Download Billy Bunter On The Nile (Billy Bunter, Book 44) by Frank Richards PDF

By Frank Richards

One other Billy Bunter experience at Greyfriars university

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Additional info for Billy Bunter On The Nile (Billy Bunter, Book 44)

Sample text

Das heißt, es gibt ganze Zahlen s und t mit 1 = s ⋅ a + t ⋅ b . Erfreulicherweise kann man den euklidischen Algorithmus erweitern und so s und t bestimmen. 8=1⋅5+3 1 = −1 ⋅ 5 + 2 ⋅ (8 − 1 ⋅ 5) = 2 ⋅ 8 − 3 ⋅ 5 ⇒ 1 = 2 ⋅ 8 − 3 ⋅ 5 5=1⋅3+2 1 = 3 − 1 ⋅ (5 − 1 ⋅ 3) = −1 ⋅ 5 + 2 ⋅ 3 ⇑ 3=1⋅2+1 ⇒ 1=3−1⋅2 ⇑ Wenn man beim euklidischen Algorithmus unten bei 1 angekommen ist, stellt man die 1 als Differenz dar und geht von dort nach oben, indem man stets den letzten Rest ersetzt. Die Reste sind hier blau und grün dargestellt, damit man sie gut verfolgen kann.

Potenz zugeordnet (b). Der Wert 224 ist jeweils durch die waagerechte Gerade hervorgehoben Die reelle Potenzfunktion mit dem Exponenten 281 ist in Abb. 4 Kryptografische Verfahren 39 224 zustande kommt. Als Hilfe ist die waagerechte Gerade in der Höhe 224 eingetragen. Jeder Wert wird nur durch eine einzige Einsetzung erreicht. Dicht benachbarte Werte werden auch durch dicht benachbarte Einsetzungen erhalten. Genau wegen dieser Eigenschaft kann man eine Funktion stetig nennen. Im Gegensatz dazu ist die diskrete Potenzfunktion modulo 437 mit dem Exponenten 281 in Abb.

3 und 7 sind invers zueinander in Z∗10 , denn 3 ⋅ 7 ≡ 1. 10 2 und 4 sind invers zueinander in Z∗7 , denn 2 ⋅ 4 ≡ 1. 7 Das Wort invers kommt vom lateinischen Wort invertere, was umdrehen, zurückdrehen, umwenden bedeutet. Hiermit sind wir an dem tiefsinnigen Grund angekommen, warum die Kryptografie mit den Gruppen Z∗n funktioniert: Hier hat jedes Element ein Inverses und mit diesem kann eine verschlüsselte Zahl entschlüsselt werden. In der Vorschau auf Seite 18 sind e und d invers zueinander, ihr Produkt ist 1 in der Gruppe, die für die Exponenten relevant ist.

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