- ACR97.Alexander Andreev, Andrea Clementi, and Jos6 Rolim. Worstcase hardness suffices for derandomization: a new method for hardness-randomness trade-offs. In Proceedings oflCALP'97, pages 177-187. LNC 1256S, Springer-Vertag, 1997. Google ScholarDigital Library
- AK97.V. Arvind and J. KObler. On resource-bounded measure and pseudorandomness. In Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science, pages 235-249. LNCS 1346, Springer-Verlag, 1997, Google ScholarDigital Library
- ALRS92.Sigal At, Richard J. Lipton, Ronitt Rubinfeld, and Madhu Sudan. Reconstructing algebraic functions from mixed data. In 33rd Annual Symposium on Foundations of Computer Science, pages 503-512, Pittsburgh, Pennsylvania, 24-27 October 1992. IEEE.Google Scholar
- AS97.Sanjeev Arora and Madhu Sudan. Improved low degree testing and its applications. In Proceedings of the TWenty-Ninth Annual ACM Symposiumon Theory of Computing, pages 485- 495, El Paso, Texas, 4-6 May t 997. Google ScholarDigital Library
- BBR85.Charles H. Bennett, Gilles Brassard, and Jean-Marc Robert. How to reduce your enemy's information (extended abstract). In Hugh C. Williams, editor, Advances in Cryptology-- CRYPTO '85, volume 218 of Lecture Notes in Computer Science, pages 468--476. Springer-Verlag, 1986, 18-22 August 1985, Google ScholarDigital Library
- BF90.Donald Beaver and Joan Feigenbaum. Hiding instances in multioracle queries. In 7th Annual Symposium on Theoretical Aspects of Computer Science, volume 415 of Lecture Notes in Computer Science, pages 37-48, Rouen, France, 22-24 February 1990. Springer. Google ScholarDigital Library
- BFNW93.LAszl6 Bahai, Lance Fortnow, Noam Nisan, and Avi Wigderson. BPP has subexponentiat time simulations unless EX- PTIME has publishable proofs. Computational Complexity, 3(4):307-318,1993. Google ScholarDigital Library
- BM84.Manuel Blum and Silvio Micali, How to generate cryptographically strong sequences of pseudo-random bits. SIAM Journal on Computing, 13(4):850-864, November 1984, Google ScholarDigital Library
- CG89.Benny Chor and Oded Goldreich. On the power of two-point based sampling. Journal of Complexity, 5(1):96-106, March 1989. Google ScholarDigital Library
- CGH+85.Benny Chor, Oded Goldreich, Johan Hastad, Joel Friedman, Steven Rudieh, and Roman Smolensky. The bit extraction problem or t-resilient functions (preliminary version). In 26th Annual Symposium on Foundations of Computer Science, pages 396-407, Porfiand, Oregon, 21-23 October 1985. IEEE.Google ScholarDigital Library
- CPS99.Jin-Yi Cai, A. Pavan, and D. Sivakumar. On the hardness of the permanent. In 16th International Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Trier, Germany, March 4-6 1999. Springer-Verlag. To appear. Google ScholarDigital Library
- CT91.Thomas M. Cover and Joy A. Thomas. Elements oflnformalion Theory. Wiley Series in Telecommunications. John Wiley & Sons, Inc., 2nd edition, 1991. Google ScholarDigital Library
- CW89.Aviad Cohen and Avi Wigderson. Dispersers, determinislic amplification, and weak random sources (extended abstrac0. In 30th Annual Symposium on Foundations of Computer Science, pages 14-19, Research Triangle Park, North Carolina, 30 October-I November t989. IEEE.Google Scholar
- FF93.Joan Feigenbaum and Lance Formow. Random-selfreducibility of complete sets. SIAM Journal on Computing, 22(5):994-1005, October t 993. Google ScholarDigital Library
- FL96.Uriel Feige and Carsten Lund. On the hardness of computing the permanent of random matrices. Computational Complexity, 6(2):t01-132, 1996. Google ScholarDigital Library
- Fri92.loet Friedman. On the bit extraction problem, In 33rdAnnual Symposium on Foundations of Computer Science, pages 314- 319, Pittsburgh, Pennsylvania, 24--27 October 1992. IEEE.Google Scholar
- GL89.Oded Goldreich and Leonid A. Levin. A hard.core predicate for all one-way functions. In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing, pages 25- 32, Seattle, Washington, 15-17 May 1989. Google ScholarDigital Library
- GLR+91.Peter Gemme!t, Richard Lipton, Ronitt Rubinfeld, Madhu Sudan, and Avi Wigderson. Self-testing/correcting for polynomia/s and for approximate functions. In Proceedings qf the Twenty Third Annual ACM Symposium on Theory of Computing, pages 32-42, New Orleans, Louisiana, 6--8 May 1991. Google ScholarDigital Library
- GM84.Shaft Goldwasser and Silvio Micali. Probabilistic encryplion. Journal of Computer and System Sciences, 28(2):270- 299, April t 984.Google ScholarCross Ref
- GNW95.Oded Goldreich, Noam Nisan, and Avi Wigderson. On Yao's XOR lemma. Technical Report TR95--050, Electronic Colloquium on Computational Complexity, March 1995. http: / / www. eccc. uni- trier, de / eccc.Google Scholar
- Gol95.Oded Goldreich. Foundations of Cryptography (Fragments of a Book). Weizmann Institute of Science, 1995. Available, along with revised version 1/98, from http:// www. wisdom, weizmann, ac. 51 / ~oded. Google ScholarDigital Library
- Gol97a.Oded Goldreich. A computational perspective on sampling (survey). Available from http: / / www. wis dora. wel zmann, ac. i 1 / ~odor/, May 1997.Google Scholar
- Gol97b.Oded Goldreich. Three XOR lemmas- an exposition. Available from http://www.wisdom.weizmann.ac, il/ -oded/, November 1997.Google Scholar
