One-way Function - Theoretical Implications of One-way Functions

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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