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Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Complexity measures for public-key cryptosystems
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Foundations of Cryptography: Basic Tools
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Journal of Computer and System Sciences - STOC 2002
Derandomizing polynomial identity tests means proving circuit lower bounds
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Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
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Computational Complexity
Computational Complexity: A Conceptual Perspective
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SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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SIAM Journal on Computing
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CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
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We show that proving results such as BPP = P essentially necessitate the construction of suitable pseudorandom generators (i.e., generators that suffice for such derandomization results). In particular, the main incarnation of this equivalence refers to the standard notion of uniform derandomization and to the corresponding pseudorandom generators (i.e., the standard uniform notion of "canonical derandomizers"). This equivalence bypasses the question of which hardness assumptions are required for establishing such derandomization results, which has received considerable attention in the last decade or so (starting with Impagliazzo and Wigderson [JCSS, 2001]). We also identify a natural class of search problems that can be solved by deterministic polynomial-time reductions to BPP. This result is instrumental to the construction of the aforementioned pseudorandom generators (based on the assumption BPP = P), which is actually a reduction of the "construction problem" to BPP.