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Note that since we do not know how to construct a one-way permutation from any one-way function, this section reduces the strength of the cryptographic assumption necessary to construct a bit-commitment protocol.
In 1991 Moni Naor showed how to create a bit-commitment scheme from a [[cryptographically secure pseudorandom number generator]].<ref>{{cite web|url=http://citeseer.ist.psu.edu/context/22544/0 |title=Citations: Bit Commitment using Pseudorandom Generators - Naor (ResearchIndex) |publisher=Citeseer.ist.psu.edu |access-date=2014-06-07 |url-access=registration}}</ref> The construction is as follows. If ''G'' is a pseudo-random generator such that ''G'' takes ''n'' bits to 3''n'' bits, then if Alice wants to commit to a bit ''b'':
*Bob selects a random 3''n''-bit vector ''R'' and sends ''R'' to Alice.
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