A fast deterministic algorithm for factoring polynomials over finite fields of small characteristic

We present a new algorithm for factoring polynomials over finite fields. Our algorithm is deterministic, and its running time is “almost” quadratic when the characteristic is a small fixed prime. As such, our algorithm is asymptotically faster than previously known deterministic algorithms for factoring polynomials over finite fields of small characteristic.

[1]  E. Berlekamp.  Factoring polynomials over large finite fields* , 1970, SYMSAC '71.

[2]  D. A. Burgess.  A Note on the Distribution of Residues and Non-Residues , 1963 .

[3]  Victor Shoup.  On the Deterministic Complexity of Factoring Polynomials over Finite Fields , 1990, Inf. Process. Lett..

[4]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[5]  Walter Baur,et al.  The Complexity of Partial Derivatives , 1983, Theor. Comput. Sci..

[6]  Allan Borodin,et al.  The computational complexity of algebraic and numeric problems , 1975, Elsevier computer science library.

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

[8]  Robert T. Moenck,et al.  On the efficiency of algorithms for polynomial factoring , 1977 .

[9]  Erich Kaltofen,et al.  Solving systems of nonlinear polynomial equations faster , 1989, ISSAC '89.

[10]  Paul Camion.  Improving an algorithm for factoring polynomials over a finite field and constructing large irreducible polynomials , 1983, IEEE Trans. Inf. Theory.

[11]  David G. Kirkpatrick,et al.  Addition Requirements for Matrix and Transposed Matrix Products , 1988, J. Algorithms.

[12]  Joachim von zur Gathen,et al.  Factoring Polynomials and Primitive Elements for Special Primes , 1987, Theor. Comput. Sci..

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