On the efficiency of algorithms for polynomial factoring
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- by Robert T. Moenck PDF
- Math. Comp. 31 (1977), 235-250 Request permission
Abstract:
Algorithms for factoring polynomials over finite fields are discussed. A construction is shown which reduces the final step of Berlekamp’s algorithm to the problem of finding the roots of a polynomial in a finite field ${Z_p}$. It is shown that if the characteristic of the field is of the form $p = L \cdot {2^l} + 1$, where $l \simeq L$, then the roots of a polynomial of degree n may be found in $O({n^2}\log p + n{\log ^2}p)$ steps. As a result, a modification of Berlekamp’s method can be performed in $O({n^3} + {n^2}\log p + n{\log ^2}p)$ steps. If n is very large then an alternative method finds the factors of the polynomial in $O({n^2}{\log ^2}n + {n^2}\log n\log p)$. Some consequences and empirical evidence are discussed.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 235-250
- MSC: Primary 12-04; Secondary 68A10, 68A20
- DOI: https://doi.org/10.1090/S0025-5718-1977-0422193-8
- MathSciNet review: 0422193