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All Journal Jurnal Matematika & Sains Jurnal Fourier BAREKENG: Jurnal Ilmu Matematika dan Terapan International Journal on Emerging Mathematics Education Community Empowerment Journal of Fundamental Mathematics and Applications (JFMA) Journal of Mathematics UNP Jurnal Matematika Integratif
Uha Isnaini
Universitas Gadjah Mada, Yogyakarta, Indonesia
Arts Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation

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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.
Developing Number Theory Textbook for Pre-Service Mathematics Teacher of International Program Prahmana, Rully Charitas Indra; Prasetyo, Puguh Wahyu; Istiandaru, Afit; Isnaini, Uha; Nurnugroho, Burhanudin Arif
International Journal on Emerging Mathematics Education IJEME, Vol. 5 No. 2, September 2021
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/ijeme.v5i2.19779

Abstract

The long-term objective of this research is to produce valid, practical, and effective textbooks for courses in international program of mathematics education of Universitas Ahmad Dahlan. For the short-term, this research aims to produce valid and practical textbook for number theory course. The validity was based on the relevancy towards the students’ expected competence, while the practicality was measured from the implementation of learning using the textbook. This research used design research with the type of development studies. It followed four steps, i.e. (1) preliminary research, (2) prototyping stage, (3) summative evaluation, and (4) systemic reflection and documentation. In the preliminary research, we analyzed the need of the textbook in the international program and found that the textbook of number theory course is very needed. In the prototyping stage, we wrote the textbook based on the need analysis. The prototype was then discussed with expert and revised in the stage of summative evaluation and applied to the lecture meetings. The result was the final product of the textbook used for the stage of systemic reflection and documentation when we wrote all the results according to the preset research framework. Finally, the developed number theory textbook is valid and practical.
Partisi Dengan Penjumlah Bilangan Asli Berurutan Berselisih $2$ Isnaini, Uha -
Jurnal Matematika Integratif Vol 21, No 1: April 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n1.60997.15-22

Abstract

Partisi dari bilangan bulat positif $n$ didefinisikan sebagai barisan bilangan bulat positif tak naik yang jumlahnya sama dengan $n$. Salah satu topik yang menjadi perhatian dalam kajian partisi bilangan bulat adalah partisi dengan penjumlahan bilangan asli berurutan. Penelitian ini menyajikan formula untuk menghitung jumlah partisi dari $n$ yang terdiri atas penjumlahan bilangan asli berurutan dengan syarat banyaknya penjumlahan tersebut adalah ganjil atau genap. Selain itu, penelitian ini mengembangkan hasil tersebut dengan memperluas batasan pada syarat penjumlahan. Hasil utama menunjukkan bahwa jumlah partisi dari $n$ dengan syarat penjumlahan ganjil (genap) dan berselisih $2$ sama dengan jumlah faktor ganjil (genap) dari $n$ yang tidak melebihi $\sqrt{n}$.
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.
On the necessary and sufficient condition of a k-Euler pair Wijaya, Yosua Feri; Isnaini, Uha; Susanti, Yeni
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.v8i1.24953

Abstract

In this paper, we discuss George Andrews’ definition of an Euler pair andSubbarao’s generalization of the Euler pair to a k-Euler pair. Let N and M be non-empty sets of natural numbers. A pair (N, M) is called a k-Euler pair if, for any natural number n, the number of partitions of n into parts from N is equal to the number of partitions of n into parts  from M, with  the  condition  that  each  part  appears  fewer than k times. We further explore several theorems concerning Euler pairs that were established by Andrews and Subbarao, and we present proofs using a method distinct from those previously utilized.
Diseksi-4 atas Fungsi Pembangkit Partisi Frobenius Diperumum dengan 4-pewarnaan Muna, Naelufa Syifna Wifaqotul; Isnaini, Uha
Jurnal Matematika Integratif Vol 20, No 1: April 2024
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v20.n1.53999.81-88

Abstract

Suatu partisi dari bilangan bulat positif $n$ adalah barisan tak naik atas bilangan bulat positif sedemikian hingga jumlahnya adalah $n$. Frobenius memperkenalkan suatu simbol yang merepresentasikan partisi dalam bentuk matriks yang kemudian disebut simbol Frobenius. Tahun 1984, Andrews mengenalkan konsep partisi Frobenius diperumum atau F-partisi serta partisi Frobenius diperumum dengan $k$-pewarnaan. Banyaknya F-partisi dengan $k$-pewarnaan dari suatu bilangan bulat positif $n$ disebut sebagai fungsi partisi Frobenius diperumum dengan $k$-pewarnaan, dinotasikan dengan $c\phi_k (n)$. Baruah dan Salmah kemudian mengkaji F-partisi 4-pewarnaan dan memperoleh fungsi pembangkit $c\phi_4 (4n+3)$ dan kongruensi-kongruensi terkait $c\phi_4 (n)$. Dalam paper ini, ditemukan fungsi pembangkit $c\phi_4 (4n)$ dan $c\phi_4 (4n+1)$ yang melengkapi diseksi-4 dari $c\phi_4(n)$. Lebih lanjut, ditemukan pula kongruensi $c\phi_4(4n+1) \equiv 0 \pmod{16}$ yang mengakibatkan $c\phi_4 (n) \equiv 0 \pmod 4$, untuk setiap $n \not \equiv 0 \pmod 4$.
Co-Authors Afit Istiandaru Afit Istiandaru, Afit Agung Aldhi Prastya Ali, Saifullah Burhanudin Arif Nurnugroho Fadhlan Zhaahiran Fauzi, Prastudy Fitria Khasanah Handayani, Annisa Dini Inayati, Syarifah Indah Emilia Wijayanti Jituprasojo Hatma, Carolus Pasha Lazuardi Marsono Marsono Muna, Naelufa Syifna Wifaqotul Naelufa Syifna Wifaqotul Muna Prastya, Agung Aldhi Puguh Wahyu Prasetyo, Puguh Pujiati, Eko Rully Charitas Indra Prahmana Setiawan, Aisyah Nooravieta Wijaya, Yosua Feri Yeni Susanti