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- W3037977018 abstract "We study time/memory tradeoffs of function inversion: an algorithm, i.e., an inverter, equipped with an s-bit advice on a randomly chosen function (f:[n] mapsto [n]) and using q oracle queries to f, tries to invert a randomly chosen output y of f, i.e., to find (xin f^{-1}(y)). Much progress was done regarding adaptive function inversion—the inverter is allowed to make adaptive oracle queries. Hellman [IEEE transactions on Information Theory ’80] presented an adaptive inverter that inverts with high probability a random f. Fiat and Naor [SICOMP ’00] proved that for any s, q with (s^3 q = n^3) (ignoring low-order terms), an s-advice, q-query variant of Hellman’s algorithm inverts a constant fraction of the image points of any function. Yao [STOC ’90] proved a lower bound of (sqge n) for this problem. Closing the gap between the above lower and upper bounds is a long-standing open question." @default.
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- W3037977018 date "2020-01-01" @default.
- W3037977018 modified "2023-09-28" @default.
- W3037977018 title "Lower Bounds on the Time/Memory Tradeoff of Function Inversion." @default.
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