BAB IV HASIL DAN DISKUSI
4.11. Komparasi Kinerja Algoritma Baru terhadap Pollard rho
Pada subbab ini disajikan komparasi hasil algoritma Pollard rho dengan algoritma baru yang merupakan metode eksak yang menggunakan batas atas dan batas bawah totient dan metode
akar kuadrat).
Berikut ini disajikan output algoritma Pollard rho untuk pemfaktoran n = 2021, 846319, 33672839, 363325493, 135531947861, dan 95220345446563, 8055774719883797.
New Algorithm
time = 9.05990600586e-06 secs
Pollard rho Factorization Algorithm
2021 = 43 * 47 True iterations = 6
time = 0.000359058380127 secs
New Algorithm
time = 1.31130218506e-05 secs
Pollard rho Factorization Algorithm
846319 = 911 * 929 True iterations = 18
time = 0.000149965286255 secs
New Algorithm
p = 6053 q = 5563
ratio = 0.919048405749 n = 33672839
nbin = 10000000011100111010000111 bits = 26
33672839 = 6053 * 5563 True iterations = 3
time = 2.21729278564e-05 secs
Pollard rho Factorization Algorithm
33672839 = 5563 * 6053 True iterations = 136
time = 0.00290703773499 secs
New Algorithm
p = 19997 q = 18169
ratio = 0.908586287943 n = 363325493
nbin = 10101101001111110100000110101 bits = 29
363325493 = 19997 * 18169 True iterations = 11
time = 4.6968460083e-05 secs
Pollard rho Factorization Algorithm
363325493 = 18169 * 19997 True iterations = 206
time = 0.00408291816711 secs
New Algorithm
p = 373211 q = 363151
ratio = 0.973044738767 n = 135531947861
nbin = 1111110001110010101010110011101010101 bits = 37
135531947861 = 373211 * 363151 True iterations = 18
time = 6.69956207275e-05 secs
Pollard rho Factorization Algorithm
135531947861 = 363151 * 373211 True iterations = 192
time = 0.00505304336548 secs
New Algorithm
p = 9828293 q = 9688391
ratio = 0.985765381639 n = 95220345446563
nbin = 10101101001101000110110110111011010000010100011 bits = 47
95220345446563 = 9828293 * 9688391 True iterations = 126
time = 0.00021505355835 secs
Pollard rho Factorization Algorithm
95220345446563 = 9688391 * 9828293 True iterations = 1908
time = 0.0245251655579 secs
New Algorithm
p = 90529669 q = 88984913
ratio = 0.982936466939 n = 8055774719883797
nbin = 11100100111101010111100110110100100011011101000010101 bits = 53
8055774719883797 = 90529669 * 88984913 True iterations = 1662
time = 0.00494885444641 secs
Pollard rho Factorization Algorithm
8055774719883797 = 90529669 * 88984913 True iterations = 2976
time = 0.0473909378052 secs
Dapat dilihat bahwa algoritma baru yang merupakan kombinasi Metode Eksak menggunakan batas atas dan batas bawah totient dan metode akar kuadrat ini memiliki kecepatan yang lebih tinggi daripada algoritma Pollard rho.
BAB V
KESIMPULAN DAN SARAN
5.1 Kesimpulan
Dari penelitian ini, dapat disimpulkan hal-hal sebagai berikut:
1. Algoritma random search sama sekali tidak layak untuk digunakan untuk memfaktorkan modulus RSA. Hal ini dikarenakan random search hanya bergantung kepada lompatan-lompatan besar (explorations), sedangkan pemfaktoran modulus RSA lebih banyak bergantung kepada langkah-langkah kecil (walks).
2. Kendati algoritma iterated local search dan random restart hill climbing mengungguli kelima algoritma metaheuristik yang diuji, seluruh metode metaheuristik tersebut ternyata hanya dapat memfaktorkan modulus RSA yang kecil, sehingga secara umum tidak cukup layak untuk memfaktorkan modulus RSA bila dibandingkan dengan algoritma eksak.
3. Dari kelima metode eksak yang diteliti, kecepatan algoritma Pollard rho mengungguli kecepatan metode eksak lainnya dalam faktorisasi modulus RSA.
4. Algoritma baru yang merupakan kombinasi Metode Eksak menggunakan batas atas dan batas bawah totient dan metode akar kuadrat memiliki kecepatan yang lebih tinggi daripada algoritma Pollard rho.
5.2 Saran
Untuk penelitian lanjutan, dapat disarankan hal-hal sebagai berikut:
1. Kendati metode metaheuristik dinyatakan tidak layak untuk faktorisasi RSA, metode ini mungkin masih berguna untuk menghemat iterasi pada algoritma baru tersebut.
2. Algoritma baru hanya dapat digunakan untuk faktorisasi RSA. Diperlukan penelitian lebih lanjut di bidang teori bilangan untuk mengarahkan algoritma ini kepada faktorisasi integer biasa.
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Mohammad Andri Budiman, S.T., M.Comp.Sc., M.E.M., S.C.J.P.
Bidang Riset Ilmu Komputer Kriptografi, Desain Algoritma
Pendidikan
1. Sarjana Teknik, Institut Teknologi Bandung
2. Master of Computer Science, University of New South Wales, Sydney, Australia 3. Master of Engineering Management, University of Technology, Sydney, Australia 4. Certified Java Programmer, Sun Microsystems, United States of America
Riwayat Tugas dan Jabatan
1. Sekretaris Program Studi Magister (S-2) Teknik Informatika USU (2009-2017) 2. Ketua Satgas TIK USU (2012-2013)
3. Anggota Senat USU (2013-2014)
4. Anggota Tim Perumus Renstra dan RPJM USU (2014)
5. Ketua Dewan Pertimbangan Fakultas Ilmu Komputer dan Teknologi Informasi USU (2013-2017) 6. Kepala Laboratorium Algoritma dan Pemrograman Fasilkom-TI USU (2017)
7. Lektor dalam bidang Algoritma (2018)
Penghargaan, Prestasi, Afiliasi, dan Lain-lain
1. Peringkat 1 (Satu) Prajabatan CPNS Golongan III Reguler Angkatan I 2009 2. Dosen Favorit Prodi S-1 Ilmu Komputer USU 2013
3. Dosen Favorit Prodi S-1 Ilmu Komputer USU 2014
4. Pemakalah Terbaik II Kategori Dosen Dies Natalis USU 2015 5. Member of IHIQS (The International High IQ Society) 2016 6. Member of Mensa International High IQ Society 2017 7. Dosen Terbaik, Fasilkom-TI Awards 2019
8. Peneliti Bidang Ilmu Komputer dengan 42 Karya Ilmiah Internasional Terindeks Scopus 2021