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

Authors:
R. Kannan, A. K. Lenstra and L. Lovász

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

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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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DOI:
https://doi.org/10.1090/S0025-5718-1988-0917831-4

Article copyright:
© Copyright 1988
American Mathematical Society