Mask generation function: Difference between revisions

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{{Short description|Cryptographic tool}}

{{lead missing|date=February 2017}}

{{Use American English|date = April 2019}}

A '''mask generation function''' ('''MGF''') is a cryptographic primitive similar to a [[cryptographic hash function]] except that while a hash function's output has a fixed size, a MGF supports output of a variable length. In this respect, a MGF can be viewed as a [[extendable-output function]] (XOF): it can accept input of any length and process it to produce output of any length. Mask generation functions are completely deterministic: for any given input and any desired output length the output is always the same.

== OverviewDefinition ==

<blockquote>

A Mask Generation Function (MGF) is a cryptographic primitive similar to a [[Cryptographic hash function]] except that while a hash function's output is a fixed size, a MGF supports output of a variable length. In this respect, a MGF can be viewed as a single-use [[Sponge function]], it can absorb any length of input and process it to produce any length of output. Mask Generation Functions are completely deterministic. For any given input and desired output length the output is always the same.

A mask generation function takes an octet string of variable length and a desired output length as input, and outputs an octet string of the desired length. There may be restrictions on the length of the input and output octet strings, but such bounds are generally very large. Mask generation functions are deterministic; the octet string output is completely determined by the input octet string. The output of a mask generation function should be pseudorandom, that is, if the seed to the function is unknown, it should be infeasible to distinguish the output from a truly random string.<ref name="rsa">{{cite web |url=https://www.ietf.org/rfc/rfc2437.txt |title=RFC 2437 PKCS #1 |author=RSA Laboratories}}</ref>

</blockquote>

=== Definition ===

"A mask generation function takes an octet string of variable length

and a desired output length as input, and outputs an octet string of

the desired length. There may be restrictions on the length of the

input and output octet strings, but such bounds are generally very

large. Mask generation functions are deterministic; the octet string

output is completely determined by the input octet string. The output

of a mask generation function should be pseudorandom, that is, if the

seed to the function is unknown, it should be infeasible to

distinguish the output from a truly random string."<ref>{{cite web |url=https://www.ietf.org/rfc/rfc2437.txt |title=RFC 2437 PKCS #1 |author=RSA Laboratories}}</ref>

== Applications ==

Mask Generationgeneration Functionsfunctions, as generalizations of hash functions, are useful in all the same caseswherever hash functions are useful. However, use of a MGF is desirable in cases where a fixed-size hash would be inadequate. Examples include generating [[Padding (cryptography)|padding]], producing [[Oneone-time pad|one time pads]]s or other[[keystream|keystreams]] forms ofin [[Symmetric-key_algorithm|symmetric -key encryption]], orand asyielding aoutputs component of afor [[pseudorandom number generator]]s.

=== Padding Schemesschemes ===

Mask Generationgeneration Functionsfunctions were first proposed as part of the specification for passingpadding in the [[Optimal_asymmetric_encryption_padding|RSA-OAEP]] algorithm. The OAEP algorithm required a cryptographic hash function that could generate an output equal in size to a "data block" whose length was proportional to an arbitrarily sized input message.<ref>{{cite web |urlname=https:"rsa"//www.ietf.org/rfc/rfc2437.txt |title=RFC 2437 PKCS #1 |author=RSA Laboratories}}</ref>

=== KeyedRandom Encryptionnumber generators ===

NIST Special Publication 800-90A<ref>{{cite journal |url=http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf |title=Recommendation for Random Number Generation Using Deterministic Random Bit Generators |author=National Institute of Standards and Technology|year=2012 |doi=10.6028/NIST.SP.800-90A }}</ref> defines a class of cryptographically secure random number generators, one of which is the "Hash&nbsp;DRBG", which uses a hash function with a counter to produce a requested sequence of random bits equal in size to the requested number of random bits.

The [[Salsa20]] stream cipher may be viewed as a Mask Generation Function as its [[keystream]] is produced by hashing the key and nonce with a counter, to yield an arbitrarily long output.<ref>{{cite web |url=https://cr.yp.to/snuffle/salsafamily-20071225.pdf | title=The Salsa20 family of stream ciphers |author=Daniel J. Bernstein}}</ref>

<pre>

"Salsa20 generates the stream in 64-byte (512-bit) blocks. Each block is an

independent hash of the key, the nonce, and a 64-bit block number; there is no

chaining from one block to the next. The Salsa20 output stream can therefore

be accessed randomly, and any number of blocks can be computed in parallel."

</pre>

=== Random Number Generators ===

The NIST Special Publication 800-90A<ref>{{cite web |url=http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf | title=Recommendation for Random Number Generation Using Deterministic Random Bit Generators |author=National Institute of Standards and Technology}}</ref> defines a class of cryptographically secure random number generators, one of which is the "Hash DRBG" which uses a hash function with a counter to produce a requested sequence of random bits equal in size to the requested number of random bits.

== Examples ==

Perhaps the most common and straight forwardstraightforward mechanism to build a MGF is to iteratively apply a hash function together with an incrementing counter value. The counter may be incremented indefinitely to yield new output blocks until a sufficient amount of output is collected. This is the approach used in MGF1 shown below.

