Arithmetic and factorization of polynomial over F2 (extended abstract)

We describe algorithms for polynomial multiplication and polynomial factorization over the binary field IF2.and their implementation. They allow polynomials of degree up to 100,000 to be factored in about one dqy of CPU time.

[1]  Philippe Flajolet,et al.  Random Polynomials and Polynomial Factorization , 1996, ICALP.

[2]  Joachim von zur Gathen,et al.  Arithmetic and factorization of polynomials over F_2 , 1996, ISSAC 1996.

[3]  Anatolij A. Karatsuba,et al.  Multiplication of Multidigit Numbers on Automata , 1963 .

[4]  Michael Ben-Or,et al.  Probabilistic algorithms in finite fields , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[5]  Joachim von zur Gathen,et al.  Berlekamp's and niederreiter's polynomial factorization algorithms , 1994 .

[6]  Victor Shoup,et al.  A New Polynomial Factorization Algorithm and its Implementation , 1995, J. Symb. Comput..

[7]  Erich Kaltofen,et al.  Factoring high-degree polynomials by the black box Berlekamp algorithm , 1994, ISSAC '94.

[8]  E. Berlekamp Factoring polynomials over finite fields , 1967 .

[9]  Volker Strassen,et al.  The computational complexity of continued fractions , 1981, SYMSAC '81.

[10]  Erich Kaltofen,et al.  Polynomial Factorization 1987-1991 , 1992, LATIN.

[11]  David Y. Y. Yun,et al.  On square-free decomposition algorithms , 1976, SYMSAC '76.

[12]  David G. Cantor,et al.  On arithmetical algorithms over finite fields , 1989, Journal of combinatorial theory. Series A.

[13]  E. Berlekamp Factoring polynomials over large finite fields* , 1971, SYMSAC '71.

[14]  D. Cantor,et al.  A new algorithm for factoring polynomials over finite fields , 1981 .

[15]  Joachim von zur Gathen,et al.  Computing Frobenius maps and factoring polynomials , 2005, computational complexity.

[16]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[17]  Joachim von zur Gathen,et al.  Computing Frobenius maps and factoring polynomials , 1992, STOC '92.

[18]  Donald E. Knuth,et al.  Analysis of a Simple Factorization Algorithm , 1976, Theor. Comput. Sci..

[19]  Erich Kaltofen,et al.  Subquadratic-time factoring of polynomials over finite fields , 1995, STOC '95.

[20]  Volker Strassen,et al.  The Computational Complexity of Continued Fractions , 1983, SIAM J. Comput..

[21]  David G. Gantor On arithmetical algorithms over finite fields , 1989 .

[22]  Keith O. Geddes,et al.  Algorithms for computer algebra , 1992 .