328071, by the Alon Fellowship, and by NSF Grant CCR8612563. Supported by Israel National Academy of Science Grant No. t This work was done while the first author was a student in the University of California at Berkeley. Presented at the 29th IEEE Conference on Foundations of Computer Science, October 24-26, 1988.In all these papers, the generator uses the one-way function f essentially as follows: From a random string X0 (the seed), it computes a sequence Yao's result was recently generalized by Impagliazzo, Levin, and Luby JILL\] who succeeded in constructing a pseudorandom generator based on an arbitrary one-way function. This result gave the first explicit hardness-randomness trade-off: if no poly-size circuit can invert the one-way permutation, then RP ~ (~ > o DTIME(2n") These ideas were generalized by Yao \, who showed that any one-way permutation can be used to construct generators that foor every polynomial time computation. The first secure pseudorandom bit-generator was built by Blum and Micali \, who used the intractabiliy of the discrete logarithm function. The fundamental idea of trading hardness for randomness is due to Shamir \, who suggested that the RSA function can be used to construct good pseudorandom sequences.
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