We show that a black-box construction of a pseudorandom generator from a one-way function needs to make Omega(n/log(n)) calls to the underlying one-way function. The bound even holds if the one-way function is guaranteed to be regular. In this case it matches the best known construction due to Gold Reich, Krawczyk, and Luby (SIAM J. Comp. 22, 1993), which uses O(n/log(n)) calls.
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机译:我们表明,从单向函数的伪随机发生器的黑匣子构造需要使OMEGA(n / log(n))调用底层单向函数。如果保证单向函数是常规的,则绑定甚至保持。在这种情况下,它与Gold Reich,Krawczyk和Luby(Siam J. Comp.22,1993)相匹配,它使用O(n / log(n))来电。
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