Abstract
In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of R(u)S(u) mod Q(u)l have multiplications of the form R(α j)S(α j) hence the algorithm requires large coefficients (as in l=1). Therefore using the identity R(u)S(u)=R(u)S(u) mod P(u) where degP(u)=2n − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of R(u)S(u) mod Q(u)l remains open.
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© 1986 Springer-Verlag Berlin Heidelberg
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Averbuch, A., Winograd, S., Galil, Z. (1986). Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_52
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DOI: https://doi.org/10.1007/3-540-16761-7_52
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