**ERIC Number:**EJ908762

**Record Type:**Journal

**Publication Date:**2011-Jan

**Pages:**12

**Abstractor:**As Provided

**Reference Count:**12

**ISBN:**N/A

**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.)

Descriptors: Numbers, Mathematics Instruction, Tables (Data), Arithmetic, Multiplication, Mathematics Education, Computation, Foreign Countries, Universities, College Mathematics

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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