- Gol98.Oded Goldreich. Modern Cryptography, Probabifistic Proofs and Pseudorandomness, June 1998. To be published by Springer. Google ScholarDigital Library
- GRS98.Oded Goldreich, Ronitt Rubinfeld, and Madhu Sudan. Learning polynomials with queries- the highly noisy case. Technical Report TR98~060, Electronic Colloquium on Computational Complexity, 1998. Preliminary version in FOC$ '95. Google ScholarDigital Library
- GS92.Peter Gemmell and Madhu Sudan. Highly resilient correctors for polynomials. Information Processing Letters, 43(4): 169- 174, 28 September 1992. Google ScholarDigital Library
- GS98.Venkatesan Guruswami and Madhu Sudan. Improved decoding of Reed-Solomon and algebraic-geometric codes. Technical Report 98--043, Electronic Colloquium on Computalional Complexity, 1998. Preliminary version in FOCS '98. Google ScholarDigital Library
- HILL98.J. H,Sstad, R. Impagliazzo, L. Levin, and M. Luby. A pseudorandom generator from any one-way function. To appear in SIAM J. on Computing, 1998.Google Scholar
- Imp95.Russell Impagliazzo. Hard-core distributions for somewhat hard problems. In 36th Annual Symposium on Foundations of Computer Science, pages 538-545, Milwaukee, Wisconsin, 23-25 October 1995. IEEE. Google ScholarDigital Library
- IW97.Russell Impagliazzo and Avi Wigderson. P = BPP if E requires exponential circuits: Derandomizing the XOR !emma. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 220---229, E1 Paso, Texas, 4-6 May 1997. Google ScholarDigital Library
- IW98.Russell Impagtiazzo and Avi Wigderson. Randomness vs. time: De-randorrdzation under a uniform assumption. In 36th Annual Symposium on Foundations of Computer Science, Polo Alto, CA, November 8-11 1998. IEEE. Google ScholarDigital Library
- KS98.S. Ravi Kumar and D. Sivakumar. Personal communication, October 1998.Google Scholar
- KvM98.Adam Klivans and Dieter van Melkebeek. Graph nonisomorphism has subexponenfial size proofs unless the polynomiallime hierarchy collapses. Technical Report TR-98-12, University of Chicago, Department of Computer Science, December 1998. Extended abstract in these proceedings. Google ScholarDigital Library
- Lip89.Richard Lipton. New directions in testing. In Proceedings of DIMACS Workshop on Distributed Computing and Cryptography, 1989.Google Scholar
- NW94.Noam Nisan and Avi Wigderson. Hardness vs randomness. Journal of Compute r and System Sciences, 49(2): 149-167, October 1994. Google ScholarDigital Library
- NZ96.Noam Nisan and David Zuckerman. Randomness is linear in apace. Journal of Computer and System Sciences, 52(1):43- 52, February 1996. Google ScholarDigital Library
- STV98.Madhu Sudan, Luca Trevisan, and Salil Vadhan. Pseudorandom generators without the XOR temma. Technical Report TR98-074, Electronic Colloquium on Computational Complexity, December 1998. http://www.eccc.uni-trier, de/eccc. Google ScholarDigital Library
- Sud97.Madhu Sudan. Decoding of Reed SoIomon codes beyond the error-correction bound. Journal of Complexity, 13(1):I 80- 193, March 1997. Google ScholarDigital Library
- Tre98.Luca Trevisan. Constructions of near-optimal extractors using pseudo-random generators. Technical Report TR98-055, Electronic Colloquium on Computational Complexity, 1998. Extended abstract in these proceedings.Google Scholar
- Vaz85.Umesh V. Vazirani. Towards a strong communication complexity theory or generat/ng quasi-random sequences from two communicating slightly-random sources (extended abstract). In Proceedings of the SeventeenthAnnual ACM Symposium on Theory of Computing, pages 366-378, Providence, Rhode Island, 6-8 May 1985. Google ScholarDigital Library
- Wig98.Avi Wigderson. Personal communication, October 1998.Google Scholar
- Yao82.Andrew C. Yao. Theory and applications of trapdoor functions (extended abstracl). In 23rd Annual Symposium on Foundations of Computer Science, pages 80--.91, Chicago, Illinois, 3-5 November 1982. IEEE.Google Scholar
- Zuc96.David Zuckerman. Simulating BPP using a general weak random source. Algorithmica, 16(415):367-391, October/November 1996.Google ScholarCross Ref
Index Terms
- Pseudorandom generators without the XOR Lemma (extended abstract)
Recommendations
Pseudorandom Generators without the XOR Lemma
Special issue on the fourteenth annual IEE conference on computational complexityR. Impagliazzo and A. Wigderson (1997, in “Proceedings of the twenty-ninth Annual ACM Symposium on Theory of Computing,” pp. 220 229) have recently shown that if there exists a decision problem solvable in time 2O(n) and having circuit complexity 2 (n) (...
Pseudorandom Generators without the XOR Lemma
COCO '99: Proceedings of the Fourteenth Annual IEEE Conference on Computational ComplexityImpagliazzo and Wigderson (STOC 97) have recently shown that if there exists a decision problem solvable in time 2^{O(n)} and having circuit complexity 2^{Omega(n)} (for all but finitely many n) then P=BPP. This result is a culmination of a series of ...
Paradigms for Unconditional Pseudorandom Generators
This is a survey of unconditional pseudorandom generators (PRGs). A PRG uses a short, truly random seed to generate a long, "pseudorandom" sequence of bits. To be more specific, for each restricted model of computation (e.g., bounded-depth circuits or ...
Comments