Construction of Logarithm Tables for Galois Fields

Autor/inn/en	Torres-Jimenez, Jose; Rangel-Valdez, Nelson; Gonzalez-Hernandez, Ana Loreto; Avila-George, Himer
Titel	Construction of Logarithm Tables for Galois Fields
Quelle	In: International Journal of Mathematical Education in Science and Technology, 42 (2011) 1, S.91-102 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Numbers; Mathematics Instruction; Tables (Data); Arithmetic; Multiplication; Mathematics Education; Computation; Foreign Countries; Universities; College Mathematics; Spain + Suchen Sie Ihr Suchwort? Zahlenraum; Mathematics lessons; Mathematikunterricht; Tabelle; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Multiplikation; Mathematische Bildung; Ausland; University; Universität; Spanien
Abstract	A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on logarithm and antilogarithm tables. A primitive element of a GF(p[superscript n]) is a key part in the construction of such tables, but it is generally hard to find a primitive element for arbitrary values of p and n. This article presents a naive algorithm that can simultaneously find a primitive element of GF(p[superscript n]) and construct its corresponding logarithm and antilogarithm tables. The proposed algorithm was tested in GF(p[superscript n]) for several values of p and n; the results show a good performance, having an average time of 0.46 seconds to find the first primitive element of a given GF(p[superscript n]) for values of n = {2, 3, 4, 5, 8, 12} and prime values p between 2 and 97. (Contains 6 tables.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10