One-way function: Difference between revisions

Revision as of 10:16, 25 November 2021

Revision as of 10:53, 26 November 2021

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{{Short description|Function that is easy to compute on every input, but hard to invert given the image of a random input}}

{{unsolved|computer science|Do one-way functions exist?}}

[[In]] [[computer science]], a '''one-way function''' is a [[function (mathematics)|function]] that is easy to compute on every input, but hard to [[Inverse function|invert]] given the [[image (mathematics)|image]] of a random input. Here, "easy" and "hard" are to be understood in the sense of [[computational complexity theory]], specifically the theory of [[polynomial time]] problems. Not being [[One-to-one function|one-to-one]] is not considered sufficient for a function to be called one-way (see [[#Theoretical definition|Theoretical definition]], below).

The existence of such one-way functions is still an open [[conjecture]]. In fact, their existence would prove that the [[complexity classes]] [[P = NP problem|P and NP are not equal]], thus resolving the foremost unsolved question of theoretical computer science.<ref name=Goldreich>[[Oded Goldreich]] (2001). Foundations of Cryptography: Volume 1, Basic Tools, ([http://www.wisdom.weizmann.ac.il/~oded/PSBookFrag/part2N.ps draft available] from author's site). Cambridge University Press. {{isbn|0-521-79172-3}}. (see also [http://www.wisdom.weizmann.ac.il/~oded/foc-book.html wisdom.weizmann.ac.il])</ref>{{rp|ex. 2.2, page 70}} The converse is not known to be true, i.e. the existence of a proof that P≠NP would not directly imply the existence of one-way functions.<ref>[[Shafi Goldwasser|Goldwasser, S.]] and Bellare, M. [http://cseweb.ucsd.edu/~mihir/papers/gb.html "Lecture Notes on Cryptography"]. Summer course on cryptography, MIT, 1996–2001</ref>