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International Journal of Neutrosophic Science
Volume 11 , Issue 1, PP: 39-52 , 2020 | Cite this article as | XML | Html |PDF

Title

Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications

  Ali Hamza 1 * ,   Muhammad Naveed Jafar 2 ,   Ahtasham Habib 3 ,   Sara Farooq 4 ,   Ezgi Türkarslan 5

1  Department of Mathematics Lahore Garrison University, Sector-C, Av-4, DHA Phase VI 54000 Lahorer, Pakistan
    (Alihamza@lgu.edu.pk)

2  Department of Mathematics Lahore Garrison University, Sector-C, Av-4, DHA Phase VI 54000 Lahorer, Pakistan
    (naveedjafar@lgu.edu.pk)

3  Department of Mathematics Lahore Garrison University, Sector-C, Av-4, DHA Phase VI 54000 Lahorer, Pakistan
    (Ahtashamhabib@lgu.edu.pk)

4  Department of Mathematics Lahore Garrison University, Sector-C, Av-4, DHA Phase VI 54000 Lahorer, Pakistan
    (Sarafarooq@lgu.edu.pk)

5  Department of Mathematics, TED University, Ön Cebeci, Ziya Gökalp Cd. 48/A, 06420 Çankaya/Ankara, Turkey
    (ezgi.turkarslan@tedu.edu.tr)


Doi   :   https://doi.org/10.54216/IJNS.0110105

Received: Jun 04, 2020 Accepted: September 14, 2020

Abstract :

 

In this article, our main focus is to put forward the concept of Cryptography in terms of triangular neutrosophic numbers. This kind of cryptography is really reliable, manual, secure, and based on few simple steps. All the encryption and decryption are easy to proceed (mention below). As we know, Public-key cryptography as an indefatigable defender for human privacy and use as information transfer from the ages. various concepts are available with regard to cryptography e.g. Elliptic curve cryptography. TNNC (Triangular neutrosophic numbers cryptography) is familiar with basic concepts of math as well as applicable in different situations e.g. code cryptography, detailed view cryptography, and Graph cryptography encryption facilitate.

 

Keywords :

Cryptography , Triangular Neutrosphic numbers , Code Encryption , Detailed overview encryption.

References :

[1]       Delfs, H.and Knebl, H. Introduction to Cryptography Principles and Applications, Springer,2007.

[2]        Daemen.J and V. Rijmen, The Design of RIJNDAEL: AES - The Advanced Encryption Standard, Springer, Berlin, Germany, 2002. 

[3]        H. Al-Assam, R. Rashid, and S. Jassim, “Combining steganography and biometric cryptosystems for        secure mutual authentication and key exchange, ”in Proceedings of the 2013 8th International     Conference for Internet Technology and Secured Transactions (ICITST ’13), pp. 369–374, IEEE, London,             UK, March 2013.

[4]        A. Philip, “A generalized pseudo-Knight’s tour algorithm for encryption of an image,”IEEE         Potentials, vol.32,no.6,pp.10–16, 2013. 

[5]        D. Bloisi and L. Iocchi, “Image based steganography and cryptography, ”in Proceedings of the     2nd        International Conference on Computer Vision Theory and Applications’’ (VISAPP’07),         pp.127– 134,Barcelona,Spain,March2007. 

[6]        H. Sharma, “Secure image hi dingal gorithm using cryptography and steganography, ”IOSR          Journal of Computer Engineering, vol. 13,no.5,pp.1–6,2013. 

[7]        J. Liu, H. Jin, L. Ma, Y. Li, and W. Jin, “Optical color image encryption based on computer          generated hologram and chaotic theory, ”Optics Communications,vol.307,pp.76–79,2013. [3] C. E.    Shannon, “Communication theory of secrecy systems,” Bell System Technical Journal,    vol.28,no.4,pp.656–715,1949.  

[8].       Bachman, D. J.; Brown, E. A.; Norton, A.H, Chocolate Key Cryptography, Mathematics Teacher, 104(2),2010, p100-104. 

