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- W1518083319 abstract "In a seminal paper, Hastad, Impagliazzo, Levin, and Luby showed that pseudorandom generators exist if and only if one-way functions exist. The construction they propose to obtain a pseudorandom generator from an n-bit one-way function uses $mathcal{O}(n^8)$ random bits in the input (which is the most important complexity measure of such a construction). In this work we study how much this can be reduced if the one-way function satisfies a stronger security requirement. For example, we show how to obtain a pseudorandom generator which satisfies a standard notion of security using only $mathcal{O}(n^4log^2(n))$ bits of randomness if a one-way function with exponential security is given, i.e., a one-way function for which no polynomial time algorithm has probability higher than 2−cn in inverting for some constant c.Using the uniform variant of Impagliazzo's hard-core lemma given in [7] our constructions and proofs are self-contained within this paper, and as a special case of our main theorem, we give the first explicit description of the most efficient construction from [6]." @default.
- W1518083319 created "2016-06-24" @default.
- W1518083319 creator A5003729831 @default.
- W1518083319 date "2006-01-01" @default.
- W1518083319 modified "2023-09-23" @default.
- W1518083319 title "Pseudorandom Generators from One-Way Functions: A Simple Construction for Any Hardness" @default.
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- W1518083319 doi "https://doi.org/10.1007/11681878_23" @default.
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