Extendable-output function: Difference between revisions

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{{Technical|date=July 2023}}

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'''Extendable-output function''' ('''XOF''') is an extension{{sfn|Peyrin|Wang|2020|p=7}} of the [[cryptographic hash]] that allows its output to be arbitrarily long. In particular, the nature of the [[sponge construction]] makes aany [[sponge hash]] a natural XOF: the squeeze operation can be repeated, and (the regular hash functions with a fixed-size result are obtained from a sponge mechanism by stopping the squeezing phase after obtaining the fixed number of bits).{{sfn | Mittelbach | Fischlin | 2021 | p=526}}

The genesis of a XOF makes it [[Collision resistance|collision]], [[Preimage resistance|preimage]] and [[second preimage]] resistant. Technically, any XOF can be turned into a cryptographic hash by truncating the result to a fixed length (in practice, hashes and XOFs are defined differently for [[Domain separation (cryptography)|___domain separation]]{{sfn|Dworkin|2014|p=3}}). The examples of XOF include the algorithms from the [[Keccak]] family: [[SHAKE128]], [[SHAKE256]], and a variant with higher efficiency, [[KangarooTwelve]].{{sfn|Peyrin|Wang|2020|p=7}}

XOFs are used as [[key derivation function]]s (KDFs), [[stream cipher]]s,{{sfn|Peyrin|Wang|2020|p=7}} [[mask generation function]]s.{{sfn|Perlner|2014|p=4}}

==Related-output issues==

By their nature, XOFs can produce related outputs (a longer result includes a shorter one as a prefix). The use of KDFs for key derivation can therefore cause related-output problems. As a "naïve" example, if the [[Triple DES]] keys are generated with a XOF, and there is a confusion in the implementation that causes some operations to be performed as 3TDEA (3x56 = 168-bit key), and some as 2TDEA (2x56 = 112 bit key), comparing the encryption results will lower the attack complexity to just 56 bits; similar problems can occur if hashes in the NIST [[SP 800-108]] are naïvely replaced by the KDFs.{{sfn|Perlner|2014|p=5}}

==References==

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==Sources==

* {{cite book | lastlast1=Mittelbach | firstfirst1=Arno | last2=Fischlin | first2=Marc | title=The Theory of Hash Functions and Random Oracles: An Approach to Modern Cryptography | publisher=Springer International Publishing | series=Information Security and Cryptography | year=2021 | chapter = Extendable Output Functions (XOFs) | isbn=978-3-030-63287-8 | chapter-url=https://books.google.com/books?id=Ly8WEAAAQBAJ&pg=PA526 | access-date=2023-06-22}}

* {{cite book | lastlast1=Peyrin | firstfirst1=Thomas | last2=Wang | first2=Haoyang | series=Lecture Notes in Computer Science | volume=12172 | pages=249–278 | title=Advances in Cryptology – CRYPTO 2020 | chapter=The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers | publisher=Springer International Publishing | publication-place=Cham | year=2020 | isbn=978-3-030-56876-4 | issn=0302-9743 | doi=10.1007/978-3-030-56877-1_9 | s2cid=221107066 | chapter-url=https://eprint.iacr.org/2020/986.pdf}}

* {{cite web |last1=Perlner |first1=Ray |title=Extendable-Output Functions (XOFs) |url=https://csrc.nist.gov/events/2014/sha-3-2014-workshop |website=csrc.nist.gov |publisher=[[NIST]] |access-date=22 June 2023 | date = August 22, 2014}}

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* {{cite web |last1=Dworkin |first1=Morris |title=Domain Extensions |url=https://csrc.nist.gov/events/2014/sha-3-2014-workshop |website=csrc.nist.gov |publisher=[[NIST]] |access-date=22 June 2023 | date = August 22, 2014}}

[[Category:Extendable-output functions]]

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