ABSTRACT
(MATH) We construct the first pseudo-random generators with logarithmic seed length that convert s bits of hardness into sΩ(1) bits of 2-sided pseudo-randomness for any s}. This improves [8] and gives a direct proof of the optimal hardness vs. randomness tradeoff in [15]. A key element in our construction is an augmentation of the standard low-degree extension encoding that exploits the field structure of the underlying space in a new way.
- A. Andreev, A. Clementi, and J. Rolim. A new general derandomization method. J. ACM, 45(1), 1998.]] Google Scholar
Digital Library
- M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput., 13(4):850--864, Nov. 1984.]] Google Scholar
Digital Library
- O. Goldreich, S. Vadhan, and A. Wigderson. Simplified derandomization of BPP using a hitting set generator. Technical Report TR00-004, Electronic Colloquium on Computational Complexity, January 2000.]]Google Scholar
- V. Guruswami and M. Sudan. List decoding algorithms for certain concatenated codes. In Proceedings of the 32nd ACM Symposium on Theory of Computing, 2000.]] Google Scholar
Digital Library
- V. Guruswami and M. Sudan. Extensions to the Johnson bound. Manuscript, February 2001.]]Google Scholar
- R. Impagliazzo, V. Kabanets, and A. Wigderson. In search of an easy witness: Exponential time vs. probabilistic polynomial time. In Sixteenth Annual IEEE Conference on Computational Complexity, pages 1--12, 2001.]] Google Scholar
Digital Library
- R. Impagliazzo, R. Shaltiel, and A. Wigderson. Near-optimal conversion of hardness into pseudo-randomness. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999.]] Google Scholar
Digital Library
- R. Impagliazzo, R. Shaltiel, and A. Wigderson. Extractors and pseudo-randomn generators with optimal seed-length. In Proceedings of the Thirty-second Annual ACM Symposium on the Theory of Computing, 21--23 May 2000.]] Google Scholar
Digital Library
- R. Impagliazzo and A. Wigderson. P = BPP if E requires exponential circuits: Derandomizing the XOR lemma. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 220--229, El Paso, Texas, 4--6 May 1997.]] Google Scholar
Digital Library
- V. Kabanets. Easiness assumptions and hardness tests: Trading time for zero error. In Fifteenth Annual IEEE Conference on Computational Complexity, pages 150--157, 2000.]] Google Scholar
Digital Library
- A. R. Klivans and D. van Melkebeek. Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, 1999.]] Google Scholar
Digital Library
- C. J. Lu. Derandomizing arthur-merlin games under uniform assumptions. In 11th Annual International Symposium on Algorithms And Computation, pages 302--312, 2000.]] Google Scholar
Digital Library
- P. B. Miltersen and N. V. Vinodchandran. Derandomizing Arthur-Merlin games using hitting sets. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999.]] Google Scholar
Digital Library
- N. Nisan and A. Wigderson. Hardness vs randomness. Journal of Computer and System Sciences, 49(2):149--167, Oct. 1994.]] Google Scholar
Digital Library
- R. Shaltiel and C. Umans. Simple extractors for all min-entropies and a new pseudo-random generator. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, 2001.]] Google Scholar
Digital Library
- M. Sudan. Decoding of Reed Solomon codes beyond the error-correction bound. Journal of Complexity, 13, 1997.]] Google Scholar
Digital Library
- M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the xor lemma. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, 1999.]] Google Scholar
Digital Library
- A. Ta-Shma, D. Zuckerman, and S. Safra. Extractors from Reed-Muller codes. In Proceedings of the 42th Annual IEEE Symposium on Foundations of Computer Science, 2001.]] Google Scholar
Digital Library
- L. Trevisan. Construction of extractors using pseudorandom generators. In Proceedings of the 31st ACM Symposium on Theory of Computing, 1999.]] Google Scholar
Digital Library
- R. Urbanke. Modern coding theory -- SS2001. Technical Report DSC-LTHC, EPFL, 2001. Available from http://lthcwww.epfl.ch/content.php?title=coding2001!]]Google Scholar
- A. C. Yao. Theory and applications of trapdoor functions (extended abstract). In 23rd Annual Symposium on Foundations of Computer Science, pages 80--91, Chicago, Illinois, 3--5 Nov. 1982. IEEE.]]Google Scholar
Digital Library
Index Terms
Pseudo-random generators for all hardnesses
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