Abstract
Yao showed how to use a sufficiently secure cryptographic permutation to construct pseudo-random generators to de-randomize arbitrary randomized algorithms. To do this, he used the fact that the XOR of independent random instances of a somewhat hard Boolean problem becomes almost completely unpredictable, a “direct product lemma”. In this survey, we try to sketch various connections between hard problems, direct product results, and de-randomization of algorithms.
Research supported by NSF YI Award CCR-92-570979, Sloan Research Fellowship BR-3311, grant #93025 of the joint US-Czechoslovak Science and Technology Program, and USA-Israel BSF Grant 92-00043
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Impagliazzo, R. (1997). Using hard problems to derandomize algorithms: An incomplete survey. In: Rolim, J. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1997. Lecture Notes in Computer Science, vol 1269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63248-4_14
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DOI: https://doi.org/10.1007/3-540-63248-4_14
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