article

The unified theory of pseudorandomness: guest column

Author:

S. VadhanAuthors Info & Claims

ACM SIGACT News, Volume 38, Issue 3

Pages 39 - 54

https://doi.org/10.1145/1324215.1324225

Published: 01 September 2007 Publication History

Get Access

Abstract

We survey the close connections between a variety of "pseudorandom objects," namely pseudorandom generators, expander graphs, list-decodable error-correcting codes, randomness extractors, averaging samplers, and hardness amplifiers.

References

[1]

N. Alon. Eigenvalues and expanders. Combinatorica, 6(2):83--96, 1986.

Digital Library

Google Scholar

[2]

L. Babai, L. Fortnow, N. Nisan, and A. Wigderson. BPP has subexponential time simulations unless EXPTIME has publishable proofs. Computational Complexity, 3(4):307--318, 1993.

Digital Library

Google Scholar

[3]

M. Bellare and J. Rompel. Randomness-efficient oblivious sampling. In Proc. 35th FOCS, pages 276--287, 1994.

Digital Library

Google Scholar

[4]

M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Computing, 13(4):850--864, Nov. 1984.

Digital Library

Google Scholar

[5]

B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Computing, 17(2):230--261, Apr. 1988.

Digital Library

Google Scholar

[6]

B. Chor and O. Goldreich. On the power of two-point based sampling. J. Complexity, 5(1):96--106, Mar. 1989.

Digital Library

Google Scholar

[7]

A. E. F. Clementi, J. D. P. Rolim, and L. Trevisan. Recent advances towards proving P=BPP. Bull. of the EATCS, 64:96--103, 1998.

Google Scholar

[8]

D. Galvin and P. Tetali. Slow mixing of Glauber dynamics for the hard-core model on regular bipartite graphs. Random Structures & Algorithms, 28(4):427--443, 2006.

Digital Library

Google Scholar

[9]

D. Gillman. A Chernoff bound for random walks on expander graphs. SIAM J. Comput., 27(4):1203--1220, 1998.

Digital Library

Google Scholar

[10]

O. Goldreich. A sample of samplers - a computational perspective on sampling (survey). Electronic Colloquium on Computational Complexity (ECCC), 4(20), 1997.

Google Scholar

[11]

O. Goldreich. Modern cryptography, probabilistic proofs and pseudorandomness. Springer-Verlag, 1999.

Digital Library

Google Scholar

[12]

S. Goldwasser and S. Micali. Probabilistic encryption. J. Computer & System Sci., 28(2):270--299, Apr. 1984.

Crossref

Google Scholar

[13]

V. Guruswami. Algorithmic Results in List Decoding, volume 2, number 2 of Foundations and Trends in Theoretical Computer Science. now publishers, 2006.

Digital Library

Google Scholar

[14]

V. Guruswami, C. Umans, and S. Vadhan. Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. In Proc. 22nd CCC, 2007.

Digital Library

Google Scholar

[15]

J. Håstad, R. Impagliazzo, L. A. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM J. Computing, 28(4):1364--1396, 1999.

Digital Library

Google Scholar

[16]

S. Hoory, N. Linial, and A. Wigderson. Expander graphs and their applications. Bull. of the AMS, 43(4):439--561, 2006.

Crossref

Google Scholar

[17]

V. Kabanets. Derandomization: a brief overview. Bull. of the EATCS, 76:88--103, 2002.

Google Scholar

[18]

P. Miltersen. Handbook of Randomized Computing, chapter Derandomizing Complexity Classes. Kluwer, 2001.

Google Scholar

[19]

N. Nisan and A. Ta-Shma. Extracting randomness: A survey and new constructions. J. Computer & System Sci., 58(1):148--173, February 1999.

Digital Library

Google Scholar

[20]

N. Nisan and A. Wigderson. Hardness vs randomness. J. Computer & System Sci., 49(2):149--167, Oct. 1994.

Digital Library

Google Scholar

[21]

N. Nisan and D. Zuckerman. Randomness is linear in space. J. Computer & System Sci., 52(1):43--52, Feb. 1996.

Digital Library

Google Scholar

[22]

J. Radhakrishnan and A. Ta-Shma. Bounds for dispersers, extractors, and depth-two super-concentrators. SIAM J. Discrete Math., 13(1):2--24, 2000.

Digital Library

Google Scholar

[23]

J. P. Schmidt, A. Siegel, and A. Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. SIAM J. Discrete Math., 8(2):223--250, 1995.

Crossref

Google Scholar

[24]

R. Shaltiel. Recent developments in extractors. In Current Trends in Theoretical Computer Science, vol. 1: Algorithms and Complexity. World Scientific, 2004.

Google Scholar

[25]

M. Sudan. List decoding: Algorithms and applications. SIGACT News, 31(1):16--27, 2000.

Digital Library

Google Scholar

[26]

M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. J. Computer & System Sci., 62:236--266, 2001.

Digital Library

Google Scholar

[27]

A. Ta-Shma, C. Umans, and D. Zuckerman. Loss-less condensers, unbalanced expanders, and extractors. In Proc. 33rd STOC, pages 143--152, 2001.

Digital Library

Google Scholar

[28]

A. Ta-Shma and D. Zuckerman. Extractor codes. IEEE Trans. Information Theory, 50(12):3015--3025, 2004.

Digital Library

Google Scholar

[29]

L. Trevisan. Extractors and pseudorandom generators. J. ACM, 48(4):860--879, 2001.

Digital Library

Google Scholar

[30]

L. Trevisan. Some applications of coding theory in computational complexity. Quaderni di Matematica, 13:347--424, 2004.

Google Scholar

[31]

L. Trevisan and S. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th Annual IEEE Conference on Computational Complexity (CCC '02), pages 129--138, Montréal, CA, May 2002. IEEE.

