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All Journal Jurnal Matematika MATEMATIKA Jurnal Ilmu Dasar Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains Journal of Mathematics and Mathematics Education Jurnal Fourier Science and Technology Indonesia BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Kajian Matematika dan Aplikasinya Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif
Indah Emilia Wijayanti
Department Of Mathematics, Universitas Gadjah Mada
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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Learning With Error for Digital Image Encryption Setiawan, Aisyah Nooravieta; Wijayanti, Indah Emilia; Isnaini, Uha
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.21073

Abstract

Learning With Error (LWE) is one of the development of a system linear equation that add some noise or error. These problems have good potential for cryptography, especially for the development of Key Exchange Mechanism (KEM). Moreover, the question is whether LWE can be applied for digital image security or not. The digital image consists of hundreds of pixels that can be interpreted as a matrix. Each Pixel is encrypted with LWE so that the image becomes unidentified or cipher.
ON THE SECURITY OF GENERALIZED MULTILINEAR MAPS BASED ON WEIL PAIRING Handayani, Annisa Dini; Wijayanti, Indah Emilia; Isnaini, Uha; Fauzi, Prastudy
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp1307-1316

Abstract

In 2017, Tran et al. proposed a multilinear map based on Weil pairings to realize the Boneh-Silverberg scheme. They proposed an algorithm to evaluate the Boneh-Silverberg multilinear map and showed that it could be used to establish a shared key in multipartite key exchange for five users. They claimed their scheme was secure and computable in establishing a shared key between 5 users. Unfortunately, they did not prove that their scheme meets three additional computational assumptions proposed by Boneh and Silverberg. In this paper, with some computational modifications, we show that the algorithm proposed by Tran et al. does not satisfy three security assumptions proposed by Boneh and Silverberg. Therefore, every user involved in this multipartite key exchange can obtain the shared key and other users' secret values. We also show that the computation to obtain a shared key is inefficient because it requires a lot of computation and time.
Commuting and Centralizing Maps on Modules Fitriani, Fitriani; Wijayanti, Indah Emilia; Faisol, Ahmad; Ali, Shakir
Science and Technology Indonesia Vol. 10 No. 3 (2025): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.3.690-697

Abstract

A ring is a mathematical structure composed of a set with two binary operations that follow certain axioms. One important function within a ring is the centralizing and commuting mapping, which has been extensively studied in recent decades. Commuting mappings are a special case of centralizing mappings. A module is a generalization of a ring. In this paper, we extend the concept of commuting mappings from ring to module structures. However, defining commuting mappings in modules presents a challenge, as multiplication is required for their definition, yet modules do not have this operation. Additionally, constructing nonzero centralizing and commuting mappings on modules is a nontrivial task. To address these challenges, we employ the concept of idealization as a framework for defining commuting mappings in modules. We also propose a method for constructing nonzero commuting mappings on modules by leveraging existing commuting mappings in rings. Specifically, if α is a commuting mapping on a ring T, then a corresponding commuting mapping α’ can be defined on the module by utilizing α. Moreover, we establish that the finite sum of commuting mappings is also a commuting mapping and that a linear combination of  commuting mappings is also a commuting mapping under certain conditions.
HPPCv: a Modification of HPPC Scheme with Vinegar Variables Ali, Saifullah; Wijayanti, Indah Emilia; Isnaini, Uha
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.23279

Abstract

The Hidden Product of Polynomial Composition (HPPC) Digital Signature is multivariate-based cryptography using an HFE trapdoor. The HPPC scheme provides the technique for choosing the HFE central map. Its technique utilizes the product of the composition of two linearized polynomials. In this research, we proposed the modification of the HPPC scheme. We modify the HPPC scheme such that the scheme is based on HFEv. The linearized polynomial with vinegar variables will be chosen for constructing the central map. In our modification version, the public key becomes a system of polynomials of degree 4 and a map from n+v to n-dimension vector space. For a final remark, Despite an increase in the polynomial degree, HPPCv maintains a computational cost similar to HPPC.
Co-Authors A.A. Ketut Agung Cahyawan W AA Sudharmawan, AA Ahmad Faisol Ali, Saifullah Ananditya Dwi Candra Bp Arif Munandar Budi Surodjo Desi Rahmadani Dewi Kartika Sari Dian Ariesta Yuwaningsih Era Setya Cahyati Fauzi, Prastudy Fibriyanti, Regita Agustin Wahyu Fitriani Handayani, Annisa Dini I Irawati Irawati Irawati Isnaini, Uha Isnaini, Uha Kartika Sari Kartika Sari Khurul Wardati Mohammad Agung Nikken Prima Puspita Rizka 'Abid Fadhiilah S Suprapto Setiawan, Aisyah Nooravieta SHAKIR ALI Sri Wahyuni Sri Wahyuni Yeni Susanti Yunita Septriana Anwar