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.
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