ALGORITHM DESIGN OF ELGAMAL MAX-PLUS ALGEBRA FOR LETTER AND NUMBER CRYPTOGRAPHY WITH UNI-CUSTOM CIPHERTEXT
Abstract
This study focuses on the design and implementation of a prototype cryptographic algorithm using the integration of Uni-Custom ciphertext transformation and Max-Plus algebra in the ElGamal scheme. The integration is performed through a sequential process, where the Uni-Custom ciphertext transformation converts plaintext into a dynamic numeric form, and then we use the ElGamal max plus-based algorithm in the encryption process through a public-key mechanism. The primary objective of this research is to explore the feasibility and functional correctness of the proposed hybrid framework rather than to provide a complete cryptographic performance evaluation. The implementation results show that the system exhibits high computational and structural complexity. The security of the proposed system is associated with the hardness of the discrete logarithm problem in the ElGamal scheme, while additional transformation layers enhance variability and reduce pattern predictability. Experimental results show consistent reconstruction of the original message without data loss, indicating promising potential for the development of alternative cryptographic methods based on non-conventional mathematical structures.
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References
Adi Ahmad, Riyan Maulana, and Muhammad Yassir, “CYBERSECURITY CHALLENGES IN THE ERA OF DIGITAL TRANSFORMATION A COMPREHENSIVE ANALYSIS OF INFORMATION SYSTEMS,” Journal Informatic, Education and Management (JIEM), vol. 6, no. 1, pp. 7–11, Feb. 2024. doi: https://doi.org/10.61992/jiem.v6i1.57.
S. Quach, P. Thaichon, K. D. Martin, S. Weaven, and R. W. Palmatier, “DIGITAL TECHNOLOGIES: TENSIONS IN PRIVACY AND DATA,” J Acad Mark Sci, vol. 50, pp. 1299–1323, 2022. doi: https://doi.org/10.1007/s11747-022-00845-y
Y. T. Y. Azura, M. A. Azad, and Y. Ahmed, “AN INTEGRATED CYBER SECURITY RISK MANAGEMENT FRAMEWORK FOR ONLINE BANKING SYSTEMS,” Journal of Banking and Financial Technology, May 2025. doi: https://doi.org/10.1007/s42786-025-00056-3
N. Alanazi, E. Khan, and A. Gutub, “INCLUSION OF UNICODE STANDARD SEAMLESS CHARACTERS TO EXPAND ARABIC TEXT STEGANOGRAPHY FOR SECURE INDIVIDUAL USES,” Journal of King Saud University - Computer and Information Sciences, vol. 34, no. 4, pp. 1343–1356, Apr. 2022. doi: https://doi.org/10.1016/j.jksuci.2020.04.011
S. N. Nugraha, “PENERAPAN ALGORITMA KRIPTOGRAFI ELGAMAL PADA APLIKASI PENGAMANAN PESAN BERBASIS WEBSITE,” Jurnal Informatika dan Teknik Elektro Terapan, vol. 12, no. 3, pp. 2513–2524, Aug. 2024. doi: https://doi.org/10.23960/jitet.v12i3.4794.
L. De Feo, B. Poettering, and A. Sorniotti, “ON THE (IN)SECURITY OF ELGAMAL IN OPENPGP,” ACM, 2021. Accessed: Oct. 01, 2025. [Online]. Available: https://dl.acm.org/doi/10.1145/3460120.3485257. doi: https://doi.org/10.1145/3460120.3485257
H. Li, G. Yang, J. Ming, Y. Zhou, and C. Jin, “TRANSPARENCY ORDER VERSUS CONFUSION COEFFICIENT: A CASE STUDY OF NIST LIGHTWEIGHT CRYPTOGRAPHY S-BOXES,” Cybersecurity, vol. 4, no. 1, pp. 1–20, Dec. 2021. doi: https://doi.org/10.1186/s42400-021-00099-1.
F. Liu et al., “A SURVEY ON LATTICE-BASED DIGITAL SIGNATURE,” Cybersecurity, vol. 7, no. 1, pp. 1–18, Dec. 2024. doi: https://doi.org/10.1186/s42400-023-00198-1
F. Husaini, A. M. H. Pardede, and I. Gultom, “PENERAPAN ENKRIPSI MENGGUNAKAN METODE ELGAMAL GUNA MENINGKATKAN KEAMANAN DATA TEKS DAN GAMBAR,” JUKI : Jurnal Komputer dan Informatika, vol. 4, pp. 67–73, May 2022.
K. A. Sattar, T. Haider, U. Hayat, and M. D. Bustamante, “AN EFFICIENT AND SECURE CRYPTOGRAPHIC ALGORITHM USING ELLIPTIC CURVES AND MAX-PLUS ALGEBRA-BASED WAVELET TRANSFORM,” Applied Sciences (Switzerland), vol. 13, no. 14, pp. 1–19, Jul. 2023. doi: https://doi.org/10.3390/app13148385.
