caa a22 4500 475807405 CHVBK 20180406123750.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1008389508626 doi (NATIONALLICENCE)springer-10.1023/A:1008389508626 Parallel Multiplication in GF(2k) using Polynomial Residue Arithmetic [Elektronische Daten] [A. Halbutogullari, C. Koc] We present a novel method of parallelization of the multiplication operation in GF(2k) for an arbitrary value of k and arbitrary irreducible polynomial n(x) generating the field. The parallel algorithm is based on polynomial residue arithmetic, and requires that we find L pairwise relatively prime modulim i(x) such that the degree of the product polynomialM(x)=m 1(x)m 2(x)··· mL(x) is at least 2k. The parallel algorithm receives the residue representations of the input operands (elements of the field) and produces the result in its residue form, however, it is guaranteed that the degree of this polynomial is less than k and it is properly reduced by the generating polynomial n(x), i.e., it is an element of the field. In order to perform the reductions, we also describe a new table lookup based polynomial reduction method. Kluwer Academic Publishers, 2000 Finite field multiplication nationallicence residue arithmetic nationallicence parallel algorithm nationallicence cryptography nationallicence Halbutogullari A. Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut Koc C. Electrical & Computer Engineering, Oregon State University, 97331, Corvallis, Oregon aut Designs, Codes and Cryptography Kluwer Academic Publishers 20/2(2000-06-01), 155-173 0925-1022 20:2<155 2000 20 10623 https://doi.org/10.1023/A:1008389508626 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008389508626 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Halbutogullari A. Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100, Potenza, (Italy) aut NATIONALLICENCE 700 1- Koc C. Electrical & Computer Engineering, Oregon State University, 97331, Corvallis, Oregon aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 20/2(2000-06-01), 155-173 0925-1022 20:2<155 2000 20 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer