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

It is shown 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 the authors to devise a simple algorithm to factorise polynomials with rational coefficients. All algorithms work in polynomial time


Published in:
Mathematics of Computation, 50, 181, 235 - 50
Year:
1988
ISSN:
0025-5718
Keywords:
Laboratories:




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