Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm

Judul: Algoritme LLL dan Aplikasinya dalam Pembongkaran Sistemkripto Knapsack Merkle-Hellman
Abstrak: LLL algorithm is an algorithm that can be used to determine an approximation of the shortest vector in a lattice. Size reduction algorithm is an important step of LLL algorithm. The LLL algorithm can be applied in many elds. This paper shows how LLL algorithm can be used in breaking one of the famous cryptosystem, namely the Merkle-Hellman knapsack cryptosystem. Merkle-Hellman knapsack cryptosystem is an asymmetric cryptosystem using the subset sum problem as the support of security. Subset sum problem can be transformed into the problem of determining shortest vector in a lattice, so that LLL algorithm can also be used to solve the subset sum problem. Since the subset sum problem can be easily solved by applying LLL algorithm, then the Merkle-Hellman knapsack cryptosystem can also be easily be destructed.
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Judul: Pengaruh Persepsi Risiko, Pengetahuan Fatwa Merokok, dan Perilaku Merokok terhadap Niat Berhenti Merokok pada Remaja
Abstrak: Persentase perokok remaja semakin meningkat, namun hasil survei menunjukkan banyak perokok remaja sebenarnya ingin berhenti merokok. Penelitian ini bertujuan untuk menganalisis pengaruh persepsi risiko, pengetahuan fatwa merokok, dan perilaku merokok terhadap niat berhenti merokok. Desain penelitian ini adalah cross sectional study, melibatkan 100 remaja yang beragama islam, berusia 13-18 tahun, dan merokok aktif selama tiga bulan terakhir. Persepsi risiko diukur terhadap lima dimensi: fungsi, keuangan, fisik, psikologis, dan sosial. Pengetahuan fatwa merokok mengacu pada fatwa merokok dari MUI. Hasil penelitian menunjukkan bahwa persepsi risiko yang paling tinggi dirasakan contoh adalah risiko fungsi dan yang paling rendah adalah risiko sosial, hanya 32 persen contoh yang mengetahui fatwa yang ditetapkan MUI, rata-rata jumlah rokok yang dihisap adalah 6.3 batang per hari, dan 81 persen contoh adalah perokok harian ringan. Pengetahuan fatwa yang ditetapkan dan jumlah rokok yang dihisap per hari tidak berpengaruh terhadap niat berhenti merokok. Persepsi risiko sosial berpengaruh positif terhadap niat berhenti merokok.
Keyword: Niat berhenti merokok, pengetahuan fatwa merokok, perilaku merokok, persepsi risiko