A Systematic Literature Review of Mathematical Concepts in Hill Cipher-Based Cryptography for Mathematics Education
DOI:
https://doi.org/10.61255/jupiter.v4i3.1337Keywords:
Caesar Cipher, Cryptography Education, Hill Cipher, Hybrid Cryptosystem, Linear Algebra, Mathematics EducationAbstract
Purpose: This study aims to systematically review the mathematical concepts represented in Hill Cipher-based cryptography and examine their applications and implications for mathematics education across different educational levels. Methods: A systematic literature review was conducted following the PRISMA 2020 guidelines. Literature searches were performed across five academic databases, yielding 1,247 initial records. Following identification, screening, eligibility assessment, and quality appraisal, 14 primary studies published between 2020 and 2023 were included for qualitative thematic synthesis. Findings: The review identified modular arithmetic, matrix multiplication, and matrix inversion as the predominant mathematical concepts represented in the reviewed studies. Modular arithmetic appeared in all 14 studies and was primarily associated with secondary-level mathematics, whereas matrix operations were predominantly implemented in undergraduate contexts. The reviewed studies reported educational applications including mathematics learning media, simulation-based learning, and project-based learning. However, only a limited number of studies explicitly investigated classroom implementation, while most focused on algorithmic development and technical applications. In addition, the available evidence was dominated by studies conducted in Indonesia, limiting the broader generalizability of the findings. Research Implications: This review provides a conceptual synthesis that connects mathematical concepts, classical cryptographic algorithms, and their potential educational applications. The findings may inform mathematics educators, teacher educators, and curriculum developers in designing contextual mathematics learning activities while also highlighting the need for more classroom-based empirical studies across diverse educational settings. Originality: Unlike previous reviews emphasizing cryptographic performance and algorithm development, this study synthesizes the educational dimensions of Hill Cipher-based cryptography by mapping the relationships among mathematical concepts, instructional applications, and research gaps. The review contributes an evidence-based conceptual framework to support future research and curriculum development in mathematics education.
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References
Agung, A., Heryana, N., & Solehudin, A. (2020). Combination of Hill Cipher Algorithm and Caesar Cipher Algorithm for Exam Data Security. Buana Information Technology and Computer Sciences (BIT and CS), 1(2), 42–45.
Alawiyah, T., Hikmah, A. B., Wiguna, W., Kusmira, M., Sutisna, H., & Simpony, B. K. (2020). Generation of rectangular matrix key for Hill Cipher algorithm using Playfair Cipher. Journal of Physics: Conference Series, 1641(1). https://doi.org/10.1088/1742-6596/1641/1/012094
Arifin, S. (2025). Mathematical foundations of data science and cryptography: Implications for mathematics education. Bandung, Indonesia: Institut Teknologi Sains Bandung.
Ayo-Aderele, S., Misra, S., & Maskeliūnas, R. (2022). A review of classical cryptographic techniques and their modern applications. Informatics, 9(2), 45. https://doi.org/10.3390/informatics9020045
Bartzia, E.-I., Lodi, M., Sbaraglia, M., Modeste, S., Durand-Guerrier, V., & Martini, S. (2023). An unplugged didactical situation on cryptography between informatics and mathematics. Informatics in Education, 23, 25–56. https://doi.org/10.15388/infedu.2024.06
Deolika, A. (2020). Modifikasi metode Hill Cipher dan Vernam Cipher menggunakan kode administrasi dan pajak. Jurnal Teknologi Informasi (JurTI), 4(2), 224–227. https://doi.org/10.36294/JURTI.V4I2.1345
Elhabshy, A. A. (2019). Augmented Hill Cipher. International Journal of Network Security, 21(5), 812. https://doi.org/10.6633/IJNS.201909
Endaryono, E., Dwitiyanti, N., & Setiawan, H. S. (2021). Aplikasi operasi matriks pada perancangan simulasi metode Hill Cipher menggunakan Microsoft Excel. String (Satuan Tulisan Riset dan Inovasi Teknologi), 6(1). https://doi.org/10.30998/String.V6i1.8603
Fadlilah, S. N., Turmudi, T., & Khudzaifah, M. (2022). Penggabungan algoritma Hill Cipher dan Elgamal untuk mengamankan pesan teks. Jurnal Riset Mahasiswa Matematika, 1(5). https://doi.org/10.18860/Jrmm.V1i5.14496
Fitroti, H., Romdhini, M. U., & Switrayni, N. W. (2021). Hill Cipher algorithm with generalized Fibonacci matrix in message encoding. Eigen Mathematics Journal, 4(2).
