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- W2043814918 abstract "We consider the question of constructing pseudorandom generators that simultaneously have linear circuit complexity (in the output length), exponential security (in the seed length), and a large stretch (linear or polynomial in the seed length). We refer to such a pseudorandom generator as an asymptotically optimal PRG. We present a simple construction of an asymptotically optimal PRG from any one-way function f:{0,1}n→{0,1}n which satisfies the following requirements: f can be computed by linear-size circuits; f is 2βn-hard to invert, for some constant β>0; f either has high entropy, in the sense that the min-entropy of f(x) on a random input x is at least γn where β/3+γ>1, or alternatively it is regular in the sense that the preimage size of every output of f is fixed. Our construction relies on a technical result about hardcore functions that may be of independent interest. We obtain a family of hardcore functions H={h:{0,1}n→{0,1}αn} that can be computed by linear-size circuits for any 2βn-hard one-way function f:{0,1}n→{0,1}n where β>3α. Our construction of asymptotically optimal PRGs uses such hardcore functions, which are obtained via linear-size computable affine hash functions (Ishai et al. (2008) [24])." @default.
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- W2043814918 date "2014-10-01" @default.
- W2043814918 modified "2023-10-16" @default.
- W2043814918 title "On linear-size pseudorandom generators and hardcore functions" @default.
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- W2043814918 doi "https://doi.org/10.1016/j.tcs.2014.06.013" @default.
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