JOACItIM VON ZUR GATHEN
نویسنده
چکیده
2 • • • , o q r L 1 I fFq C_ Fq, are finite fields, a E Fq, , and the conjugates a, aq , aq , of a form a basis for Fq, as a vector space over Fq, then this is called a normal basis. We call a a normal element (of Fq. over Fq). Normal bases are useful for implementing fast ari thmetic in Fq, , in par t icular exponentlation. Of special interest is q = 2 and n reasonably large; as an example, the Diffie &: t tel lman key exchange is based on exponentiat ion in F2-. Algori thms and possible MOS implementat ions are given in Laws ~ Rushforth 1971, Wang et al. 1985, Beth et al. 1986, Agnew et al. 1988, Stinson 1990. The basic assumpt ion in tha t work is tha t comput ing qth powers in Fq, is for free (i.e., of negligible cost compared to a general multiplication in Fq, ; only q = 2 is considered). The assumption can be justified if a normal element is given, since then for an a rb i t r a ry q ' ~l = r'-,o<_i<~ uia E Fq., with uo . . . . . u~i E Fq, we helve
منابع مشابه
Multiplicative Order of Gauss Periods
We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of J. von zur Gathen and I. E. Shparlinski.
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