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ERIC Number: EJ908762
Record Type: Journal
Publication Date: 2011-Jan
Pages: 12
Abstractor: As Provided
Reference Count: 12
ISSN: ISSN-0020-739X
Construction of Logarithm Tables for Galois Fields
Torres-Jimenez, Jose; Rangel-Valdez, Nelson; Gonzalez-Hernandez, Ana Loreto; Avila-George, Himer
International Journal of Mathematical Education in Science and Technology, v42 n1 p91-102 Jan 2011
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.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Spain