Literaturnachweis - Detailanzeige
| Autor/in | Farag, Mark |
|---|---|
| Titel | Hill Ciphers over Near-Fields |
| Quelle | In: Mathematics and Computer Education, 41 (2007) 1, S.46-54 (9 Seiten)
PDF als Volltext |
| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
| ISSN | 0730-8639 |
| Schlagwörter | Mathematics Instruction; Coding; Algebra; Geometric Concepts; Matrices; Equations (Mathematics); Mathematical Formulas; Mathematical Logic; Demonstrations (Educational) |
| Abstract | Hill ciphers are linear codes that use as input a "plaintext" vector [p-right arrow above] of size n, which is encrypted with an invertible n x n matrix E to produce a "ciphertext" vector [c-right arrow above] = E [middle dot] [p-right arrow above]. Informally, a near-field is a triple [left angle bracket]N; +, *[right angle bracket] that satisfies all the axioms of a field with the possible exception of one distributive law and the commutativity of *. Formally, a (left) near-field [left angle bracket]N; +, *[right angle bracket] is a nonempty set N together with binary operations + and * for which [left angle bracket]N, +[right angle bracket] is a group with identity element denoted by 0[subscript N], [left angle bracket]N; *[right angle bracket] is a monoid, [left angle bracket]N / [left curley bracket]0[subscript N][right curley bracket], *[right angle bracket] is a group, and for any a,b,c [is a member of] N, a*(b+c) = a*b + a*c holds. Right near-fields may be defined analogously by substituting the right distributive law for the left distributive law. This paper discusses matrices over near-fields, explains coding matrices over near-fields, and presents three projects in coding matrices over near-fields. (ERIC). |
| Anmerkungen | MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2017/4/10 |
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