt,
...     info=info,
... )
>>> hkdf.verify(b"input key", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is 255 * (algorithm.digest_size // 8).

  • salt (bytes) – A salt. Randomizes the KDF’s output. Optional, but highly recommended. Ideally as many bits of entropy as the security level of the hash: often that means cryptographically random and as long as the hash output. Worse (shorter, less entropy) salt values can still meaningfully contribute to security. May be reused. Does not have to be secret, but may cause stronger security guarantees if secret; see RFC 5869 and the HKDF paper for more details. If None is explicitly passed a default salt of algorithm.digest_size // 8 null bytes will be used.

  • info (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

Raises:

TypeError – This exception is raised if salt or info is not bytes.

derive(key_material)
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material by performing both the extract and expand operations.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

class cryptography.hazmat.primitives.kdf.hkdf.HKDFExpand(algorithm, length, info)

New in version 0.5.

HKDF consists of two stages, extract and expand. This class exposes an expand only version of HKDF that is suitable when the key material is already cryptographically strong.

Warning

HKDFExpand should only be used if the key material is cryptographically strong. You should use HKDF if you are unsure.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.hkdf import HKDFExpand
>>> info = b"hkdf-example"
>>> key_material = os.urandom(16)
>>> hkdf = HKDFExpand(
...     algorithm=hashes.SHA256(),
...     length=32,
...     info=info,
... )
>>> key = hkdf.derive(key_material)
>>> hkdf = HKDFExpand(
...     algorithm=hashes.SHA256(),
...     length=32,
...     info=info,
... )
>>> hkdf.verify(key_material, key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is 255 * (algorithm.digest_size // 8).

  • info (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

Raises:

TypeError – This exception is raised if info is not bytes.

derive(key_material)
Parameters:

key_material (bytes) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material by performing both the extract and expand operations.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

KBKDF

class cryptography.hazmat.primitives.kdf.kbkdf.KBKDFHMAC(algorithm, mode, length, rlen, llen, location, label, context, fixed)

New in version 1.4.

KBKDF (Key Based Key Derivation Function) is defined by the NIST SP 800-108 document, to be used to derive additional keys from a key that has been established through an automated key-establishment scheme.

Warning

KBKDFHMAC should not be used for password storage.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.kbkdf import (
...    CounterLocation, KBKDFHMAC, Mode
... )
>>> label = b"KBKDF HMAC Label"
>>> context = b"KBKDF HMAC Context"
>>> kdf = KBKDFHMAC(
...     algorithm=hashes.SHA256(),
...     mode=Mode.CounterMode,
...     length=32,
...     rlen=4,
...     llen=4,
...     location=CounterLocation.BeforeFixed,
...     label=label,
...     context=context,
...     fixed=None,
... )
>>> key = kdf.derive(b"input key")
>>> kdf = KBKDFHMAC(
...     algorithm=hashes.SHA256(),
...     mode=Mode.CounterMode,
...     length=32,
...     rlen=4,
...     llen=4,
...     location=CounterLocation.BeforeFixed,
...     label=label,
...     context=context,
...     fixed=None,
... )
>>> kdf.verify(b"input key", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • mode – The desired mode of the PRF. A value from the Mode enum.

  • length (int) – The desired length of the derived key in bytes.

  • rlen (int) – An integer that indicates the length of the binary representation of the counter in bytes.

  • llen (int) – An integer that indicates the binary representation of the length in bytes.

  • location – The desired location of the counter. A value from the CounterLocation enum.

  • label (bytes) – Application specific label information. If None is explicitly passed an empty byte string will be used.

  • context (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

  • fixed (bytes) – Instead of specifying label and context you may supply your own fixed data. If fixed is specified, label and context is ignored.

  • break_location (int) – A keyword-only argument. An integer that indicates the bytes offset where counter bytes are to be located. Required when location is MiddleFixed.

Raises:

  • TypeError – This exception is raised if label or context is not bytes. Also raised if rlen, llen, or break_location is not int.

  • ValueError – This exception is raised if rlen or llen is greater than 4 or less than 1. This exception is also raised if you specify a label or context and fixed. This exception is also raised if you specify break_location and location is not MiddleFixed.

derive(key_material)
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

class cryptography.hazmat.primitives.kdf.kbkdf.KBKDFCMAC(algorithm, mode, length, rlen, llen, location, label, context, fixed)

New in version 35.0.

KBKDF (Key Based Key Derivation Function) is defined by the NIST SP 800-108 document, to be used to derive additional keys from a key that has been established through an automated key-establishment scheme.

Warning

KBKDFCMAC should not be used for password storage.

