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Finite Field Towers: Iterated Presentation and Complexity of Arithmetic

✍ Scribed by Valentine B. Afanassiev; Alexander A. Davydov

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 162 KB
Volume: 8
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0337

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✦ Synopsis

Finite "eld towers GF(q.) are considered, where P"p L p L 2 p LR R and all primes p G are distinct factors of (q!1). Under this condition irreducible binomials of the form x.!c can be used for recursive extension of "nite "elds. We give description of an in"nite sequence of irreducible binomials, new e!ective algorithms for fast multiplication and inversion in the tower, and "nite and asymptotic estimates of arithmetic complexity. It is important that the achievable asymptotic estimate of the complexity has the form O (log Q logKlog Q), Q"q., where log 5 51 and is the minimal factor of q!1.

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