Multiplication of polynomials modulo x(n)

Date

2011-07-01

Author

Cenk, Murat
Özbudak, Ferruh

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Let n, l be positive integers with l <= 2n - 1. Let R be an arbitrary nontrivial ring, not necessarily commutative and not necessarily having a multiplicative identity and R[x] be the polynomial ring over R. In this paper, we give improved upper bounds on the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(n) over R. Moreover, we introduce a new complexity notion, the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(l) over R. This new complexity notion provides improved bounds on the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(n) over R.

Subject Keywords

Multiplication of power series, Multiplication algorithms, Multiplicative complexity, Multiplication of polynomials

URI

https://hdl.handle.net/11511/30894

Journal

THEORETICAL COMPUTER SCIENCE

DOI

https://doi.org/10.1016/j.tcs.2011.02.031

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. Cenk and F. Özbudak, “Multiplication of polynomials modulo x(n),” THEORETICAL COMPUTER SCIENCE, pp. 3451–3462, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30894.