Ginting, V. S. (2020). Penerapan algoritma Vigenere Cipher dan Hill Cipher menggunakan satuan massa. Jurnal Teknologi Informasi, 4(2), 241–246. https://doi.org/10.36294/jurti.v4i2.1365
Gusmana, R., Haryansyah, & Wibisono, A. D. (2023). Implementasi algoritma Hill Cipher menggunakan kunci matriks 2x2 dalam mengamankan data teks. Generation Journal, 7(3), 31–39.
Gusmana, R., Haryansyah, H., & Fitria, F. (2022). Implementasi algoritma Affine Cipher dan Caesar Cipher dalam mengamankan data teks. Sebatik, 26(2). https://doi.org/10.46984/Sebatik.V26i2.2084
Hamdani, D., & Junaidi, J. (2020). Modifikasi karakter kode pada cipher Hill menggunakan kode ASCII. Eigen Mathematics Journal. https://doi.org/10.29303/Emj.V3i1.54
Hasan, P., Yunita, S., & Ariyus, D. (2020). Implementasi Hill Cipher pada kode telepon dan five modulus method dalam mengamankan pesan. Sisfotenika, 10(1). https://doi.org/10.30700/Jst.V10i1.521
Hasibuan, Y. W., Isnarto, I., & Veronica, R. B. (2022). Perancangan dan implementasi aplikasi kriptografi algoritma Hill Cipher dalam dekripsi enkripsi data keuangan nasabah Bank Sampoerna menggunakan kode ASCII. Unnes Journal of Mathematics, 11(1). https://doi.org/10.15294/Ujm.V11i1.29356
Hasoun, R. K., & Khlebus, E. A. (2021). Enhancing Hill Cipher using dynamic key matrices. International Journal of Computer Science and Network Security, 21(3), 45–52.
Hasoun, R. K., Khlebus, S. F., & Tayyeh, H. K. (2021). A new approach of classical Hill Cipher in public key cryptography. International Journal of Nonlinear Analysis and Applications, 12(2). https://doi.org/10.22075/Ijnaa.2021.5176
Hidayat, M., Tahir, M., Sukriyadi, A., & Sulton, A. (2023). Penerapan kriptografi Caesar Cipher dalam pengamanan data. Jurnal Ilmiah Multidisiplin, 2(3), 35–41. https://doi.org/10.56127/jukim.v2i03.619
Kesuma, P. A. D., & Rahayuda, I. G. S. (2024). Pengembangan algoritma Caesar Cipher dalam game-based learning untuk pendidikan kriptografi pada anak. Jurnal Nasional Teknologi Informasi dan Aplikasinya (JNATIA), 2(3), 531–536.
Krisma Budi Ziliwu, A. M. (2022). Implementasi Caesar Cipher pada algoritma kriptografi dalam penyandian pesan Whatsapp. Jurnal Comasie, 117–125.
