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"Kriptografi merupakan ilmu yang mempelajari teknik-teknik matematika yang berhubungan dengan keamanan pesan. Suatu pesan jika hanya disimpan oleh satu orang saja terdapat resiko dimana orang tersebut menyalahgunakan atau memanipulasi pesan. Sedangkan jika terlalu banyak orang yang dapat mengakses pesan, kemungkinan kebocoran pesan menjadi lebih besar. Salah satu studi kriptografi yang digunakan untuk mengatasi masalah ini yaitu skema pembagian rahasia. Skema pembagian rahasia adalah metode mengamankan pesan dengan mendistribusikan pesan tersebut menjadi beberapa bagian kepada partisipan (orang), sedemikian sehingga hanya kombinasi partisipan (orang) tertentu yang dapat membuka isi pesan. Dalam tugas akhir ini dibahas mengenai bagaimana mengkonstruksi skema pembagian rahasia menggunakan matriks proyeksi. Selanjutnya, skema akan diimplementasikan pada pesan berupa string yang diubah ke bentuk kode ASCII (American Standart Code for Information Interchange) dan dapat direpresentasikan sebagai matriks bujur sangkar.

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Cryptography is a study of mathematical techniques related to message security. When a message is only saved by one person, there will be a risk that the person will misuse or manipulate the message. Whereas, when too many peope have access to the message, there will be more possibilities of message to be leaked. One of the ways to overcome this problem is by secret sharing scheme. Secret sharing scheme is a method to secure message by distributing it to participants (people), so that only certain combinations of people can open the message. In this undergraduate thesis, the discussion is focused on how to construct secret sharing scheme by using matrix projection. Then, the scheme will be implemented to message in the form of string which has been changed into ASCII (American Standart Code for Information Interchange) and can represented as a square matrix."

"Skema pembagian rahasia adalah teknik untuk membagi data rahasia menjadi n bagian dengan menggunakan threshold k, n, dimana partisipan dapat dengan mudah merekonstruksi rahasia jika diketahui minimum k bagian, tetapi pengetahuan dari k-1 bagian tidak dapat mengurai rahasia. Skema pembagian rahasia ini diperkenalkan oleh Shamir pada tahun 1979. Permasalahan pada skema pembagian rahasia Shamir adalah tidak tersedianya cara untuk melakukan verifikasi bahwa dealer terbukti jujur dalam membagikan rahasia, dan bagian dari rahasia terbukti valid, begitu juga dengan skema pembagian rahasia pada gambar yang diajukan oleh Thien dan Lin, atau metode konstruksi menggunakan matriks proyeksi yang dipublikasikan oleh Li Bai. Di sisi lain, sebuah protokol yang dikembangkan disebut skema pembagian rahasia yang diverifikasi memperbolehkan setiap partisipan melakukan validasi terhadap bagian rahasia yang diterima, untuk memastikan autentikasi dari rahasia. Sebuah gambar watermark berukuran m x m akan digunakan untuk menentukan akurasi dari gambar hasil rekonstruksi. Berdasarkan permasalahan di atas, pada skripsi ini akan dibahas skema pembagian rahasia yang diverifikasi, dimana matriks proyeksi digunakan untuk mengkonstruksi bagian rahasia dan matriks publik dari gambar watermark. Gambar rahasia akan direpresentasikan dalam sebuah matriks persegi, dan gambar watermark digunakan untuk autentikasi, dimana hasil rekonstruksi gambar watermark menjamin akurasi dari hasil rekonstruksi gambar rahasia.

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Secret sharing scheme is a technique to share secret data into n pieces based on a simple k, n threshold scheme. Participants will easily reconstruct the secret if there are minimum k pieces, while knowledge of any k-1 pieces of shares will not be able to decipher the secret. This scheme is introduced by Shamir in 1979. The problem with Shamirs secret sharing scheme is the scheme do not provide any way to verify that the dealer is honest and the shares are indeed valid. Thien and Lin proposed image secret sharing in 2002, and Bai proposed construction scheme using matrix projection in 2006, but both of the schemes do not solve the existing problem. On the other hand, a developed protocol for secret sharing called verifiable secret sharing allows every participant to validate their received piece to confirm the authenticity of the secret. An m x m watermark image is used to verify the accuracy of the reconstructed image. Based on the explanation above, this thesis discuss a proposed scheme based on verifiable secret sharing, in which the matrix projection is used to create image shares and a public matrix from watermark image. The secret are represented as a square matrix, the watermark image is used for verifiability, where the reconstructed watermark image verifies the accuracy of reconstructed secret image."

""The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises"--"

"This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats the derivation and implementation of the more important algorithms in detail. The notes and references sections contain pointers to other methods along with historical comments.The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method.The volumes in this survey are not intended to be encyclopedic. By treating carefully selected topics in depth, each volume gives the reader the theoretical and practical background to read the research literature and implement or modify new algorithms. The algorithms treated are illustrated by pseudocode that has been tested in MATLAB implementations."

"This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study."