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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Cyber Security dan Forensik Digital (CSFD) Jurnal Riset Mahasiswa Matematika Journal of Research on Community Engagement
Muhammad Khudzaifah
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Humanities Computer Science & IT Mathematics Social Sciences

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Penerapan Kriptosistem Niederreiter Menggunakan Kode Goppa Biner untuk Mendukung Keamanan Data dalam Sistem Kriptografi Modern Chusnia, Aldina Laili; Khudzaifah, Muhammad; Herawati, Erna
Jurnal Riset Mahasiswa Matematika Vol 4, No 3 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i3.31216

Abstract

The advancement of modern cryptography presents new challenges posed by quantum computers, necessitating the development of stronger encryption processes. One of the post-quantum cryptographic methods capable of providing protection against such threats is the Niederreiter cryptosystem based on binary Goppa codes. In this study, binary Goppa codes are utilized in the formation of public and private keys, as well as in the decoding process. The implementation employs a specific polynomial over a finite field of order sixteen, resulting in code parameters with a length of 12, a dimension of 4, and the capability to correct up to two errors. Goppa codes are applied in the error correction process through syndrome calculation, enabling the detection and correction of erroneous bits and accurate recovery of the original message. The results demonstrate that binary Goppa codes are effective in detecting and correcting errors, thereby ensuring message integrity. This research is expected to contribute to the development of more robust cryptosystems for maintaining information confidentiality in the rapidly evolving digital era.
Implementasi Kode Goppa dalam Kriptosistem McEliece untuk Keamanan Data Terhadap Serangan Kuantum Khoiriyah, Lili; Khudzaifah, Muhammad; Herawati, Erna
Jurnal Riset Mahasiswa Matematika Vol 4, No 3 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i3.31212

Abstract

The importance of data security in the digital era is growing, particularly in the face of quantum computing threats against classical cryptographic algorithms. One of the main candidates for post-quantum cryptography is the McEliece cryptosystem, which employs error-correcting codes to enhance encryption strength. This study implements Goppa codes within the McEliece cryptosystem to increase resistance against quantum attacks. A degree-two polynomial over a finite field with sixteen elements was used, resulting in code parameters with a length of twelve, a dimension of four, and the ability to correct two errors. Encryption is carried out by multiplying the binary message with the public key and adding a random error vector, while decryption utilizes the private key to correct errors through syndrome calculation. The results demonstrate that employing Goppa codes enhances system security by complicating the ciphertext structure, thereby strengthening resilience against quantum-based attacks. This implementation confirms that classical coding techniques remain relevant and effective in supporting modern cryptography.
Random Forest Classification of Infant Mortality Rate in Indonesia: A Gini-Based Analysis Karisma, Ria Dhea Layla Nur; Pagalay, Usman; Khudzaifah, Muhammad
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.v10i2.29508

Abstract

One of the indicators used to measure the success of development programs in Indonesia is the Infant Mortality Rate (IMR). IMR is a sensitive indicator and represents maternal and child health problems in a country. Random forest is an ensemble machine learning method that combines multiple decision trees using bootstrap aggregation. It aims to improve the prediction accuracy and robustness of the model. In addition, it can be applied to both case classification and regression because it can handle high-dimensional and complex cases and non-linear relationships. In this study, Random Forest is used to solve the classification of IMR cases in Indonesia, making them easy to interpret and related to policy relevance. The aim of this study is to predict infant mortality factors using the Gini Index to determine which variables need to be improved. The Gini Index is used to identify key factors, enabling targeted policy interventions. It highlights the most influential variables, helping policymakers focus on areas that require improvement for more effective outcomes. The evaluation model in this study uses out-of-bag estimation and k-fold validation. The model achieves an overall accuracy of 99.97%, with a sensitivity of 99.87% and specificity of 100\%, indicating excellent performance. The most important variables in this study are breastfeeding, type of birth (single and twin), and birth weight of the baby. The parent node in IMR is breastfeeding, where live IMRs that are breastfed have a greater chance of survival than dead IMRs that are not breastfed.
Cross-Dataset Evaluation of Support Vector Machines: A Reproducible, Calibration-Aware Baseline for Tabular Classification Syafi'ah, Nurus; Jamhuri, Mohammad; Pranata, Farahnas Imaniyah; Kusumastuti, Ari; Juhari, Juhari; Pagalay, Usman; Khudzaifah, Muhammad
Jurnal Riset Mahasiswa Matematika Vol 4, No 6 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i6.33438

