Soft Encryption and Diffie-Hellman Algorithm
Abstract
Cryptography is the practice of transforming data into different forms without losing data, enabling secure processing and transmission. The Diffie-Hellman algorithm, whose primary purpose is to exchange key, allows two parties to collaboratively generate an agreed-upon private key exchanged through an unprotected communication channel. Complex problems are not only prevalent in mathematics but also in fields such as engineering, medicine, and departures. The term "soft set," introduced by Molodtsov, was developed to manage uncertainties more effectively than traditional mathematical methods. Because of its versatility, soft set theory has a broad range of applications. Subsequently, Roy, Biswas, and Maji conducted extensive studies on soft sets, defining various applications within set theory and developing numerous operations for soft sets. In 2010, Çağman and Enginoğlu presented the idea of the "soft matrix," which offered a novel perspective on soft sets and increased their practical usability. This study, inspired by Diffie-Hellman and soft set theory, aims to create a new, more robust encryption method by integrating the matrix-based depiction of soft sets with cryptographic algorithms to enhance security.
Keywords
Cryptology, Diffie-Hellman Algorithm, Soft Set, Soft Matrix, Soft Encryption
References
- [1] Molodtsov, D. (1999). Soft set theory—First results. Computers & Mathematics with Applications, 37(4-5), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
- [2] Atagün, A. O., & Sezgin, A. (2011). Soft substructures of rings, fields and modules. Computers & Mathematics with Applications, 61(3), 592–601.
- [3] Atagün, A. O., Kamacı, H., & Oktay, O. (2018). Reduced soft matrices and generalized products with applications in decision making. Neural Computing and Applications, 29(2), 445–456. https://doi.org/10.1007/S00521-016-2542-Y
- [4] Atagün, A. O., Sezgin, A., & Aygün, E. (2011). A note on soft near-rings and idealistic soft near-rings. Filomat, 25(1), 53–68. https://doi.org/10.2298/FIL1101053S
- [5] Çağman, N., & Enginoğlu, S. (2010). Soft matrix theory and its decision making. Computers & Mathematics with Applications, 59(10), 3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015
- [6] Çağman, N., & Enginoğlu, S. (2010). Soft set theory and uni-int decision making. European Journal of Operational Research, 207(2), 848–855. https://doi.org/10.1016/j.ejor.2010.05.004
- [7] Çimen, C., Akleylek, S., & Akyıldız, E. (2007). Şifrelerin matematiği: Kriptografi. ODTÜ Yayıncılık, Ankara, 1: 5-10
- [8] Erdinç, S. (2018). Esnek kümeler yardımıyla elde edilen yeni bir kriptosistem [Yüksek lisans tezi, Erciyes Üniversitesi]. YÖK Ulusal Tez Merkezi.
- [9] Aygün, E. (2019). AES encryption and a cryptosystem obtained with soft set II. Cumhuriyet Science Journal, 40(1), 69–78. https://doi.org/10.17776/csj.416395
- [10] Aygün, E. (2019). AES şifreleme ve esnek kümeler yardımıyla elde edilen yeni bir kriptosistem. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 35(1), 1–11.