[9]        J. Liu, B. Wei, X. Cheng, and X. Wang, “An AESS-box to increase complexity and cryptographic analysis,” in Proceedings of the 19th International Conference on Advanced Information      Networking and   Applications (AINA ’05), pp. 724–728, Taipei, Taiwan, March2005.

[10]       J. Rosenthal, “A polynomial description of the Rijndael advanced encryption standard,” Journal   of          Algebra and Its Applications, vol.2,no.2,pp.223–236,2003. 

[11].      Koç, Ç.K, Cryptographic Engineering, Springer, 2009, PP 125-128. 

[12]       K. Challita and H. Farhat, “Combining steganography and cryptography: new directions,”            International Journal of New Computer Architectures and their Applications, vol. 1, no. 1, pp.        199–     208,2011.

[13]       N. Ferguson, R. Schroeppel, and D. Whiting, “A simple algebraic representation of Rijndael,” in   Selected Areas in Cryptography SAC’01, vol.2259 of Lecture Notesin Computer Science, pp.103–           111, Springer,                 2001. 

[14]       S. Murphy and M. J. Robshaw, “Essential algebraic structure within the AES,” in Advances in      Cryptology—CRYPTO 2002: 22nd Annual International Cryptology Conference Santa Barbara,           California, USA, August18–22,2002 Proceedings, vol.2442 of Lecture Notesin Computer Science, pp.1–    16,Springer,Berlin, Germany,2002. 

[15]       L. Cui and Y. Cao, “A new S-box structure named affine-power affine, ”International Journal of   Innovative Computing, Information and Control, vol.3, no.3, pp.751–759,2007. 

[16]       L. Jingmei, W. Baodian, and W. Xinmei, “One AES S-box to increase complexity and its             cryptanalysis,” Journal of Systems Engineering and Electronics, vol.18, no.2, pp.427–433,2007. 

[17]       M. Khan and N.A. Azam, “Right translated AES gray S-boxes,” Security and Communication       Networks, vol. 8, no. 9, pp. 1627– 1635,2015. 

[18]       M. Khan and N.A. Azam, “S-boxes based on affine mapping and orbitofpowerfunction,”3D         Research, vol.6, article12,2015.

[19]       M.-T. Tran, D.-K. Bui, and A.-D. Duong, “Gray S-box for advanced encryption standard,” in       Proceedings of the International Conference on Computational Intelligence and Security   (CIS’08),            pp.253–258, December2008. 

[20]       Molodtsov, D.(1999). Soft set theory - First results, Computers and mathematics with applications. 37, 19- 31.

[21]      Zadeh, L.A. Fuzzy sets. Inf. Control 1965, 8, 338–353.

[22]       Chang, S.S.L.; Zadeh, L.A. On fuzzy mappings and control. IEEE Trans. Syst. Man Cybern. 1972, 2, 30–34.

[23]       Dubois, D.; Prade, H. Operations on fuzzy numbers. Int. J. Syst. Sci. 1978, 9, 613–626.

[24]       Atanassov, K.T. Intuitionistic Fuzzy Sets; VII ITKR’s Session: Sofia, Bulgarian, 1983.

[25]       Smarandache, F. A Unifying Field in Logics Neutrosophy: Neutrosophic Probability; American Research    Press: Rehoboth, DE, USA, 1998.

[26]       F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, Inter. J. Pure Appl.        Math. Vol.24 , pp. 287–297, 2005. 

[27]       Chakraborty, A.; Mondal, S. P.; Ahmadian, A.; Senu, N.; Alam, S.; and Salahshour, S.; Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications, Symmetry, vol 10, 327, 2018. ; doi:10.3390/sym10080327.

[28]       Abdel-Basset, M., Atef, A., & Smarandache, F. A hybrid Neutrosophic multiple criteria group decision      making approach for project selection. Cognitive Systems Research, vol 57, pp. 216-227, 2019. 

[29]       Abdel-Baset, M., Chang, V., & Gamal, A. Evaluation of the green supply chain management practices: A    novel neutrosophic approach. Computers in Industry, vol 108, pp. 210-220, 2019.

