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Computing in the composite GF (qm) of characteristic 2 formed by means of an irreducible binomial

Kościelny Cz.

Applied Mathematics and Computer Science

1998

Vol. 8, no 3

671-680

Since the operation of reduction modulo a polynomial needed for parallel computing in GF(qm) is the simplest possible in the case of a binomial, in this paper the main properties of irreducible binomials over GF(q) of characteristic 2 are given. It is shown that P(x) = xm - Po is irreducible over GF(q) for [ ... ] divides q-1. The method of performing all multiplicative operations in GF(qm) of characteristic 2 (multiplication, rising to an arbitrary power, multiplicative inversion) formed by means of an irreducible polynomial is also presented. The use of irreducible binomials may be attractive for those engineers and researches who deal with implementation of hardware and microprogrammed devices for computing in GF(qm), even if m and q are large.