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All Journal MAGISTRA BAREKENG: Jurnal Ilmu Matematika dan Terapan Indonesian Journal of Combinatorics Jurnal Matematika UNAND Jurnal Saintika Unpam : Jurnal Sains dan Matematika Unpam InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Pattimura Proceeding : Conference of Science and Technology Pattimura International Journal of Mathematics (PIJMath) Jurnal Matematika Integratif
Kiki Ariyanti Sugeng
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Indonesia
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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BILANGAN KETERHUBUNGAN PELANGI DAN KETERHUBUNGAN PELANGI KUAT pada GRAF K_m⊙C_n dan GRAF K_m⊙W_n Hirawati lubis; Kiki Ariyanti Sugeng; Denny Silaban
JURNAL SAINTIKA UNPAM Vol 5, No 2 (2023)
Publisher : Program Studi Matematika FMIPA Universitas Pamulang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32493/jsmu.v6i1.34723

Abstract

Lintasan pelangi merupakan lintasan pada sesuatu graf yang setiap busurnya diwarnai dengan warna berbeda. Bilangan keterhubungan pelangi pada graf  ataupun dapat disimbolkan  adalah warna minimal yang dibutuhkan untuk memberikan warna busur-busur di suatu lintasan pada graf  sehingga setiap pasang simpul dihubungkan oleh suatu lintasan dengan warna yang berbeda. Lintasan pelangi  geodesic di  adalah lintasan pelangi yang panjangnya sama dengan  dimana  merupakan jarak antara  dan . Graf  dikatakan memiliki keterhubungan pelangi kuat  jika geodesic  untuk dua simpul  dan  di  adalah lintasan pelangi. Bilangan keterhubungan pelangi kuat  merupakan banyaknya pewarnaan minimum yang dibutuhkan untuk membuat  terhubung pelangi kuat. Misalkan  adalah graf dengan . Suatu korona  dari dua graf  dan  adalah graf yang diperoleh dengan mengambil satu salinan dari graf  dan  salinan dari , kemudian pada simpul ke-  dari  dikaitkan, ke setiap simpul salinan ke-  dari . Pada penelitian ini meliputi hasil kajian tentang  dan  pada graf K_m⊙C_n dan GRAF K_m⊙W_n
Comparison Between Algebraic Cryptanalysis on DES and NTRU Paradise, Fadila; Sugeng, Kiki Ariyanti
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.32011

Abstract

AbstractAlgebraic cryptanalysis is a cryptanalysis method that aims to exploit the algebraic structure of an encryption algorithm to obtain the secret key. Algebraic cryptanalysis becomes interesting because it uses a small amount of known plaintext, which in real life very few known plaintexts are available. Algebraic cryptanalysis has previously been performed on several block cipher algorithms and public key lattice-based algorithms. In this study, DES and NTRU were chosen as the objects of algebraic cryptanalysis. This research aims to compare algebraic cryptanalysis on DES and NTRU in terms of their applicability, and to what extent algebraic cryptanalysis can be successful in obtaining keys.Keywords: Algebraic Cryptanalysis; DES; NTRU; polynomial equation. AbstrakAlgebraic cryptanalysis adalah metode kriptanalisis yang bertujuan untuk memanfaatkan struktur aljabar pada algoritma enkripsi untuk mendapatkan kunci. Algebraic cryptanalysis menarik karena hanya membutuhkan sedikit plaintext, di mana pada kehidupan nyata hanya sedikit plaintext yang bisa didapatkan. Algebraic cryptanalysis sebelumnya dilakukan pada algorima block cipher dan algoritma kunci publik berbasis latis. Pada penelitian ini, DES dan NTRU dipilih sebagai objek algebraic cryptanalysis. Penelitian ini bertujuan untuk membandingkan algebraic cryptanalysis pada DES dan NTRU, serta sejauh mana algebraic cryptanalysis bisa mendapatkan nilai kunci.Kata Kunci: Kriptanalisis aljabar; DES; NTRU; persamaan polinomial. 2020MSC: 94A60.
CHARACTERISTIC ANTIADJACENCY MATRIX OF GRAPH JOIN Irawan, Wahri; Sugeng, Kiki Ariyanti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (947.33 KB) | DOI: 10.30598/barekengvol16iss1pp041-046

Abstract

Let be a simple, connected, and undirected graph. The graph can be represented as a matrix such as antiadjacency matrix. An antiadjacency matrix for an undirected graph with order is a matrix that has an order and symmetric so that the antiadjacency matrix has a determinant and characteristic polynomial. In this paper, we discuss the properties of antiadjacency matrix of a graph join, such as its determinant and characteristic polynomial. A graph join is obtained of a graph join operation obtained from joining two disjoint graphs and .
ON ANTIADJACENCY MATRIX OF A DIGRAPH WITH DIRECTED DIGON(S) Prayitno, Muhammad Irfan Arsyad; Sugeng, Kiki Ariyanti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (481.231 KB) | DOI: 10.30598/barekengvol16iss2pp497-506

Abstract

The antiadjacency matrix is one representation matrix of a digraph. In this paper, we find the determinant and the characteristic polynomial of the antiadjacency matrix of a digraph with directed digon(s). The digraph that we will discuss is a digraph obtained by adding arc(s) in an arborescence path digraph such that it contained directed digon(s), and a digraph obtained by deleting arc(s) in a complete star digraph. We found that the determinant and the coefficient of the characteristic polynomial of the antiadjacency matrix of a digraph obtained by adding arc(s) in an arborescence path digraph such that it contained directed digon(s) is different depending on the location of the directed digon. Meanwhile, the determinant of the antiadjacency matrix of a digraph obtained by deleting arc(s) in the complete star digraph is zero.
ALGEBRAIC CRYPTANALYSIS ON NTRU-HPS AND NTRU-HRSS Paradise, Fadila; Sugeng, Kiki Ariyanti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2187-2196

Abstract

NTRU is a lattice-based public-key cryptosystem designed by Hoffstein, Pipher, and Silverman in 1996. NTRU published on Algorithmic Number Theory Symposium (ANTS) in 1998. The ANTS’98 NTRU became the IEEE standard for public key cryptographic techniques based on hard problems over lattices in 2008. NTRU was later redeveloped by NTRU Inc. in 2018 and became one of the finalists in round 3 of the PQC (Post-Quantum Cryptography) standardization process organized by NIST in 2020. There are two types of NTRU algorithms proposed by NTRU Inc., which are classified based on parameter determination, NTRU-HPS (Hoffstein, Pipher, Silverman) and NTRU-HRSS (Hulsing, Rijnveld, Schanck, Schwabe). Algebraic cryptanalysis on ANTS’98 NTRU had previously been carried out in 2009 and 2012. In this paper, algebraic cryptanalysis is performed on NTRU-HPS with q=2048, n=509 (ntruhps2048509) and NTRU-HRSS with n=701 (ntruhrss701). This research aims to evaluate the resistance of NTRU-HPS and NTRU-HRSS algorithms against algebraic cryptanalysis by reconstructing the private key value. As a result, NTRU-HPS and NTRU-HRSS resistance to algebraic cryptanalysis.
Co-Authors Afifan Hadi Barack, Zeveliano Zidane Daniel, Juan Denny R. Silaban Denny Silaban Eri Nugroho Fery Firmansah Hariadi, Nora Hirawati Lubis Ilham, Pandu Setya Irawan, Wahri Juan Daniel Kevin Akbar Listyaningrum, Rostika Muhammad Irfan Arsyad Prayitno Paradise, Fadila Prayitno, Muhammad Irfan Arsyad Rizqi Rachmadhani Rostika Listyaningrum