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A C implementation of Niederreiter's algorithm for factoring poly- nomials over F2 is described. The most time-consuming part of this algo- rithm, which consists of setting up and solving a certain system of linear equa- tions, is performed in parallel. Once a basis for the solution space is found, all irreducible factors of the polynomial can be extracted by suitable gcd- computations. For this purpose, asymptotically fast polynomial arithmetic algorithms are implemented. These include Karatsuba & Ofman multiplica- tion, Cantor multiplication and Newton inversion. In addition, a new ecient version of the half-gcd algorithm is presented. Sequential run times for the polynomial arithmetic and parallel run times for the factorization are given. A new \world record" for polynomial factorization over the binary eld is set by showing that a pseudo-randomly selected polynomial of degree 3 can be factored in about 10 hours on 256 nodes of the IBM SP2 at the Cornell Theory Center.

Factoring high-degree polynomials over $\mathbf F_2$ with Niederreiter's algorithm on the IBM SP2