Abstract
We describe a method that transforms every perfect random number generator into one that can be accelerated by parallel evaluation. Our method of parallelization is perfect, m parallel processors speed the generation of pseudo-random bits by a factor m; these parallel processors need not to communicate. Using sufficiently many parallel processors we can generate pseudo-random bits with nearly any speed. These parallel generators enable fast retrieval of substrings of very long pseudo-random strings. Individual bits of pseudo-random strings of length 1020 can be accessed within a few seconds. We improve and extend the RSA-random number generator to a polynomial generator that is almost as efficient as the linear congruential generator. We question the existence of polynomial random number generators that are perfect and use a prime modulus.
Research performed while visiting the Department of Computer Science of the University of Chicago. MIT — Patent Pending
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References
Alexi, W., Chor, B., Goldreich, O., and Schnorr, C.P.: RSA and Rabin Functions: certain parts are as hard as the whole. Proceeding of the 25th Symposium on Foundations of Computer Science, 1984, pp. 449–457; also: Siam Journal on Comput., 17,2 (1988).
Blum, L., Blum, M. and Shub, M.: A simple unpredictable pseudo-random number generator. Siam J. on Computing (1986), pp. 364–383.
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.
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.
Knuth D.E.: The Art of Computer Programming. Vol. 2, second edition. Addison Wesley (1981).
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 (1985) pp. 356–363.
Pollard J.: private communication (1988).
Stern, J.: Secret linear congruential generators are not cryptographically secure. Proceedings of the 28th IEEE-Symposium on Foundations of Computer Science (1987) pp. 421–426.
Stiefel, E.: Einführung in die numerische Mathematik. Teubner, Stuttgart (1969).
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.
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© 1990 Springer-Verlag Berlin Heidelberg
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Micali, S., Schnorr, C.P. (1990). Efficient, Perfect Random Number Generators. In: Goldwasser, S. (eds) Advances in Cryptology — CRYPTO’ 88. CRYPTO 1988. Lecture Notes in Computer Science, vol 403. Springer, New York, NY. https://doi.org/10.1007/0-387-34799-2_14
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DOI: https://doi.org/10.1007/0-387-34799-2_14
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