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ITS » Undergraduate Theses » Matematika
Posted by astutiknq@its.ac.id at 05/04/2010 18:04:11  •  2687 Views


THE STUDY OF GENERAL LINEAR GROUP

Author :
Hidayah, Zumrotul ( 1205100066 )




ABSTRAK

Suatu teknik kriptografi yaitu Hill cipher menggunakan matriks bujur sangkar sebagai kunci untuk menyandikan 26 huruf abjad. Kriptografi ini sederhana dan berkecepatan tinggi tetapi memiliki kesulitan untuk mendapatkan matriks kunci yang dapat diinverskan atas Z26. Kesulitan ini bisa diatasi dengan menyediakan ruang kunci berisi matriks-matriks bujur sangkar yang semuanya invertible. Ruang kunci semacam ini disebut grup linear umum atas field berhingga. Salah satunya GLn Z29. Pada penelitian ini dibahas mengenai definisi sifat dan order grup linear umum khususnya order grup linear umum atas field berhingga. Kemudian dijelaskan aplikasi order grup tersebut pada kriptografi Hill. Dengan mengambil GLn Z29 sebagai ruang kunci berarti teknik kriptografi Hill diterapkan pada persandian 29 karakter. Oleh karena itu pada penelitian ini dijelaskan pula teknik persandian baru yaitu persandian 29 karakter yang terdiri dari 26 karakter abjad ditambah karakter titik . tanda tanya dan spasi _.


ABSTRACT

A cryptography technique i.e. Hill cipher uses the square matrices as the key to encipher and decipher 26 upper-case letters of the English alphabet. This cryptography is simplicity and high speed but it has difficulty to get the invertible key matrix over Z26. This difficulty can be overcome by making available the keyspace which contains the square matrices all of them are invertible. This keyspace is called general linear group over finite field. One of this keyspace is GLn Z29. In this research we discuss about definition characteristic and order of the general linear group especially order of the general linear group over finite field. Then we explain an application of the order of this group in Hill cipher. By taking GLn Z29 to be the keyspace thus Hill cipher is put on the encryption and decryption of 29 characters. Therefore in this research we also explain a new technique of cryptography i.e. encryption and decryption of 29 characters contained 26 upper-case letters of the English alphabet added by the period . the question mark and the blank space _.



KeywordsField; Grup linear umum; Hill cipher; Kriptografi; Matriks invertible
 
Subject:  Kriptografi
Contributor
  1. Dr. SUBIONO, MS
Date Create: 05/04/2010
Type: Text
Format: pdf
Language: Indonesian
Identifier: ITS-Undergraduate-3100010038658
Collection ID: 3100010038658
Call Number: RSMa 005.82 Hid k


Source
Undergraduate Theses of Mathematics Department, RSMa 005.82 Hid k, 2009

Coverage
ITS Community Only

Rights
Copyright @2009 by ITS Library. This publication is protected by copyright and permission should be obtained from the ITS Library prior to any prohibited reproduction, storage in a retrievel system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to ITS Library




[ Download - Open Access ]

  1.  ITS-Undergraduate-9168-1205100066-Abstract_id.pdf - 11 KB
  2.  ITS-Undergraduate-9168-1205100066-Abstract_en.pdf - 11 KB
  3.  ITS-Undergraduate-9168-1205100066-Conclusion.pdf - 14 KB




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