Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers

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Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers

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Annual ACM Symposium on Theory of Computing archive
Proceedings of the sixteenth annual ACM symposium on Theory of computing table of contents

Pages: 191 - 200

Year of Publication: 1984

ISBN:0-89791-133-4

Authors

R. Kannan
A. K. Lenstra
L. Lovász

Sponsor

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 46, Citation Count: 2

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	A.Baker, Linear forms in the logarithms of algebraic numbers I,II,III,IV Mathematika, 13(1966); 14(1967); 14(1967) and 15(1968)
	2	L.Blum, M.Blum and M.Shub A simple secure pseudo random number generator Crypto 82
	3	M.Blum and S.Micali, How to generate cryptographically strong sequences of pseudo random bits 23rd Annual symposium on the foundations of computer science (1982) pp112-117.
	4	Borel (Lecons sur la theorie des fonctions (2 nd edition 1914 pp182-216))
	5	Champernowne, Journal of the London Math. Soc. vol.8 pp254-260 1933).
	6	George E. Collins, Subresultants and Reduced Polynomial Remainder Sequences, Journal of the ACM (JACM), v.14 n.1, p.128-142, Jan. 1967 [doi>10.1145/321371.321381]
	7	Copeland and Erdös (Bulletin of the American Math Soc. 52 (1946) pp857-860)
	8	O.Goldreich, S.Goldwasser and S.Micali, How to construct random functions MIT/LCS/TM 244 (1984)
	9	S.Goldwasser, S.Micali and P.Tong, Why and how to establish a private code on a public network 23rd Annual symposium on the foundations of computer science (1982) pp134-144
	10	i.n.herstein, Topics in algebra 2nd edition Xerox (1975)
	11	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	12	Susan Landau , Gary Lee Miller, Solvability by radicals is in polynomial time, Proceedings of the fifteenth annual ACM symposium on Theory of computing, p.140-151, December 1983 [doi>10.1145/800061.808743]
	13	A.K.Lenstra, H.W.Lenstra and L.Lovász, Factoring polynomials with rational coefficients Mathematische Annalen 261(1982) pp513-534
	14	M. O. Rabin, PROBABILISTIC ALGORITHM IN FINITE FIELDS, Massachusetts Institute of Technology, Cambridge, MA, 1979
	15	A.Schönhage, The fundamental theorem of algebra in terms of computational complexity, manuscript (1982)
	16	Barry M. Trager, Algebraic factoring and rational function integration, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.219-226, August 10-12, 1976, Yorktown Heights, New York, United States [doi>10.1145/800205.806338]
	17	A.Yao, Theory and applications of trapdoor functions 23rd Annual symposium on the foundations of computer science (1982) pp80-91

CITED BY 2

	S. Ar , M. Blum , B. Codenotti , P. Gemmell, Checking approximate computations over the reals, Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, p.786-795, May 16-18, 1993, San Diego, California, United States
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003