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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications Journal of Mathematics, Computation and Statistics (JMATHCOS)
Jaharuddin
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Journal : BAREKENG: Jurnal Ilmu Matematika dan Terapan

 1 
SECURING INFORMATION CONFIDENTIALITY: A MATHEMATICAL APPROACH TO DETECTING CHEATING IN ASMUTH-BLOOM SECRET SHARING Darmawan, Azhar Janjang; Guritman, Sugi; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1989-2002

Abstract

The Secret Sharing Scheme (SSS) based on the Chinese Remainder Theorem (CRT) is a crucial method for safeguarding confidential information. However, this scheme is vulnerable to collaborative cheating involving multiple participants. This study aims to modify the Asmuth-Bloom scheme by introducing two detection mechanisms: Threshold Range Detection and Detection Parameter Verification, to identify and prevent collaborative fraudulent activities. The research design is based on mathematical algorithms and tests the effectiveness of detection against predetermined cheating scenarios using structured parameters. The results indicate that the proposed modifications can accurately detect the manipulation of secret fragments, even in cases involving participant collusion. This robustness is achieved through the mathematical structure of the CRT, which enables the detection of inconsistencies during the secret reconstruction process. In addition to maintaining the efficiency of the original Asmuth-Bloom scheme, these modifications enhance the reliability of the scheme in protecting sensitive data. The study concludes that the implementation of dual detection mechanisms significantly strengthens the security of the SSS, particularly in applications prone to dishonest participant collaboration. Future research is recommended to explore computational efficiency and the implementation of this scheme in real-world environments, such as financial systems and blockchain technology.
OPTIMIZING THE PROCESS OF PICK-UP AND DELIVERY WITH TIME WINDOWS USING ANT COLONY AND TABU SEARCH ALGORITHMS Amalia, Imas Saumi; Bakhtiar, Toni; Jaharuddin, Jaharuddin
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 (730.711 KB) | DOI: 10.30598/barekengvol16iss2pp651-662

Abstract

The provision of goods shuttle services sometimes faces several constraints, such as the limitation on the number of vehicles, vehicle capacity, and service time, or the vehicle used has single transport access. To avoid losses, a strategy is needed in determining the optimal route and policy for arranging goods in the vehicle especially if there are two types of goods involved. Traveling Salesman Problem and Pick-up and Delivery with Handling Costs and Time Windows (TSPPDHTW) is a model of an optimization problem that aims to minimize the total travel and goods handling costs in the goods pick-up and delivery with the constraints previously mentioned. Solving that model using the exact method requires a very long computation time so it’s not effective to be implemented in real-life. This study aims to develop a (meta)heuristic based on Ant Colony Optimization (ACO) and Tabu Search (TS) to be ACOTS to solve TSPPDHTW with reasonable computation time. The development is carried out by adding functions of clustering, evaluating constraints, cutting tours, arranging of goods, and evaluating moves on the TS, as well as modifying transition rules. The result has a deviation of about 22% and 99.99% less computational time than the exact method.
THE EFFECT OF LONG-LASTING INSECTICIDAL NETS ON THE DYNAMICS OF MALARIA SPREAD IN INDONESIA Aprianti, Euis; Jaharuddin, Jaharuddin
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/barekengvol17iss4pp2443-2450

Abstract

Malaria is an infectious disease that can lead to death. Deaths from malaria globally have increased in 2020. So the spread of this disease is still a serious problem for society. The mathematical model used is the SIR-SI model, assuming that recovered individuals can be re-infected with malaria. Analysis was carried out on the effectiveness parameters of long-lasting insecticidal nets to determine their effect on the dynamics of the spread of malaria. The sensitivity analysis results showed that changes in the parameters of the effectiveness of long-lasting insecticidal nets had an inverse effect on the rate of spread of malaria. These results follow numerical simulations conducted using malaria case data in Indonesia (some assumptions). Thus, efforts can be made to suppress the spread of malaria by increasing the effectiveness of long-lasting insecticidal nets.
OPTIMIZATION MODEL FOR MULTI-DEPOT ELECTRIC VEHICLE ROUTING PROBLEM WITH SOFT TIME WINDOWS WITH SCENARIO-BASED ANALYSIS Tan, Elfina; Bakhtiar, Toni; 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/barekengvol19iss4pp2751-2764

Abstract

The adoption of electric vehicles has increased due to their cost-efficiency and environmental impact. However, limited battery capacity requires careful route planning to ensure vehicles complete deliveries efficiently. This study focuses on the Multi-Depot Electric Vehicle Routing Problem with Soft Time Windows (MDEVRPSTW), where electric vehicles can depart from and return to multiple depots, while serving customers within predefined time windows that allow limited violations with penalty costs. The model is formulated using Mixed Integer Linear Programming (MILP) and solved using the exact branch-and-bound method in Lingo 20.0. Two operational scenarios are considered: (1) vehicles must return to their original depot, and (2) vehicles are allowed to return to any depot. Hypothetical data is used to simulate delivery routes with varied time windows and battery capacity constraints. Results show that both scenarios produce feasible, cost-minimizing solutions. Allowing flexible depot return (scenario 2) consistently reduces total travel cost, highlighting the practical benefit of depot flexibility in real-world logistics. This model contributes to the EV routing literature by integrating multiple depots—both fixed and flexible return options—soft time windows, and battery constraints into a single formulation. However, it assumes constant travel speeds and does not account for charging durations, which presents an opportunity for future research.
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 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 A. KUSNANTO A. T. WIBOWO Ahkrizal, Afdhal Ali Kusnanto Amalia, Imas Saumi Bib Paruhum Silalahi Blante, Trianty Putri Cahyona, Dwizani Vinoma D. NATALIA Darmawan, Azhar Janjang E. N. BANO Ekaputri, Dhea Endar Hasafah Nugrahani Eti Rohaeti Euis Aprianti F. FAHRURRAZI F. HANUM Fahri Novi Farida Hanum Farida Hanum Fikri, Faiqul H. HASANNUDIN H. HERMANSYAH Hadi Sumarno Handoyo, Sapto Mukti I. ALDILLA L. D. OKTAFIANI L. HAKIM Mirza Farhan Azhari N. AIN Nugrahani, Endar H. Nur Aziezah P. SIANTURI Paian Sianturi Rauf, Nurul Maqfirah Sahamony, Nur Fitriyani Siswandi SISWANDI, S. Sugi Guritman T. BAKHTIAR Tan, Elfina TEDUH WULANDARI Toni Bakhtiar