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Abstrak :
Algoritma Diffie-Hellman digunakan dalam pembentukan kunci rahasia yang berdasarkan polinomial Chebyshev. Kemudian kunci rahasia tersebut digunakan pada proses enkripsi dan dekripsi.

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Diffie-Hellman algorithm is used in generating the secret key based on Chebyshev polynomials. Then the secret key is used for encryption and decryption process.

Abstrak :
Pada tugas akhir ini dibahas mengenai penurunan formula eksplisit polinomial Chebyshev dengan menggunakan komposisi fungsi pembangkit dan suatu fungsi yang disebut composita. Composita diperlukan untuk mencari koefisien-koefisien dari hasil komposisi fungsi pembangkit. Kemudian, dari koefisien-koefisien tersebut diperoleh bentuk umum formula eksplisit polinomial Chebyshev. Formula eksplisit polinomial Chebyshev jenis pertama diturunkan menggunakan komposisi dari fungsi pembangkit F(x,t)=2xt-t^(2 ) dan G(t)=1/(1-t) yang dikalikan dengan (1-xt). Formula eksplisit dari polinomial Chebyshev jenis kedua diturunkan dengan menggunakan komposisi dari fungsi pembangkit F(x,t)=2xt-t^(2 ) dan G(t)=1/(1-t). Sedangkan Formula eksplisit polinomial Chebyshev jenis ketiga dan keempat berturut-turut diturunkan menggunakan komposisi dari fungsi pembangkit F(x,t)=2xt-t^(2 ) dan G(t)=1/(1-t) yang dikalikan dengan (1-t) dan (1+t).

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In this skripsi, the way of deriving explicit formula of Chebyshev polynomials is carried out by using composition of generating functions and a function called composita. Composita is needed to find the coefficients of the composition of generating function. From the coefficients, the explicit formula of Chebyshev polynomials are obtained. Explicit formula of Chebyshev polynomials of the first kind is derived by multiplying (1-xt) to the composition of the generating function F(x,t)=2xt-t^(2 ) and G(t)=1/(1-t) . Explicit formula of Chebyshev polynomials of the second kind is derived by using the composition of the generating function F(x,t)=2xt-t^(2 ) and G(t)=1/(1-t). In addition, explicit formula of Chebyshev polynomials of the third kind is derived by multiplying (1-t) to the composition of the generating function F(x,t)=2xt-t^(2 ) and G(t)=1/(1-t) and fourth kind is derived by multiplying (1-t) to the composition of the generating function F(x,t)=2xt-t^(2 ) and G(t)=1/(1-t).

Abstrak :
The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and Teichmüller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.​