>>> from cryptography.hazmat.primitives.ciphers import algorithms
>>> from cryptography.hazmat.primitives.kdf.kbkdf import (
...    CounterLocation, KBKDFCMAC, Mode
... )
>>> label = b"KBKDF CMAC Label"
>>> context = b"KBKDF CMAC Context"
>>> kdf = KBKDFCMAC(
...     algorithm=algorithms.AES,
...     mode=Mode.CounterMode,
...     length=32,
...     rlen=4,
...     llen=4,
...     location=CounterLocation.BeforeFixed,
...     label=label,
...     context=context,
...     fixed=None,
... )
>>> key = kdf.derive(b"32 bytes long input key material")
>>> kdf = KBKDFCMAC(
...     algorithm=algorithms.AES,
...     mode=Mode.CounterMode,
...     length=32,
...     rlen=4,
...     llen=4,
...     location=CounterLocation.BeforeFixed,
...     label=label,
...     context=context,
...     fixed=None,
... )
>>> kdf.verify(b"32 bytes long input key material", key)
Parameters:

  • algorithm – A class implementing a block cipher algorithm being a subclass of CipherAlgorithm and BlockCipherAlgorithm.

  • mode – The desired mode of the PRF. A value from the Mode enum.

  • length (int) – The desired length of the derived key in bytes.

  • rlen (int) – An integer that indicates the length of the binary representation of the counter in bytes.

  • llen (int) – An integer that indicates the binary representation of the length in bytes.

  • location – The desired location of the counter. A value from the CounterLocation enum.

  • label (bytes) – Application specific label information. If None is explicitly passed an empty byte string will be used.

  • context (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

  • fixed (bytes) – Instead of specifying label and context you may supply your own fixed data. If fixed is specified, label and context is ignored.

  • break_location (int) – A keyword-only argument. An integer that indicates the bytes offset where counter bytes are to be located. Required when location is MiddleFixed.

Raises:
derive(key_material)
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material.

verify(key_material, expected_key)
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

cryptography.exceptions.InvalidKey – This is raised when the derived key does not match the expected key.

Raises:

Exceptions raised by derive().

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

class cryptography.hazmat.primitives.kdf.kbkdf.Mode

An enumeration for the key based key derivative modes.

CounterMode

The output of the PRF is computed with a counter as the iteration variable.

class cryptography.hazmat.primitives.kdf.kbkdf.CounterLocation

An enumeration for the key based key derivative counter location.

BeforeFixed

The counter iteration variable will be concatenated before the fixed input data.

AfterFixed

The counter iteration variable will be concatenated after the fixed input data.

MiddleFixed

New in version 38.0.

The counter iteration variable will be concatenated in the middle of the fixed input data.

X963KDF

class cryptography.hazmat.primitives.kdf.x963kdf.X963KDF(algorithm, length, otherinfo)[source]

New in version 1.1.

X963KDF (ANSI X9.63 Key Derivation Function) is defined by ANSI in the ANSI X9.63:2001 document, to be used to derive keys for use after a Key Exchange negotiation operation.

SECG in SEC 1 v2.0 recommends that ConcatKDFHash be used for new projects. This KDF should only be used for backwards compatibility with pre-existing protocols.

Warning

X963KDF should not be used for password storage.

>>> import os
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.kdf.x963kdf import X963KDF
>>> sharedinfo = b"ANSI X9.63 Example"
>>> xkdf = X963KDF(
...     algorithm=hashes.SHA256(),
...     length=32,
...     sharedinfo=sharedinfo,
... )
>>> key = xkdf.derive(b"input key")
>>> xkdf = X963KDF(
...     algorithm=hashes.SHA256(),
...     length=32,
...     sharedinfo=sharedinfo,
... )
>>> xkdf.verify(b"input key", key)
Parameters:

  • algorithm – An instance of HashAlgorithm.

  • length (int) – The desired length of the derived key in bytes. Maximum is hashlen * (2^32 -1).

  • sharedinfo (bytes) – Application specific context information. If None is explicitly passed an empty byte string will be used.

Raises:

TypeError – This exception is raised if sharedinfo is not bytes.

derive(key_material)[source]
Parameters:

key_material (bytes-like) – The input key material.

Return bytes:

The derived key.

Raises:

Derives a new key from the input key material.

verify(key_material, expected_key)[source]
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match.

Interface

class cryptography.hazmat.primitives.kdf.KeyDerivationFunction[source]

New in version 0.2.

derive(key_material)[source]
Parameters:

key_material (bytes) – The input key material. Depending on what key derivation function you are using this could be either random bytes, or a user supplied password.

Returns:

The new key.

Raises:

cryptography.exceptions.AlreadyFinalized – This is raised when derive() or verify() is called more than once.

This generates and returns a new key from the supplied key material.

verify(key_material, expected_key)[source]
Parameters:

  • key_material (bytes) – The input key material. This is the same as key_material in derive().

  • expected_key (bytes) – The expected result of deriving a new key, this is the same as the return value of derive().

Raises:

This checks whether deriving a new key from the supplied key_material generates the same key as the expected_key, and raises an exception if they do not match. This can be used for something like checking whether a user’s password attempt matches the stored derived key.