[30]       Abdel-Baset, M., Chang, V., Gamal, A., & Smarandache, F. An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in the importing field. Computers in Industry, vol 106, pp. 94-110, 2019. 

[31]       Abdel-Basset, Mohamed, Mumtaz Ali, and Asma Atef. "Resource levelling problem in construction          projects under neutrosophic environment." The Journal of Supercomputing, pp.1-25, 2019.  

[32]       Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. A group decision making framework      based on neutrosophic TOPSIS approach for smart medical device selection. Journal of medical systems,            vol 43(2), pp. 38, 2019. 

[33]       Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. A group decision-making framework based on the neutrosophic TOPSIS approach for smart medical device selection. Journal of medical systems, vol 43, issue 2, pp. 38-43, 2019.

[34]      Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. A hybrid approach of neutrosophic sets and DEMATEL method for developing supplier selection criteria. Design Automation for Embedded    Systems, pp.1-22, 2018. 

[35]       Abdel-Basset, M., Saleh, M., Gamal, A., & Smarandache, F. An approach of TOPSIS technique for           developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft        Computing, vol 77, pp. 438-452, 2019.

[36]       Saqlain,  M., Jafar, M. N.,  Riaz, M.  “A New Approach of Neutrosophic Soft Set with Generalized Fuzzy   TOPSIS in Application of Smart Phone Selection,” Neutrosophic Sets and Systems, vol. 32, pp. 307-316, 2020. DOI: 10.5281/zenodo.3723161.

[37]       Saqlain M, Jafar N, Hamid R, Shahzad A. “Prediction of Cricket World Cup 2019 by TOPSIS Technique    of MCDM-A Mathematical Analysis,” International Journal of Scientific & Engineering Research, vol     10(2), pp. 789-792, 2019. 

[38]       Saqlain. M, Jafar. N. M, and Muniba. K, “Change in The Layers of Earth in Term of Fractional Derivative: A Study,” Gomal University Journal of Research, vol 34(2), pp. 1-13, 2018. 

[39]       Saqlain. M., Jafar. N. and Riffat. A., “Smart phone selection by consumers’ in Pakistan: FMCGDM fuzzy   multiple criteria group decision making approach,” Gomal University Journal of Research, vol 34(1), pp.                       27-31, 2018. 

[40]      Saqlain M, Saeed M, Ahmad M. R, Smarandache F, Generalization of TOPSIS for Neutrosophic Hypersoft set using Accuracy Function and its Application, Neutrosophic Sets and Systems (NSS), vol 27,           pp. 131137, 2019.  

[41]       Wang, H.B.; Smarandache, F.; Zhang, Y.Q.; Sunderraman, R. Single Valued Neutrosophic Sets. Tech. Sci. Appl. Math. 2010. Available online:             http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.309.9470&re p=rep1&type=pdf (accessed on 31 July 2018).

[42]       Ye, J. A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets.            J. Int. Fuzzy Syst., vol 26,pp.  2459–2466, 2014.

[43]      P. Biswas, S. Pramanik, and B. C. Giri. “A new methodology for neutrosophic multi-attribute decision      making with unknown weight information,” Neutrosophic Sets and Systems, vol 3, pp. 42-52, 2014. 

[44]       Parimala ,M,. Karthika, M, Florentin Smarandache , Said Broumi, “On αω-closed sets and its       connectedness in terms of neutrosophic topological spaces,” International Journal of Neutrosophic Science,         Volume 2 , Issue 2, pp. 82-88 , 2020.

[45]       Riaz. M., Saqlain. M. and Saeed. M., “Application of Generalized Fuzzy TOPSIS in Decision Making for   Neutrosophic Soft set to Predict the Champion of FIFA 2018: A Mathematical Analysis,” Punjab     University Journal of Mathematics, vol 51(8), pp.111-126, 2019.     

[46]       Riaz. M., Saeed. M. Saqlain. M. and Jafar. N, ”Impact of Water Hardness in Instinctive Laundry System     based on Fuzzy Logic Controller,” Punjab University Journal of Mathematics, vol 51(4), pp. 73-84, 2018.

