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All Journal Jurnal Teknologi Industri Pertanian CAUCHY: Jurnal Matematika Murni dan Aplikasi TELKOMNIKA (Telecommunication Computing Electronics and Control) JREC (Journal of Electrical and Electronics) Jurnal Ilmu Komputer dan Agri-Informatika Jurnal Karya Pendidikan Matematika Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Krea-TIF: Jurnal Teknik Informatika Jambura Journal of Mathematics Jurnal Matematika UNAND Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif Jurnal Sistem Informasi MILANG Journal of Mathematics and Its Applications
Sugi Guritman
Department Of Mathematics, Faculty Of Science And Mathematics, IPB University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680,
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Library & Information Science Mathematics Mechanical Engineering Medicine & Pharmacology Physics Transportation

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Explicit Determinant and Inverse Formulas of Skew Circulant Matrices with Alternating Fibonacci Numbers Handoyo, Sapto Mukti; Guritman, Sugi; Mas'oed, Teduh Wulandari; Jaharuddin, Jaharuddin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32358

Abstract

Skew circulant matrices have various applications such as cryptography, signal processing, and many more. Their structure can potentially simplify their determinant and inverse computations. This study presents explicit formulas for the determinant and inverse of skew circulant matrices with entries from the alternating Fibonacci sequence. Elementary row and column operations are used to derive simple explicit formulas for the determinant and inverse. Computational tests using Wolfram Mathematica show that the algorithm built from these explicit formulas performs with much faster execution time than the built-in functions, especially for large matrix size. The proposed approach offers a practical method for the numerical computation of the determinant and inverse of these matrices
NEW SCHEME OF MIGNOTTE (t,n) COLLABORATIVE SECRET SHARING ON CLOUD STORAGE Ekaputri, Dhea; Guritman, Sugi; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2981-2992

Abstract

Cloud storage is an internet-based data storage service that allows users to collaborate to store, manage, and access data remotely. However, this collaborative characteristic creates challenges in security and privacy. One potential solution to these issues is implementing a collaborative secret sharing scheme. This research proposes a modified Mignotte collaborative secret sharing scheme by introducing a detector parameter to detect cheating. Additionally, the scheme is designed so that participants with multiple privileges only need to store a single share. The main contribution of this research is the integration of a cheating detection mechanism into the Mignotte collaborative secret sharing scheme while maintaining storage efficiency. Experimental results show that the scheme produces correct outputs across various test cases. The proposed modification enhances the security of the secret sharing scheme for cloud storage applications by protecting against cheating and unauthorized access. However, the current scheme is limited to detection without identifying the cheater. Future research can focus on developing mechanisms for further identifying cheaters to enhance overall security.
A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE Guritman, Sugi; Jaharuddin; Mas'oed, Teduh Wulandari; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.69-80

Abstract

In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.
DETERMINAN, INVERS, DAN NILAI EIGEN MATRIKS SKEW-CIRCULANT DENGAN ENTRI BARISAN GEOMETRI Azhari, Mirza Farhan; Wulandari Mas'oed, Teduh; Guritman, Sugi; Jaharuddin; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 2 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.2.129-140

Abstract

Matriks skew-circulant adalah matriks segi yang entri terakhir setiap baris berpindah ke posisi utama dan berganti tanda disertai pergeseran semua entri lainnya ke posisi berikutnya. Dalam artikel ini, entri dari matriks circulant berupa entri barisan bilangan geometri. Tujuannya adalah merumuskan suatu formulasi sederhana dari determinan, invers, dan nilai eigen dari suatu matriks skew circulant. Formulasi determinan ditentukan dengan menerapkan serangkaian operasi baris dasar dan kolom dasar sampai diperoleh matriks diagonal. Langkah untuk mencari invers dilakukan dengan mengadaptasi metode dalam mencari determinan dan ekuivalensi baris dan kolom pada matriks. Dalam mencari nilai eigen digunakan konsep akar kesatuan (roots of unity) dan subgrup siklik.
On the Explicit Formula for Eigenvalues, Determinant, and Inverse of Circulant Matrices Aliatiningtyas, Nur; Guritman, Sugi; Wulandari, Teduh
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8616

Abstract

Determining eigenvalues, determinants, and inverse for a general matrix is computationally hard work, especially when the size of the matrix is large enough. But, if the matrix has a special type of entry, then there is an opportunity to make it much easier by giving its explicit formulation. In this article, we derive explicit formulas for determining eigenvalues, determinants, and inverses of circulant matrices with entries in the first row of those matrices in any formation of a sequence of numbers. The main method of our study is exploiting the circulant property of the matrix and associating it with cyclic group theory to get the results of the formulation. In every discussion of those concepts, we also present some computation remarks. 
A NOVEL PUBLIC-KEY CRYPTOGRAPHY SCHEME UTILIZING SKEW CIRCULANT MATRICES WITH GENERALIZED ALTERNATING FIBONACCI Handoyo, Sapto Mukti; Guritman, Sugi; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0657-0672

Abstract

Circulant and skew circulant matrices play a significant role in various applications, especially in cryptography. Their determinants and inverses can be used in the decryption process. In classical cryptography, the Hill cipher is known to be susceptible to known-plaintext attacks and requires matrix-based key transmission. This study introduces a new public-key cryptography scheme that combines the Hill cipher with the ElGamal technique, utilizing skew circulant matrices with generalized alternating Fibonacci numbers. These numbers provide a pattern that simplifies the explicit formulas of the determinant and inverse of the matrices. The proposed scheme is the first of its kind to use these matrices and numbers for public-key cryptography. Explicit formulas for the determinant and inverse of these matrices are derived using elementary row and column operations. The proposed scheme is resistant to the discrete logarithm problem, known-plaintext, and brute-force attacks and requires only the transmission of key parameters. The implementation of the scheme has been tested using Wolfram Mathematica. In practice, the computational time of the scheme is significantly faster than three other related schemes, with up to 500 times faster in encryption and 17 times faster in decryption.
Co-Authors AHMADI Azhari, Mirza Farhan Berlian Setiawaty Bib Paruhum Silalahi Darmawan, Azhar Janjang Ekaputri, Dhea Endang Purnama Giri Fitrah Satrya Fajar Kusumah Handoyo, Sapto Mukti Hendra Rahmawan Hendra Rahmawan Heru Sukoco Jaharuddin Jaharuddin Khoerul Fatihin Lindayati Lindayati Lindayati Lindayati Mirza Farhan Azhari Mu'min, Ulil Albab Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Taufik Abdillah Nur Ahzan, Zulkaidah Nur Aliatiningtyas Nur Aliatiningtyas Pizaini Pizaini Prapto Tri Suprio Prapto Tri Suprio Prapto Tri Supriyo Rafika Husnia Munfa'ati Retno Nugroho Whidhiasih Retno Nugroho Whidhiasih Saputra, T Murdani Shelvie Nidya Neyman Siswandi Siswandi Siswandi Siswandi TEDUH WULANDARI