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

R. Kannan, A. K. Lenstra, L. Lovász

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

Manuel Ilium raised the following interesting question : suppose we are given an approximate root of an unknown polynomial with integer coefficients and a bound on the degree and maguitude of the coefficients of the polynomial. Is it possible to infer the polynomial ? we answer his question in the affirmative. We are able to show that if a complex number α satisfies an irredueible primitive polynomial p(x) off degree d with integer coefficients each of magnitude at most H then given O(d2 + d. loglI) bits off time binary expansion of the real and complex parts of , we can find p(x) in deterministic polynomial time (and then compute in polytJomlal time arty further bit of c). Using the concept o! secure pseudo random sequences formulated by Blunt, Micali and Yao we show then that the binary (oz p-ary for arty p) expansions of algebraic numbers do not, from secure sequences in a certain well delined sence.

Original languageEnglish
Title of host publicationProceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984
PublisherAssociation for Computing Machinery
Pages191-200
Number of pages10
ISBN (Electronic)0897911334
DOIs
Publication statusPublished - Dec 1 1984
Event16th Annual ACM Symposium on Theory of Computing, STOC 1984 - Washington, United States
Duration: Apr 30 1984May 2 1984

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference16th Annual ACM Symposium on Theory of Computing, STOC 1984
CountryUnited States
CityWashington
Period4/30/845/2/84

Fingerprint

Factorization
Polynomials

ASJC Scopus subject areas

  • Software

Cite this

Kannan, R., Lenstra, A. K., & Lovász, L. (1984). Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984 (pp. 191-200). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/800057.808681

Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. / Kannan, R.; Lenstra, A. K.; Lovász, L.

Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Association for Computing Machinery, 1984. p. 191-200 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kannan, R, Lenstra, AK & Lovász, L 1984, Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. in Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 191-200, 16th Annual ACM Symposium on Theory of Computing, STOC 1984, Washington, United States, 4/30/84. https://doi.org/10.1145/800057.808681
Kannan R, Lenstra AK, Lovász L. Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Association for Computing Machinery. 1984. p. 191-200. (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/800057.808681
Kannan, R. ; Lenstra, A. K. ; Lovász, L. / Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984. Association for Computing Machinery, 1984. pp. 191-200 (Proceedings of the Annual ACM Symposium on Theory of Computing).
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