Abstract

Support Vector Machines (SVMs) remain competitive for small and medium-sized tabular classification problems, yet reported results on benchmark datasets vary widely due to inconsistent preprocessing, validation, and probability calibration. This paper presents a calibration-aware, cross-dataset benchmark that evaluates SVMs against classical baselines—Logistic Regression, Decision Tree, and Random Forest—under leakage-safe pipelines and statistically principled protocols. Using three representative binary datasets (Titanic survival, Pima Indians Diabetes, and UCI Heart Disease), we standardize imputation, encoding, scaling, and nested cross-validation to ensure comparability. Performance is assessed not only on discrimination metrics (accuracy, precision, recall, F1, PR--AUC) but also on probability reliability (Brier score, Expected Calibration Error) and threshold optimization. Results show that tuned RBF--SVMs consistently outperform Logistic Regression and Decision Trees, and perform comparably to Random Forests. Calibration (Platt scaling, isotonic regression) substantially reduces error and improves decision quality, while domain-specific features enhance Titanic prediction. By embedding all steps in a transparent, reproducible protocol and validating across multiple datasets, this study establishes a rigorous methodological baseline for SVMs in tabular binary classification, providing a reference point for future machine learning research.
Code-Based Document Authentication Using SHA-3 and McEliece Maulidya, Vadillatul Ni'ma; Khudzaifah, Muhammad
Jurnal Riset Mahasiswa Matematika Vol 5, No 2 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i2.37652

Abstract

Personal data protection is essential to ensure the security and authenticity of digital documents. One approach to achieving document authenticity is through a code-based document authentication mechanism. This study proposes a document authentication scheme using the SHA-3 hash function combined with the McEliece code-based cryptosystem with Hamming code. The authentication process begins by hashing the document content using SHA-3 to generate a message digest. The resulting hash value is converted into binary form and then encoded and encrypted using the public key of the McEliece cryptosystem, producing an authentication code. During the verification phase, the received authentication code is processed through the decoding mechanism using the private key, allowing error correction and recovery of the original hash representation. A document is considered authentic if the decoded hash matches the hash value generated from the received document. Experimental results show that the authentication code depends on the McEliece key pair used, ensuring uniqueness and resistance to forgery. Furthermore, the combination of SHA-3 and the McEliece cryptosystem exhibits an Avalanche Effect close to 50%, indicating strong diffusion properties. These results demonstrate that the proposed code-based authentication scheme provides a reliable cryptographic solution for ensuring the authenticity and protection of digital documents, particularly against future cryptanalytic threats.
Implementasi Algoritma Hill Cipher Dan Arnold CAT MAP Dalam Pengamanan Data Citra Digital Pengguna Ujian Daring Muhammad Khudzaifah; Muhammad Luqman Hakim; HAWZAH SA'ADATI
Cyber Security dan Forensik Digital Vol. 9 No. 1 (2026): Edisi Mei 2026
Publisher : Fakultas Sains dan Teknologi UIN Sunan Kalijaga Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/csecurity.2026.9.1.4905

