AES Encryption and A Cryptosystem Obtained with Soft Set II

Yıl 2019, Cilt: 40 Sayı: 1, 69 - 78, 22.03.2019

Emin Aygün

https://doi.org/10.17776/csj.416395

Cited By: 2

Öz

In this paper, a new cryptographic algorithm was created with the soft sets, symmetric
groups, soft matrices representing soft sets, and AES. In 1999, by Molodtsov proposed soft set
theory as a new mathematical tool to deal with uncertainties. This theory which
has been applied to many fields which contain uncertainties received much
attention since proposed. The inverse product and characteristic product
defined on soft matrices was used in soft encryption and soft decryption. In
order to make the encryption more secure, symmetric groups included in the
algorithm.

Anahtar Kelimeler

Soft Set, AES, Inverse Product, Characteristic Product

AES Şifreleme ve Esnek Kümeler Yardımıyla Elde Edilen Kriptosistem II

Öz

Bu çalışmada, esnek kümeler, esnek kümeleri temsil eden esnek
matrisler, simetrik gruplar ve AES ile yeni bir şifreleme algoritması
oluşturulmuştur.1999’da Molodtsov tarafından esnek küme teorisi  belirsizlikleri ortadan kaldırabilmek için
yeni bir matematiksel yöntem olarak kullanılmaya başlandı. Belirsizlikleri içeren
birçok alana uygulan bu teori önerildiğinden bu yana çok dikkat çekmiştir.
Esnek matrisler üzerinde tanımlanan invers çarpım ve karakteristik çarpım esnek
şifrelemede ve esnek deşifrelemede kullanılmıştır. Şifrelemenin daha güvenli
olması için simetrik gruplar algoritmaya dahil edilmiştir.

Anahtar Kelimeler

Esnek Küme, AES, İnvers Çarpım, Karakteristik Çarpım

Kaynakça

• [1]. Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37, (1999), 19–31.
• [2]. Molodtsov, D. , The Theory of Soft Sets, URRS Puplishers. , Moscow, (in Russian) 2004.
• [3]. Rivest, R. , Adleman, L. and Dertouzos, M., On data banks and privacy homomorphisms, In Foundations of Secure Computation, 169–180. 1978.
• [4]. Roy, A.R. and Maji, P.K., A fuzzy soft set theoretic approach to decision making problem, Journal of Computational and Applied Mathematics , 203, (2007), 412–418.
• [5]. Feng, F. , Jun, Y. B. and Zhao X., Soft semirings, Computers and Mathematics with Applications, 56,( 2008), 2621–2628.
• [6]. Sezgin, A. and Atagün, A.O., On operations of soft sets, Computers and Mathematics with Applications, 61, (2011), 1457–1467.
• [7]. Aktas H., Çagman N., Soft sets and soft groups, Inform. Sci. , 177, (2007),2726-2735.
• [8]. Atagün, A.O. and Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl., 61 (3), (2011), 592-601.
• [9]. Sezgin, A .Atagün, O. and Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat, , Vol. 25, (1), (2011), 53–68.
• [10]. Atagün, A.O. and Aygün, E., Groups of soft sets, Journal of Intelligent and Fuzzy Sys., 30, (2016),729-733.
• [11]. Miller, F.P., Vandome, A.V. , McBrewster, J., Advanced Encryption Standard, Alpha Press, London, 243s. 2009.
• [12]. Aygun, E. and Akbulut, S. AES Şifreleme ve Esnek Kümeler Yardımıyla Elde Edilen Yeni Bir Kriptosistem, Erciyes University Journal of the Institute of Science and Technology, 35, (1), 2019
• [13]. Maji, P.K., Biswas , R. and Roy, A.R., Soft set theory. Computers & Mathematics with Applications, 45,( 2003), 555-562.
• [14]. Daeman, J., Rijmen, V. The design of Rijndael: AES: the Advanced Encryption Standard.Berlin Heidelberg: Springer-Verlag128s, 2002.
• [15]. Çağman, N. and Enginoğlu S., Soft matrix theory and its decions making, Computers and Mathemetics with Applications, 59,( 2010), 3308-3314.
• [16]. Stinson, D., Cyrptography: Theory and Practice , CRC Press, New Jersey 573s. 1995.