Extendable-output function (XOF) is an extension of the cryptographic hash that allows its output to be arbitrarily long. In particular, the sponge construction makes any 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).
The genesis of a XOF makes it collision, 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). The examples of XOF include the algorithms from the Keccak family: SHAKE128, SHAKE256, and a variant with higher efficiency, KangarooTwelve.
XOFs are used as key derivation functions (KDFs), stream ciphers, mask generation functions.
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.7
Sources
- Mittelbach, Arno; Fischlin, Marc (2021). "Extendable Output Functions (XOFs)". The Theory of Hash Functions and Random Oracles: An Approach to Modern Cryptography. Information Security and Cryptography. Springer International Publishing. ISBN 978-3-030-63287-8. Retrieved 2023-06-22.
- Peyrin, Thomas; Wang, Haoyang (2020). "The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers" (PDF). Advances in Cryptology – CRYPTO 2020. Lecture Notes in Computer Science. Vol. 12172. Springer International Publishing. pp. 249–278. doi:10.1007/978-3-030-56877-1_9. ISBN 978-3-030-56876-4. ISSN 0302-9743. S2CID 221107066.
- Perlner, Ray (August 22, 2014). "Extendable-Output Functions (XOFs)". csrc.nist.gov. NIST. Retrieved 22 June 2023.
- Dworkin, Morris (August 22, 2014). "Domain Extensions". csrc.nist.gov. NIST. Retrieved 22 June 2023.
References
Peyrin & Wang 2020, p. 7. - Peyrin, Thomas; Wang, Haoyang (2020). "The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers" (PDF). Advances in Cryptology – CRYPTO 2020. Lecture Notes in Computer Science. Vol. 12172. Springer International Publishing. pp. 249–278. doi:10.1007/978-3-030-56877-1_9. ISBN 978-3-030-56876-4. ISSN 0302-9743. S2CID 221107066. https://eprint.iacr.org/2020/986.pdf ↩
Mittelbach & Fischlin 2021, p. 526. - Mittelbach, Arno; Fischlin, Marc (2021). "Extendable Output Functions (XOFs)". The Theory of Hash Functions and Random Oracles: An Approach to Modern Cryptography. Information Security and Cryptography. Springer International Publishing. ISBN 978-3-030-63287-8. Retrieved 2023-06-22. https://books.google.com/books?id=Ly8WEAAAQBAJ&pg=PA526 ↩
Dworkin 2014, p. 3. - Dworkin, Morris (August 22, 2014). "Domain Extensions". csrc.nist.gov. NIST. Retrieved 22 June 2023. https://csrc.nist.gov/events/2014/sha-3-2014-workshop ↩
Peyrin & Wang 2020, p. 7. - Peyrin, Thomas; Wang, Haoyang (2020). "The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers" (PDF). Advances in Cryptology – CRYPTO 2020. Lecture Notes in Computer Science. Vol. 12172. Springer International Publishing. pp. 249–278. doi:10.1007/978-3-030-56877-1_9. ISBN 978-3-030-56876-4. ISSN 0302-9743. S2CID 221107066. https://eprint.iacr.org/2020/986.pdf ↩
Peyrin & Wang 2020, p. 7. - Peyrin, Thomas; Wang, Haoyang (2020). "The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers" (PDF). Advances in Cryptology – CRYPTO 2020. Lecture Notes in Computer Science. Vol. 12172. Springer International Publishing. pp. 249–278. doi:10.1007/978-3-030-56877-1_9. ISBN 978-3-030-56876-4. ISSN 0302-9743. S2CID 221107066. https://eprint.iacr.org/2020/986.pdf ↩
Perlner 2014, p. 4. - Perlner, Ray (August 22, 2014). "Extendable-Output Functions (XOFs)". csrc.nist.gov. NIST. Retrieved 22 June 2023. https://csrc.nist.gov/events/2014/sha-3-2014-workshop ↩
Perlner 2014, p. 5. - Perlner, Ray (August 22, 2014). "Extendable-Output Functions (XOFs)". csrc.nist.gov. NIST. Retrieved 22 June 2023. https://csrc.nist.gov/events/2014/sha-3-2014-workshop ↩