منابع مشابه
Normal bases via general Gauss periods
Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive rth root of unity, one obtains under certain conditions a normal basis for Fqn over Fq, where r is a prime and nk = r− 1 for some integer k. We generalize this construction by allowing arbitrary integers r with nk = φ(r), and find in many cases smaller values of k than i...
متن کاملAbelian Groups, Gauss Periods, and Normal Bases
A result on finite abelian groups is first proved and then used to solve problems in finite fields. Particularly, all finite fields that have normal bases generated by general Gauss periods are characterized and it is shown how to find normal bases of low complexity. Dedicated to Professor Chao Ko on his 90th birthday.
متن کاملGauss periods as constructions of low complexity normal bases
Optimal normal bases are special cases of the so-called Gauss periods (Disquisitiones Arithmeticae, Articles 343-366); in particular, optimal normal bases are Gauss periods of type (n,1) for any characteristic and type (n,2) for characteristic 2. We present the multiplication tables and complexities of Gauss periods of type (n, t) for all n and t = 3,4,5 over any finite field and give a slightl...
متن کاملMultiplicative 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.
متن کاملGauss periods: orders and cryptographical applications
Experimental results on the multiplicative orders of Gauss periods in finite fields are presented. These results indicate that Gauss periods have high order and are often primitive (self-dual) normal elements in finite fields. It is shown that Gauss periods can be exponentiated in quadratic time. An application is an efficient pseudorandom bit generator.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1999
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-99-00988-6