Abstract

Penelitian enkripsi citra digital berbasis web terus berkembang untuk menutup research gap yang ada pada algoritma tunggal. Algoritma klasik seperti Hill Cipher rentan terhadap serangan known-plaintext karena sifat linier transformasi matriksnya, sedangkan Arnold Cat Map memiliki periode pendek sehingga ruang kunci efektifnya terbatas. Sebagai solusi, penelitian ini mengusulkan metodologi hibrid dengan memadukan Hill Cipher dan Arnold Cat Map. Citra digital diujikan pada berbagai variasi kunci integer dan iterasi, dengan pengukuran kualitas menggunakan Structural Similarity Index (SSIM). Hasil eksperimen menunjukkan bahwa integrasi kedua algoritma menghasilkan cipher-image yang sangat berbeda dari citra asli (nilai SSIM enkripsi terendah ≈ 0,0097, rata-rata ≈ 0,0112) dan proses dekripsi berhasil mengembalikan citra dengan sempurna (SSIM = 1). Waktu komputasi enkripsi pada iterasi pertama sekitar 2,151 detik dan meningkat menjadi 3,661 detik pada iterasi berikutnya. Implikasi teoretisnya, kombinasi transformasi matriks (Hill Cipher) dan permutasi piksel kaotik (Arnold Cat Map) memaksimalkan difusi dan konfusi sehingga sistem enkripsi menjadi lebih aman. Penelitian ini juga mengimplementasikan sistem pada aplikasi web berbasis Django untuk menguji kelayakan penerapan praktis. Kata kunci: Hill Cipher, Arnold Cat Map, Enkripsi Citra Digital, Keamanan Data, SSIM  ---------------------------------------------------------------------- Implementation Of Hill Cipher And Arnold CAT MAP Algorithms For Securing Digital Image Data Of Online Exam Users Research on web-based digital image encryption continues to evolve to close the research gap that exists in single algorithms. Classic algorithms such as Hill Cipher are vulnerable to known-plaintext attacks due to the linear nature of their matrix transformations, while Arnold Cat Map has a short period, limiting its effective key space. As a solution, this study proposes a hybrid methodology by combining Hill Cipher and Arnold Cat Map. Digital images were tested on various integer key and iteration variations, with quality measured using the Structural Similarity Index (SSIM). The experimental results show that the integration of the two algorithms produces cipher-images that are very different from the original images (lowest encryption SSIM value ≈ 0.0097, average ≈ 0.0112) and the decryption process successfully restores the images perfectly (SSIM = 1). The encryption computation time in the first iteration was approximately 2.151 seconds and increased to 3.661 seconds in the next iteration. Theoretically, the combination of matrix transformation (Hill Cipher) and chaotic pixel permutation (Arnold Cat Map) maximizes diffusion and confusion, making the encryption system more secure. This research also implemented the system on a Django-based web application to test its practical applicability. Keywords Hill Cipher, Arnold Cat Map, Digital Image Encryption, Data Security, SSIM).
Co-Authors AA Sudharmawan, AA Afifah, Luluk Agustina, Laura Ainindita Aghniacakti Ari Kusumastuti Bakhruddin Fannani Cahyanti, Niken Dwi Chusnia, Aldina Laili Erna Herawati, Erna Evawati Alisah Fachrur Rozi Faizah, Widya Nur HAWZAH SA'ADATI Hisyam Fahmi HR, Annisa Hardiningsih Imam Sujarwo Ismiarti, Dewi Juhari Juhari, Juhari Khoiriyah, Lili Ladunniyyah, Zakiyya Dzul Ludyawati, Ludyawati Maulidya, Vadillatul Ni'ma Mohammad Jamhuri Mohammad Nafie Jauhari Muhamad Sabilal Karim, Rifqi Muhammad Luqman Hakim Novianti, Chofifah Alfin Pranata, Farahnas Imaniyah Rafika Zahrotul Fauziah Ria Dhea Layla Nur Karisma Sa'adati, Hawzah Safitri, Sukmawati Indah Siti Nur Fadlilah Syafi'ah, Nurus Syihabuddin, Riyan Fahmi Turmudi Usman Pagalay Vega, Amelia Wahyuni, Fika