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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan Al-Aqlu : Jurnal Matematika, Teknik dan Sains
Handoyo, Sapto Mukti
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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PREDIKSI INDEKS PERFORMA SISWA BERDASARKAN WAKTU BELAJAR, NILAI SEBELUMNYA, KEGIATAN EKSTRAKURIKULER, WAKTU TIDUR, DAN BANYAKNYA SOAL YANG DIKERJAKAN DENGAN REGRESI LINEAR KUADRAT-TERKECIL: Prediction of Student Performance Index Based on Hours Studied, Previous Scores, Extracurricular Activities, Sleep Hours, and Sample Question Papers Practiced with Least-Squares Linear Regression Handoyo, Sapto Mukti; Najib, Mohamad Khoirun
Al-Aqlu: Jurnal Matematika, Teknik dan Sains Vol. 3 No. 1 (2025): Januari 2025
Publisher : Yayasan Al-Amin Qalbu

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59896/aqlu.v3i1.121

Abstract

The students’ performance index is a measure used to represent the overall performance of students. One model that can be used to predict the students’ performance index is a machine learning-based regression model. Therefore, this study aims to apply a machine learning-based least-squares linear regression model to predict the performance index using these factors and interpret the model. The regression model utilized is available in the Julia programming package called MLJ. This model is evaluated based on several criteria, including R-squared, RMSE, and MAE. The results show that the previous scores have the most significant influence on the students’ performance index. Furthermore, the R-squared value for the test data is 0.988, the RMSE for the training data is 0.106, the RMSE for the test data is 0.108, the MAE for the training data is 0.84, and the MAE for the test data is 0.86. Based on the evaluation results, the model has good predictive performance with low average error, does not experience overfitting, and has good generalization ability.
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
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 Jaharuddin Najib, Mohamad Khoirun Sugi Guritman TEDUH WULANDARI