Lone, P. N., Singh, D., Stoffová, V., Mishra, D. C., & Mir, U. H. (2022). Cryptanalysis and improved image encryption scheme using elliptic curve and affine Hill Cipher. Mathematics, 10(20), 3878. https://doi.org/10.3390/math10203878
Mesran, M., & Nasution, S. D. (2020). Peningkatan keamanan kriptografi Caesar Cipher dengan menerapkan algoritma kompresi Stout Codes. Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi), 4(6), 1209–1215. https://doi.org/10.29207/RESTI.V4I6.2730
Naidoo, J., & Reddy, S. (2023). Embedding sustainable mathematics higher education in the Fourth Industrial Revolution era post-COVID-19: Exploring technology-based teaching methods. Sustainability, 15(12). https://doi.org/10.3390/su15129692
Nurjamiyah. (2020). Implementasi algoritma Affine Cipher untuk keamanan data teks. Jurnal Sistem Informasi, 50–59.
Permata Dewi, N., Sembiring, D. J. M., Br. Ginting, R., & Br. Ginting, M. (2022). Pengamanan data dengan kriptografi hibrida algoritma Hill Cipher dan algoritma LUC serta steganografi chaotic LSB. Jurnal Syntax Admiration, 3(2). https://doi.org/10.46799/Jsa.V3i2.389
Rasudin, R., Zulfan, Z., & Rizki, P. (2022). Analisis perbandingan keamanan kriptografi klasik pada algoritma secure Hill Cipher berbasis kode ASCII dan monoalphabetic. Jurnal Teknologi Terapan dan Sains.
Rosas, G. A. P., Polo, M. J. A., Hermosilla, A. S., Delgado, A., & Huamaní, E. L. (2023). Development of a web system to improve and reinforce learning in mathematics. International Journal of Recent Innovations in Trends in Computing and Communication, 11, 51–58. https://doi.org/10.17762/ijritcc.v11i5s.6597
Setyawati, N. Y., Khofid, A. N., Rundi, A. U. B., & Wati, V. (2021). Modifikasi kriptografi klasik kombinasi metode Vigenere Cipher dan Caesar Cipher. Journal of Smart System, 1(1), 1–8. https://doi.org/10.36728/jss.v1i1.1601
Sujarwo. (2024). Key analysis of the Hill Cipher algorithm (Study of literature). Jurnal Mandiri IT, 12(3), 135–141.
Sujjada, A., & Juniar, E. (2022). Implementasi algoritma Hill Cipher untuk proses enkripsi data menggunakan media citra digital. Jurnal Restikom: Riset Teknik Informatika dan Komputer, 3(1). https://doi.org/10.52005/Restikom.V3i1.76
Sujarwo. (2024). Penerapan algoritma Hill Cipher dalam pengamanan data teks. Jurnal Teknologi Informasi, 15(2), 55–63.
Supiyanto, & Mandowen, S. A. (2021). Advanced Hill Cipher algorithm for security image data with the involutory key matrix. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012116
Sylviani, S., Kartiwa, A., Permana, F. C., Hadi, A. N., Kadir, M. P., & Wilopo, R. (2023). Aplikasi matriks untuk meningkatkan keamanan proses kriptografi Caesar, Vernam, dan Hill Cipher. Jurnal Sains dan Teknologi, 12(2), 502–515.
Thanh-Giang, N. T. (2023). Applications of linear algebra in encryption. HPU2 Journal of Natural Sciences and Technology, 2(1), 46–52. https://doi.org/10.56764/hpu2.jos.2023.1.2.46-52
Wasil, M. (2023). Implementasi matriks dalam kriptografi Hill Cipher dalam mengamankan pesan rahasia. Zeta - Math Journal, 8(2). https://doi.org/10.31102/Zeta.2023.8.2.71-78
Widia Asiani, R., & Yanti, I. (2022). Penerapan kriptografi Caesar Cipher dan Hill Cipher dalam pengiriman pesan rahasia sebagai media pembelajaran matematika realistik pada materi modulo. Baitul 'Ulum, 6(1).
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Copyright (c) 2026 Auriel A. Y. Tuerah, Vivian E. Regar, Philoteus E. A. Tuerah, Regina Pakpahan
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