Title :
On "A new representation of elements of finite fields GF(2m) yielding small complexity arithmetic circuits"
Author :
Geiselmann, Willi ; Müller-Quade, Jörn ; Steinwandt, Rainer
Author_Institution :
Inst. fur Algorithmen und Kognitive Syst., Karlsruhe Univ., Germany
fDate :
12/1/2002 12:00:00 AM
Abstract :
For original article see G. Drolet, ibid., vol. 47, no. 9, p. 938-946, (Sept 1998). We characterize the smallest n with GF(2)[X]/(Xn + 1) containing an isomorphic copy of GF(2m). This characterization shows that the representation of finite fields described in a previous issue of the IEEE Transactions on Computers is not "optimal" as claimed. The representation considered there can often be improved significantly.
Keywords :
circuit complexity; digital arithmetic; logic design; residue number systems; Galois field arithmetic; VLSI implementation; characterization; finite field arithmetics; finite fields; small complexity arithmetic circuits; Arithmetic; Circuits; Galois fields; Hardware; Polynomials; Very large scale integration;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.2002.1146713
