Bit-Parallel Cubing Computation over GF(3m) for Irreducible Trinomials

Sun-Mi PARK  Ku-Young CHANG  Dowon HONG  Changho SEO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.1   pp.347-353
Publication Date: 2014/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.347
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
finite field arithmetic,  pth powering,  characteristic three,  cubing,  trinomial,  cryptography,  

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We propose a parallel pth powering method over an arbitrary finite field GF(pm). Using the proposed method, we present the explicit formulae for the computation of cubing over a ternary field GF(3m) which is defined by irreducible trinomials. We show that the field cubing computation for irreducible trinomials, which plays an important role in calculating pairing, can be implemented very efficiently.