=== MGF1 ===

MGF1 is a Maskmask Generationgeneration Functionfunction defined in the Public Key Cryptography Standard #1 published by RSA Labroatories.Laboratories:<ref>{{cite web |urlname=https:"rsa"//www.ietf.org/rfc/rfc2437.txt |title=RFC 2437 PKCS #1 |author=RSA Laboratories}}</ref> The algorithm is described as follows:

<blockquote>

====Options====

<math>\mathsf{Hash}</math>

: hash function (<math>\mathsf{hLen}</math> denotes the length in octets of the hash function output)

====Input====

<pre>

<math>Z</math>

Hash hash function (hLen denotes the length in octets of the hash

:seed from which mask is generated, an octet string

function output)

<math>l</math>

:intended length in octets of the mask, at most <math>2^{32}(\mathsf{hLen})</math>

====Output====

Input:

<math>\mathsf{mask}</math>

Z seed from which mask is generated, an octet string

:mask, an octet string of length <math>l</math>; or "mask too long"

l intended length in octets of the mask, at most 2^32(hLen)

====Steps====

Output:

{{Ordered list | list_style_type=decimal

mask mask, an octet string of length l; or "mask too long"

| If <math>l > 2^{32}(\mathsf{hLen})</math>, output "mask too long" and stop.

| Let <math>T</math> be the empty octet string.

| For <math>\mathsf{counter}</math> from <math>0</math> to <math>\left\lceil{\tfrac{l}{\mathsf{hLen}}}\right\rceil-1</math>, do the following:

{{Ordered list | list_style_type=lower-alpha

| Convert <math>\mathsf{counter}</math> to an octet string <math>C</math> of length <math>4</math> with the primitive <math>\mathsf{I2OSP}</math>:

: <math>C = \mathsf{I2OSP} (\mathsf{counter}, 4)</math>

| Concatenate the hash of the seed <math>Z</math> and <math>C</math> to the octet string <math>T</math>:

: <math>T = T \shortparallel \mathsf{Hash} (Z \shortparallel C)</math>

}}

| Output the leading <math>l</math> octets of <math>T</math> as the octet string mask.

}}

</blockquote>

=== Example code ===

Steps:

Below is Python code implementing MGF1:

1.If l > 2^32(hLen), output "mask too long" and stop.

<syntaxhighlight lang="python">

2.Let T be the empty octet string.

3.For counter from 0 to \lceil{l / hLen}\rceil-1, do the following:

a.Convert counter to an octet string C of length 4 with the primitive

I2OSP: C = I2OSP (counter, 4)

b.Concatenate the hash of the seed Z and C to the octet string T: T =

T || Hash (Z || C)

4.Output the leading l octets of T as the octet string mask.

</pre>

=== Example Code ===

Below is the python code implementing MGF1:

<source lang="python">

import hashlib

def mgf1(seed: bytes, length: int, hash_func=hashlib.sha1) -> bytes:

def i2osp(integer, size=4):

"""Mask generation function."""

return ''.join([chr((integer >> (8 * i)) & 0xFF) for i in reversed(range(size))])

hLen = hash_func().digest_size

# https://www.ietf.org/rfc/rfc2437.txt

def mgf1(input, length, hash=hashlib.sha1):

# 1. If l > 2^32(hLen), output "mask too long" and stop.

counter = 0

if length > (hLen << 32):

output = ''

raise ValueError("mask too long")

while (len(output) < length):

# 2. Let T be the empty octet string.

C = i2osp(counter, 4)

T = b""

output += hash(input + C).digest()

# 3. For counter from 0 to \lceil{l / hLen}\rceil-1, do the following:

counter += 1

# Note: \lceil{l / hLen}\rceil-1 is the number of iterations needed,

return output[:length]

# but it's easier to check if we have reached the desired length.

</source>

counter = 0

while len(T) < length:

# a. Convert counter to an octet string C of length 4 with the primitive I2OSP: C = I2OSP (counter, 4)

C = int.to_bytes(counter, 4, "big")

# b. Concatenate the hash of the seed Z and C to the octet string T: T = T || Hash (Z || C)

T += hash_func(seed + C).digest()

counter += 1

# 4. Output the leading l octets of T as the octet string mask.

return T[:length]

</syntaxhighlight>

Example outputs of MGF1:

<sourcesyntaxhighlight lang="pythonpycon">

Python 23.710.64 (defaultmain, SepApr 16 9 20142022, 1516:0428:3641) [GCC 8.3.0] on linux

[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.39)] on darwin

Type "help", "copyright", "credits" or "license" for more information.

>>> from mgf1 import mgf1

>>> from binascii import hexlify

>>> from hashlib import sha256

>>> hexlify(mgf1('b"foo'", 3).hex()

'1ac907'

>>> hexlify(mgf1('b"foo'", 5).hex()

'1ac9075cd4'

>>> hexlify(mgf1('b"bar'", 5).hex()

'bc0c655e01'

>>> hexlify(mgf1('b"bar'", 50).hex()

'bc0c655e016bc2931d85a2e675181adcef7f581f76df2739da74faac41627be2f7f415c89e983fd0ce80ced9878641cb4876'

>>> hexlify(mgf1('b"bar'", 50, sha256).hex()

'382576a7841021cc28fc4c0948753fb8312090cea942ea4c4e735d10dc724b155f9f6069f289d61daca0cb814502ef04eae1'

</syntaxhighlight>

</source>

== References ==

{{reflist}}

[[Category:Articles with example Python (programming language) code]]

[[Category:Cryptographic primitives]]

[[Category:Cryptographic hash functions]]

[[Category:Theory of cryptography]]