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On the Construction of Random Number Generators and Random Function Generators

  • C. P. Schnorr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 330)

Abstract

Blum, Micali (1982), Yao (1982), Goldreich, Goldwasser and Micali (1984), and Luby, Rackoff (1986) have constructed random number generators, random function generators and random permutation generators that are perfect if certain complexity assumptions hold. We propose random number generators that pass all statistical tests that depend on a small fraction of the bitstring. This does not rely on any unproven hypothesis. We propose improved random function generators with short function names and which minimize the number of pseudo-random bits that are necessary for the evaluation of pseudo-random functions. We announce a new very efficient perfect random number generator.

Keywords

Random Number Generator 25th IEEE Symposium Oracle Query Congruential Generator Random Function Generator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alexi, W., Chor, B., Goldreich, O., and Schnorr, C.P.: RSA and Rabin Functions: certain parts a r e a s hard as the whole. Proceeding of the 25th Symposium on Foundations of Computer Science, 1984, pp. 449–457; also: Siam Journal on Comput., (1988).Google Scholar
  2. Blum, L., Blum, M. and Shub, M.: A simple unpredictable pseudo-random number generator. Siam J. on Computing (1986), pp. 364–383.Google Scholar
  3. Blum, M. and Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. Proceedings of the 25th IEEE Symposium on Foundations of Computer Science, IEEE, New York (1982); also Siam J. Comput. 13 (1984) pp. 850–864.Google Scholar
  4. Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. Proceedings of the 25th IEEE Symposium on Foundations of Computer Science, IEEE, New York. (1984); also Journal ACM 33,4 (1986) pp. 792–807.Google Scholar
  5. Luby, M. and Rackoff, Ch.: Pseudo-random permutation generators and cryptographic composition. Proceedings of the 18th ACM Symposium on the Theory of Computing, ACM, New York (1986) pp. 356–363.Google Scholar
  6. Micali, S. and Schnorr, C.P.: Efficient, perfect random number generators. preprint MIT, Universität Frankfurt 1988.Google Scholar
  7. Yao, A.C.: Theory and applications of trapdoor functions. Proceedings of the 25th IEEE Symposium on Foundations of Computer Science, IEEE, New York (1982). PP. 80–91.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • C. P. Schnorr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität FrankfurtFrankfurtWest Germany

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