Abstract
Allender [All89] showed that if there are dense P languages containing only a finite set of Kolmogorov-simple strings, then all pseudorandom generators are insecure. We extend this by proving that if there are dense P (or even BPP) languages containing only a sparse set of Kolmogorovsimple strings, then all pseudorandom generators are insecure.
Supported in part by grants NSF-CCR-8957604, NSF-INT-9116781/JSPS-ENG-207, and NSF-CCR-9322513.
Work done in part while visiting the University of Electro-Communications-Tokyo.
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E. Allender. Some consequences of the existence of pseudorandom generators, preliminary version. In Proceedings of the 19th ACM Symposium on Theory of Computing, pages 151–159, 1987.
E. Allender. Some consequences of the existence of pseudorandom generators. Journal of Computer and System Sciences, 39:101–124, 1989.
E. Allender. Applications of time-bounded kolmogorov complexity in complexity theory. In O. Watanabe, editor, Kolmogorov Complexity and Computational Complexity, EATCS Monographs on Theoretical Computer Science, pages 4–22. Springer-Verlag, 1992.
R. Boppana and R. Hirschfeld. Pseudorandom generators and complexity classes. In Advances in Computing Research, volume 5, pages 1–26. JAI Press Inc., 1989.
M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science, pages 112–117, 1982. Final version appears as [BM84].
M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM Journal on Computing, 13(4):850–864, 1984.
R. Gavaldà and J. Balcázar. Strong and robustly strong polynomial-time reducibilities to sparse sets. Theoretical Computer Science, 88:1–14, 1991.
J. Gill. Computational complexity of probabilistic Turing machines. SIAM Journal on Computing, 6(4):675–695, 1977.
O. Goldreich, H. Krawczyk, and M. Luby. On the existence of pseudorandom generators. SIAM Journal on Computing, 22(6):1163–1175, 1993.
J. Hartmanis. Generalized Kolmogorov complexity and the structure of feasible computations. In Proceedings of the 24th IEEE Symposium on Foundations of Computer Science, pages 439–445. IEEE Computer Society Press, 1983.
J. Håstad. Pseudo-random generators under uniform assumptions. In Proceedings of the 22nd ACM Symposium on Theory of Computing, pages 395–404, 1990.
J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.
R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random generation from oneway functions. In Proceedings of the 21st ACM Symposium on Theory of Computing, pages 12–24, 1989.
L. Levin. Randomness conservation inequalities; information and independence in mathematical theories. Information and Control, 61:15–37, 1984.
L. Levin. One way functions and pseudorandom generators. Combinatorica, 7(4):357–363, 1987.
M. Li and P. Vitanyi. An Introduction to Kolmogorov Complexity and Its Applications. Springer-Verlag, 1993.
M. Sipser. A complexity theoretic approach to randomness. In Proceedings of the 15th ACM Symposium on Theory of Computing, pages 330–335, 1983.
A. Yao. Theory and applications of trapdoor functions. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science, pages 80–91, 1982.
S. Zachos and H. Heller. A decisive characterization of BPP. Information and Control, 69:125–135, 1986.
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Han, Y., Hemaspaandra, L.A. (1995). Pseudorandom generators and the frequency of simplicity. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_61
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DOI: https://doi.org/10.1007/3-540-59042-0_61
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