Title :
Polynomial Multiplication over Finite Fields Using Field Extensions and Interpolation
Author :
Cenk, Murat ; Koç, Çetin Kaya ; Özbudak, Ferruh
Author_Institution :
Dept. of Math. & Comput. Sci., Cankaya Univ., Ankara, Turkey
Abstract :
A method for polynomial multiplication over finite fields using field extensions and polynomial interpolation is introduced. The proposed method uses polynomial interpolation as Toom-Cook method together with field extensions. Furthermore, the proposed method can be used when Toom-Cook method cannot be applied directly. Explicit formulae improving the previous results in many cases are obtained.
Keywords :
interpolation; polynomials; Toom-Cook method; field extensions; finite fields; polynomial interpolation; polynomial multiplication; Algorithm design and analysis; Computer science; Digital arithmetic; Educational institutions; Galois fields; Interpolation; Mathematics; Modules (abstract algebra); Polynomials; USA Councils; Finite fields; Karatsuba; Montgomery multiplications; Toom-Cook; extension fields;
Conference_Titel :
Computer Arithmetic, 2009. ARITH 2009. 19th IEEE Symposium on
Conference_Location :
Portland, OR
Print_ISBN :
978-0-7695-3670-5
DOI :
10.1109/ARITH.2009.11
