Multiplication of polynomials modulo xn

Authors:
Murat Cenk;Ferruh Özbudak
Affiliations:
Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey
Venue:
Theoretical Computer Science
Year:
2011

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Note: A note on the paper by Murat Cenk and Ferruh Ozbudak “Multiplication of polynomials modulo xn”, Theoret. Comput. Sci. 412 (2011) 3451-3462

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Abstract

Let n,@? be positive integers with @?@?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^@? 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.