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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers
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by R. Kannan, A. K. Lenstra and L. Lovász PDF
Math. Comp. 50 (1988), 235-250 Request permission

Abstract:

We show that the binary expansions of algebraic numbers do not form secure pseudorandom sequences; given sufficiently many initial bits of an algebraic number, its minimal polynomial can be reconstructed, and therefore the further bits of the algebraic number can be computed. This also enables us to devise a simple algorithm to factor polynomials with rational coefficients. All algorithms work in polynomial time.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 50 (1988), 235-250
  • MSC: Primary 68Q20; Secondary 11A51, 11A63, 11J99, 11Y16, 68Q25
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0917831-4
  • MathSciNet review: 917831