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In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the 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 is not considered sufficient of a function for it to be called one-way (see 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 and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science.〔Oded Goldreich (2001). Foundations of Cryptography: Volume 1, Basic Tools, ((draft available ) from author's site). Cambridge University Press. ISBN 0-521-79172-3. (see also (wisdom.weizmann.ac.il )) 〕 The converse is not known to be true, i.e. the existence of a proof that P and NP are not equal would not directly imply the existence of one-way functions.〔Goldwasser, S. and Bellare, M. ("Lecture Notes on Cryptography" ). Summer course on cryptography, MIT, 1996–2001〕 In applied contexts, the terms "easy" and "hard" are usually interpreted relative to some specific computing entity; typically "cheap enough for the legitimate users" and "prohibitively expensive for any malicious agents". One-way functions, in this sense, are fundamental tools for cryptography, personal identification, authentication, and other data security applications. While the existence of one-way functions in this sense is also an open conjecture, there are several candidates that have withstood decades of intense scrutiny. Some of them are essential ingredients of most telecommunications, e-commerce, and e-banking systems around the world. ==Theoretical definition== A function ''f'' : * → * is one-way if and only if ''f'' can be computed by a polynomial time algorithm, but any polynomial time randomized algorithm ''F−'' that computes a pseudo-inverse for ''f'' succeeds with negligible probability. That is, for all ''F−'', all positive integers ''c'' and all sufficiently large ''|x|'', : where is the string of n 1s and the probability is over the choice of ''x'' from the discrete uniform distribution on ''n'', and the randomness of ''F−''. Note that, by this definition, the function must be "hard to invert" in the average-case, rather than worst-case sense. This is different from much of complexity theory (e.g., NP-hardness), where the term "hard" is meant in the worst-case. That's why even if some candidates for one-way functions (described below) are known to be NP-complete, it does not imply their one-wayness. The latter property is only based on the lack of known algorithm to solve the problem. It is not sufficient to make a function "lossy" (not one-to-one) to have a one-way function. In particular, the function that outputs the string of ''n'' zeros on any input of length ''n'' is ''not'' a one-way function because it is easy to come up with an input that will result in the same output. More precisely: For a function that simply outputs a string of zeroes, an algorithm ''F−'' that just outputs any string of length ''n'' on input ''f''(''x'') will "find" a proper preimage of the output, even if it is not the input which was originally used to find the output string. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「One-way function」の詳細全文を読む スポンサード リンク
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