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

R. Kannan, A. K. Lenstra, L. Lovász

Research output: Contribution to journalArticle

35 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)235-250
Number of pages16
JournalMathematics of Computation
Volume50
Issue number181
DOIs
Publication statusPublished - Jan 1988

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ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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