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One-way function
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==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 (complexity)|FP]] β [[FNP (complexity)|FNP]], which in turn implies that P β NP. However, P β NP does not imply the existence of one-way functions. The existence of a one-way function implies the existence of many other useful concepts, including: * [[Pseudorandom generator]]s * [[Pseudorandom function]] families * [[Commitment scheme|Bit commitment schemes]] * Private-key encryption schemes secure against [[adaptive chosen-ciphertext attack]] * [[Message authentication code]]s * [[Digital signature scheme]]s (secure against adaptive chosen-message attack)
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