Subiono, J. Cahyono, D. Adzkiya, and B. Davvaz, “A CRYPTOGRAPHIC ALGORITHM USING WAVELET TRANSFORMS OVER MAX-PLUS ALGEBRA,” Journal of King Saud University - Computer and Information Sciences, vol. 34, no. 3, pp. 627–635, Mar. 2022. doi: https://doi.org/10.1016/j.jksuci.2020.02.004.
Supriyanto, Isbandiyah, and T. A. Yeni, “INTEGRASI AKSARA DAERAH KE DALAM SISTEM INFORMASI KOMPUTER SEBAGAI UPAYA MELESTARIKAN AKSARA DAERAH,” Bina Gogik, vol. 9, no. 1, pp. 185–191, Mar. 2022.
A. Wibowo, K. Wijayanti, and R. Budhiati Veronica, “PENERAPAN ALJABAR MAX-PLUS PADA PENGATURAN SISTEM ANTRIAN TRAFFIC LIGHT,” UNNES Journal of Mathematics, vol. 7, pp. 192–205, Nov. 2018, [Online]. Available: https://journal.unnes.ac.id/sju/index.php/ujm
K. Khairani and M. Z. Siambaton, “PENGAMANAN DATA TEKS MENGGUNAKAN ALGORITMA KRIPTOGRAFI ELGAMAL DAN XOR DARI SERANGAN HACKER,” sudo Jurnal Teknik Informatika, vol. 2, no. 4, pp. 176–187, Dec. 2023. doi: https://doi.org/10.56211/sudo.v2i4.401.
K. K. Johar, “GENERATION OF A NOVEL CRYPTOGRAPHIC ALGORITHM FOR IMPLEMENTATION OF ‘PLAY COLOR CIPHER’ SUBSTITUTION TECHNIQUE WITH UNICODE TRANSFORMATION FORMAT-8.” [Online]. Available: www.ijert.org
R. N. Fitriani, “MODIFIKASI ENKRIPSI ELGAMAL DALAM ALJABAR MAX-PLUS UNTUK PENGAMANAN DOKUMEN BAHASA ARAB,” Undergraduate thesis, Universitas Islam Negri Walisongo, Semarang, 2023.
A. S. Septiany, Siswanto, and V. Y. Kurniawan, “PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA,” BAREKENG: Journal of Mathematics and Its Applications, vol. 18, no. 3, pp. 2029–2034, Aug. 2024. doi: https://doi.org/10.30598/barekengvol18iss3pp2029-2034.
A. Muanalifah, A. I. Riana, and R. Artes Jr, “THE TROPICAL VERSION OF EL GAMAL ENCRYPTION,” Journal of Natural Sciences and Mathematics Research J. Nat. Scien. & Math. Res, vol. 9, no. 2, pp. 151–157, 2023, [Online]. Available: http://journal.walisongo.ac.id/index.php/jnsmr. doi: https://doi.org/10.21580/jnsmr.v9i2.18704
D. Grigoriev and V. Shpilrain, “TROPICAL CRYPTOGRAPHY,” Jan. 2013, [Online]. Available: http://arxiv.org/abs/1301.1195
R. S. Roring, T. I. Gunawan, and Y. B. Samponu, DASAR DAN TEORI SISTEM MULTIMEDIA. Bekasi: JUI Press, 2022.
A. Kumar, R. Yadav, and R. Kumar, “UNICODE AND COLOR INTEGRATION TECHNIQUE FOR ENCRYPTION AND DECRYPTION,” International Journal of Advanced Research in Computer Science, vol. 4, no. 8, [Online]. Available: www.ijarcs.info
D. Sutanto and A. Hariyanto, PENGENALAN KRIPTOGRAFI DAN KEAMANANNYA. Yogyakarta: Andi Offset, 2020.
D. Ibrahim, K. Ahmed, M. Abdallah, and A. A. Ali, “A NEW CHAOTIC-BASED RGB IMAGE ENCRYPTION TECHNIQUE USING A NONLINEAR ROTATIONAL 16 × 16 DNA PLAYFAIR MATRIX,” Cryptography, vol. 6, no. 2, pp. 1–27, Jun. 2022. doi: https://doi.org/10.3390/cryptography6020028.
R. Sulthanah and N. Ahmad, “PENERAPAN METODE MCCULLOCH-PITTS MENGGUNAKAN PYTHON UNTUK PENGUJIAN PENGENALAN POLA OPERATOR AND, OPERATOR OR, OPERATOR XOR PADA FUNGSI LOGIKA,” J-INTECH(Journal of Information and Technology), pp. 347–360, Nov. 2022. doi: https://doi.org/10.32664/j-intech.v11i2.1022
L. Adrián Lizama-Pérez, “XOR Chain and Perfect Secrecy at the Dawn of the Quantum Era †,” vol. 7, p. 50, 2023.. doi: https://doi.org/10.3390/cryptography7040050
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