Abstract
A summary is given of an algorithm, published in [4], that uses lattice reduction to handle the combinatorial problem in the factoring algorithm of Zassenhaus. Contrary to Lenstra, Lenstra and Lovász, the lattice reduction is not used to calculate coefficients of a factor but is only used to solve the combinatorial problem, which is a problem with much smaller coefficients and dimension. The factors are then constructed efficiently in the same way as in Zassenhaus’ algorithm.
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References
H. Zassenhaus, On Hensel Factorization, I., Journal of Number Theory 1, 291–311 (1969).
A.K. Lenstra, H.W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261, 515–534 (1982).
V. Miller, Factoring polynomials via Relation-Finding. ISTCS’92, Springer Lecture Notes in Computer Science 601, 115–121 (1992).
M. van Hoeij, Factoring polynomials and the knapsack problem, preprint available from http://www.math.fsu.edu/~hoeij/ accepted for Journal of Number Theory (2000).
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© 2001 Springer-Verlag Berlin Heidelberg
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van Hoeij, M. (2001). Factoring Polynomials and 0—1 Vectors. In: Silverman, J.H. (eds) Cryptography and Lattices. CaLC 2001. Lecture Notes in Computer Science, vol 2146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44670-2_5
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DOI: https://doi.org/10.1007/3-540-44670-2_5
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