Digital Library

Google Scholar

[32]

S. Vadhan. Lecture notes on pseudorandomness. http://eecs.harvard.edu/~salil/cs225, Spring 2007.

Google Scholar

[33]

A. C. Yao. Theory and applications of trapdoor functions (extended abstract). In Proc. 23rd FOCS, pages 80--91, 1982.

Crossref

Google Scholar

[34]

D. Zuckerman. Simulating BPP using a general weak random source. Algorithmica, 16(4/5):367--391, Oct./Nov. 1996.

Crossref

Google Scholar

[35]

D. Zuckerman. Randomness-optimal oblivious sampling. Random Structures & Algorithms, 11(4):345--367, 1997.

Digital Library

Google Scholar

Cited By

View all

Foreman CWright SEdgington ABerta MCurchod F(2023)Practical randomness amplification and privatisation with implementations on quantum computersQuantum10.22331/q-2023-03-30-9697(969)Online publication date: 30-Mar-2023
https://doi.org/10.22331/q-2023-03-30-969
Molotkov S(2022)Homodyne detection in quantum optics: deterministic extractors and quantum random number generators on ‘vacuum fluctuations’Laser Physics10.1088/1555-6611/ac5ccc32:5(055202)Online publication date: 7-Apr-2022
https://doi.org/10.1088/1555-6611/ac5ccc
Zuckerman D(2019)Certifiably Pseudorandom Financial DerivativesSIAM Journal on Computing10.1137/17M116182848:6(1711-1726)Online publication date: 19-Nov-2019
https://doi.org/10.1137/17M1161828
Show More Cited By

Index Terms

The unified theory of pseudorandomness: guest column

Recommendations

Applications of unconditional pseudorandomness in complexity theory
On obtaining pseudorandomness from error-correcting codes
FSTTCS'06: Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science

A number of recent results have constructed randomness extractors and pseudorandom generators (PRGs) directly from certain error-correcting codes. The underlying construction in these results amounts to picking a random index into the codeword and ...
Pseudorandomness

This is a survey of pseudorandomness, the theory of efficiently generating objects that "look random" despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, ...

Comments

Information & Contributors

Information

Published In

ACM SIGACT News Volume 38, Issue 3

September 2007

143 pages

ISSN:0163-5700

DOI:10.1145/1324215

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2007

Published in SIGACT Volume 38, Issue 3

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
281
Total Downloads

Downloads (Last 12 months)19
Downloads (Last 6 weeks)2

Reflects downloads up to 22 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Foreman CWright SEdgington ABerta MCurchod F(2023)Practical randomness amplification and privatisation with implementations on quantum computersQuantum10.22331/q-2023-03-30-9697(969)Online publication date: 30-Mar-2023
https://doi.org/10.22331/q-2023-03-30-969
Molotkov S(2022)Homodyne detection in quantum optics: deterministic extractors and quantum random number generators on ‘vacuum fluctuations’Laser Physics10.1088/1555-6611/ac5ccc32:5(055202)Online publication date: 7-Apr-2022
https://doi.org/10.1088/1555-6611/ac5ccc
Zuckerman D(2019)Certifiably Pseudorandom Financial DerivativesSIAM Journal on Computing10.1137/17M116182848:6(1711-1726)Online publication date: 19-Nov-2019
https://doi.org/10.1137/17M1161828
Souto A(2018)Time Bounded Incompressible Theorem Reversed2018 International Conference on Intelligent Systems (IS)10.1109/IS.2018.8710590(443-447)Online publication date: 25-Sep-2018
https://dl.acm.org/doi/10.1109/IS.2018.8710590
Berta MFawzi OScholz V(2017)Quantum-Proof Randomness Extractors via Operator Space TheoryIEEE Transactions on Information Theory10.1109/TIT.2016.262753163:4(2480-2503)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1109/TIT.2016.2627531
Herrero-Collantes MGarcia-Escartin J(2017)Quantum random number generatorsReviews of Modern Physics10.1103/RevModPhys.89.01500489:1Online publication date: 22-Feb-2017
https://doi.org/10.1103/RevModPhys.89.015004
KAWACHI AYAMANE I(2015)A Fourier-Analytic Approach to List-Decoding for Sparse Random Linear CodesIEICE Transactions on Information and Systems10.1587/transinf.2014FCP0016E98.D:3(532-540)Online publication date: 2015
https://doi.org/10.1587/transinf.2014FCP0016
Fawzi OHayden PSen P(2013)From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information LockingJournal of the ACM10.1145/251813160:6(1-61)Online publication date: 1-Nov-2013
https://dl.acm.org/doi/10.1145/2518131
Santhanam R(2012)The Complexity of Explicit ConstructionsTheory of Computing Systems10.1007/s00224-011-9368-x51:3(297-312)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1007/s00224-011-9368-x
Shaltiel R(2011)An introduction to randomness extractorsProceedings of the 38th international conference on Automata, languages and programming - Volume Part II10.5555/2027223.2027226(21-41)Online publication date: 4-Jul-2011
https://dl.acm.org/doi/10.5555/2027223.2027226
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Applications of unconditional pseudorandomness in complexity theory

On obtaining pseudorandomness from error-correcting codes

Pseudorandomness

Comments

Published In

Publisher

Publication History

Check for updates

Qualifiers

Other Metrics

Article Metrics

Other Metrics

Cited By

Login options

Full Access

PDF

eReader

Abstract

References

Cited By

Index Terms

Recommendations

Applications of unconditional pseudorandomness in complexity theory

On obtaining pseudorandomness from error-correcting codes

Pseudorandomness

Comments

Information

Published In

Publisher

Publication History

Check for updates

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

Get Access

Login options

Full Access

View options

PDF

eReader

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations