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How to recycle random bits
Abstract
It is shown that modified versions of the linear congruential generator and the shift register generator are provably good for amplifying the correctness of a probabilistic algorithm. More precisely, if r random bits are needed for a BPP algorithm to be correct with probability at least 2/3, then O(r+k/sup 2/) bits are needed to improve this probability to 1-2/sup -k/. A different pseudorandom generator that is optimal, up to a constant factor, in this regard is also presented. It uses only O(r+k) bits to improve the probability to 1-2/sup -k/. This generator is based on random walks on expanders. The results do not depend on any unproven assumptions. It is shown that the modified versions of the shift register and linear congruential generators can be used to sample from distributions using, in the limit, the information-theoretic lower bound on random bits.>
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
Cited by
On lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2009) · Journal of the ACM · doi:10.1145/1568318.1568324 · Cited by 2,315
On lattices, learning with errors, random linear codes, and cryptography
Regev, O. (2005) · Proceedings of the thirty-seventh annual ACM symposium on Theory of computing · doi:10.1145/1060590.1060603 · Cited by 2,313
Experimental quantum cryptography
Bennett, C. H., Bessette, F., Brassard, G., Salvail, L., & Smolin, J. (1992) · Journal of Cryptology · doi:10.1007/bf00191318 · Cited by 1,614
Experimental Quantum Cryptography
Bennett, C. H., Bessette, F., Brassard, G., Salvail, L., & Smolin, J. (1991) · Lecture Notes in Computer Science · doi:10.1007/3-540-46877-3_23 · Cited by 959
A Framework for Efficient and Composable Oblivious Transfer
Peikert, C., Vaikuntanathan, V., & Waters, B. (2008) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-85174-5_31 · Cited by 678
Metadata
- Authors
- Impagliazzo, R., & Zuckerman, D.
- Venue
- 30th Annual Symposium on Foundations of Computer Science
- Publisher
- IEEE
- Published
- 1989
- Pages
- 248-253
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2110824700
- Cited by
- 387
- References
- 1
- FWCI
- 7.14
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Impagliazzo, R., & Zuckerman, D. (1989). How to recycle random bits. 30th Annual Symposium on Foundations of Computer Science. https://doi.org/10.1109/sfcs.1989.63486
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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