Editing Message authentication code (section)

===One-time MAC===
[[Universal hashing]] and in particular [[pairwise independent]] hash functions provide a secure message authentication code as long as the key is used at most once. This can be seen as the [[one-time pad]] for authentication.<ref name=":0">{{cite book |author-link=Gustavus Simmons |first=Gustavus |last=Simmons |chapter=Authentication theory/coding theory |title=Advances in Cryptology – Proceedings of CRYPTO 84 |pages=411–431 |year=1985 |location=Berlin |publisher=Springer |isbn= }}</ref>

The simplest such pairwise independent hash function is defined by the random key, {{nowrap|''key'' {{=}} (''a'', ''b'')}}, and the MAC tag for a message ''m'' is computed as {{nowrap|''tag'' {{=}} (''am'' + ''b'') mod ''p''}}, where ''p'' is prime.

More generally, [[k-independent hashing|''k''-independent hashing]] functions provide a secure message authentication code as long as the key is used less than ''k'' times for ''k''-ways independent hashing functions.

Message authentication codes and data origin authentication have been also discussed in the framework of quantum cryptography. By contrast to other cryptographic tasks, such as key distribution, for a rather broad class of quantum MACs it has been shown that quantum resources do not offer any advantage over unconditionally secure one-time classical MACs.<ref>{{Cite journal|last1=Nikolopoulos|first1=Georgios M.|last2=Fischlin|first2=Marc|date=2020|title=Information-Theoretically Secure Data Origin Authentication with Quantum and Classical Resources|journal=Cryptography|language=en|volume=4|issue=4|pages=31|doi=10.3390/cryptography4040031|arxiv=2011.06849|s2cid=226956062|doi-access=free}}</ref>