Open AccessComputing p th roots in extended finite fields of prime characteristic p ≥ 2
Author(s) -
Repka M.
Publication year - 2016
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2015.4141
Subject(s) - finite field , computation , mathematics , prime (order theory) , inversion (geology) , reduction (mathematics) , matrix (chemical analysis) , characteristic polynomial , polynomial , algebra over a field , discrete mathematics , pure mathematics , algorithm , combinatorics , mathematical analysis , geometry , structural basin , paleontology , materials science , composite material , biology
Direct computation of p th roots in extended finite fields of characteristic p ≥ 2 is introduced, wherein the reduction polynomial is irreducible and can be even random. Proposed method works in any case of p ≥ 2 and finite field extension. This method is the most efficient, it is even more efficient than the method, which is widely used, based on inversion of squaring matrix utilised in the case of p = 2. This method is more efficient regarding the computation and storing of the matrix as well as the computation of the roots.