Theoretical Implications of One-way Functions
If f is a one-way function, then the inversion of f would be a problem whose output is hard to compute (by definition) but easy to check (just by computing f on it). Thus, the existence of a one-way function implies that FP≠FNP, which in turn implies that P≠NP. However, it is not known whether P≠NP implies the existence of one-way functions.
The existence of a one-way function implies the existence of many other useful concepts, including:
- Pseudorandom generators
- Pseudorandom function families
- Bit commitment schemes
- Private-key encryption schemes secure against adaptive chosen-ciphertext attack
- Message authentication codes
- Digital signature schemes (secure against adaptive chosen-message attack)
The existence of one-way functions also implies that there is no natural proof for P≠NP.
Read more about this topic: One-way Function
Famous quotes containing the words theoretical, implications and/or functions:
“There are theoretical reformers at all times, and all the world over, living on anticipation.”
—Henry David Thoreau (1817–1862)
“The power to guess the unseen from the seen, to trace the implications of things, to judge the whole piece by the pattern, the condition of feeling life in general so completely that you are well on your way to knowing any particular corner of it—this cluster of gifts may almost be said to constitute experience.”
—Henry James (1843–1916)
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)