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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.
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 Bakhruddin Fannani Cahyanti, Niken Dwi Chusnia, Aldina Laili Dewi Ismiarti Erna Herawati, Erna Evawati Alisah Fachrur Rozi Faizah, Widya Nur HAWZAH SA'ADATI Hisyam Fahmi HR, Annisa Hardiningsih Imam Sujarwo Khoiriyah, Lili Ladunniyyah, Zakiyya Dzul Ludyawati, Ludyawati Mohammad Nafie Jauhari Muhamad Sabilal Karim, Rifqi Muhammad Luqman Hakim Novianti, Chofifah Alfin Rafika Zahrotul Fauziah Ria Dhea Layla Nur Karisma Sa'adati, Hawzah Safitri, Sukmawati Indah Siti Nur Fadlilah Syihabuddin, Riyan Fahmi Turmudi Vega, Amelia Wahyuni, Fika