[47]       Smarandache, F.” Neutrosophy. Neutrosophic probability, set, and logic, ProQuest Information &             Learning, Ann Arbor, Michigan, USA, 1998.

[48]       Smarandache, F., Pramanik, S., “New Neutrosophic Sets via Neutrosophic Topological Spaces,” In            Neutrosophic Operational Research; Eds.; Pons Editions: Brussels, Belgium, vol I, pp. 189–209, 2017.

[49]       S. Pramanik, P. P. Dey and B. C. Giri, “TOPSIS for single valued neutrosophic soft expert set based          multiattribute decision making problems,” Neutrosophic Sets and Systems, vol 10, pp. 88-95, 2015. 

[50]       T. Bera and N. K. Mahapatra, Introduction to neutrosophic soft groups, Neutrosophic Sets and Systems, vol             13, pp. 118-127, 2016. doi.org/10.5281/zenodo.570845. 

[51]       Chakraborty, A. “A New Score Function of Pentagonal Neutrosophic Number and its Application in          Networking Problem,” International Journal of Neutrosophic Science, Volume 1, Issue 1, pp. 40-51, 2020.

[52]       Deli I, Broumi S. Neutrosophic soft matrices and NSM decision making, Journal of Intelligent and Fuzzy   System vol 28, pp.2233–2241, 2015. 

[53]       Edalatpanah, S. A., “A Direct Model for Triangular Neutrosophic Linear Programming,” International       Journal of Neutrosophic Science, Volume 1, Issue 1, pp. 19-28, 2020. 

[54]      F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, Inter. J. Pure Appl.       Math. Vol.24, pp. 287–297, 2005.

[55]       I. Deli and S. Broumi, “Neutrosophic Soft Matrices and NSM-decision Making,” Journal of Intelligent and             Fuzzy Systems, vol 28(5), pp. 2233-2241, 2015.

[56]       K. Mondal, and S. Pramanik. Neutrosophic decision making model of school choice.  Neutrosophic Sets and           Systems, vol 7, pp. 62-68, 2015.

[57]       Ma YX, Wang JQ, Wang J, Wu XH. An interval neutrosophic linguistic multi-criteria group decision–       making the method and its application in selecting medical treatment options, Neural Computer            Application. DOI:10.1007/s00521-016-2203-1. 2016.

[58]      A. Chakraborty, S. Broumi, P.K Singh, ”Some properties of Pentagonal Neutrosophic Numbers and its      Applications  in  Transportation  Problem  Environment,”  Neutrosophic  Sets  and  Systems, vol.28,     pp.200215, 2019.

[59]       A. Chakraborty, S. Mondal, S. Broumi, “De-Neutrosophication technique of pentagonal neutrosophic         number and application in minimal spanning tree,” Neutrosophic Sets and Systems, vol. 29, pp. 1-18, 2019.          doi: 10.5281/zenodo.3514383.  


Cite this Article as :
Style #
MLA Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan. "Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications." International Journal of Neutrosophic Science, Vol. 11, No. 1, 2020 ,PP. 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)
APA Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan. (2020). Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications. Journal of International Journal of Neutrosophic Science, 11 ( 1 ), 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)
Chicago Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan. "Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications." Journal of International Journal of Neutrosophic Science, 11 no. 1 (2020): 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)
Harvard Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan. (2020). Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications. Journal of International Journal of Neutrosophic Science, 11 ( 1 ), 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)
Vancouver Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan. Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications. Journal of International Journal of Neutrosophic Science, (2020); 11 ( 1 ): 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)
IEEE Ali Hamza, Muhammad Naveed Jafar, Ahtasham Habib, Sara Farooq, Ezgi Türkarslan, Cryptography in Terms of Triangular Neutrosophic Numbers with Real Life Applications, Journal of International Journal of Neutrosophic Science, Vol. 11 , No. 1 , (2020) : 39-52 (Doi   :  https://doi.org/10.54216/IJNS.0110105)