International Journal of Computer Network and Information Security(IJCNIS)

ISSN: 2074-9090 (Print), ISSN: 2074-9104 (Online)

Published By: MECS Press

IJCNIS Vol.9, No.4, Apr. 2017

Enhancing the Security in Cryptosystems Based on Magic Rectangle

Full Text (PDF, 729KB), PP.37-47

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Mani. K, Viswambari. M

Index Terms

RSA;ElGammal;Magic Rectangle;Magic Square;Security


The security of any cryptosystems is based on the way in which it produces different ciphertext for the same plaintext. Normally, various block cipher modes viz., CBC, OFC, etc., are used in producing different ciphertext for the same plaintext but it is a time consuming process. Instead of using block cipher, a different encoding method for the plaintext is proposed in this paper using magic rectangle. The advantage of using the encoding scheme is different numerals is used in encoding each characters of a plaintext. Thus instead of considering the ASCII encoding for a character to be encrypted, the numeral which occurs at the position which corresponds to the ASCII value of the character is taken from the magic rectangle. Further, different numerals from magic rectangles for the same character are produced by considering the magic sum, starting number and template of magic rectangle. Once the magic rectangles are created, the numerals which occur in the magic rectangles are considered for the encoding of the plaintext character which is then used for encryption in the cryptosystems like RSA, ElGamal. The proposed work provides an additional layer of security to any public key cryptosystems. As this model is acting as a wrapper to any public key cryptosystems, it ensures enhanced security. The proposed methodology is implemented with different processors 1, 2, 4, 8 and 16 in a simulated environment using Maui scheduler which employs back filling philosophy.

Cite This Paper

Mani. K, Viswambari. M,"Enhancing the Security in Cryptosystems Based on Magic Rectangle", International Journal of Computer Network and Information Security(IJCNIS), Vol.9, No.4, pp.37-47, 2017.DOI: 10.5815/ijcnis.2017.04.05


[1]Hans Delfs and Helmut Knebl, "Introduction to Cryptography Principles and Applications, Springer-Verlag, Berlin Heidelberg, 2002. 

[2]Michael Springfield, Wayne Goddard, "The Existence of Domino Magic Squares and Rectangles", available at:, January 2008.

[3]Chand K. Midha, J. P. De Los Reyes, Ashish Das and L.Y. Chan, "On a method to construct magic rectangles of odd order", Statistics and Applications, Vol. 6, 2008.

[4]J. P. De Los Reyes, Ashish Das and Chand K. Midha "A matrix approach to construct magic rectangles of even order", available at:, January 2008.

[5]GopinathGanapathy, and K. Mani, "Add-On Security Model for Public-Key Cryptosystem Based on Magic Square Implementation", Proceedings of the World Congress on Engineering and Computer Science (WCECS), Vol. 1, October 2009.

[6]M. Kiran Kumar, S. MukthyarAzam, Shaik Rasool, "Efficient Digital Encryption AlgorithmBased on Matrix Scrambling Technique", International Journal of Network Security & Its Applications, IJNSA, Vol.2, No.4, October 2010.

[7]S. Praveen Kumar, K. Naveen Kumar, S. Sreenadh, B. Aravind and K. Hemnath Kumar, "Novel Advent for Add-On Security by Magic Square Intrication", Global Journal of Computer Science and Technology,Vol.11, Issue. 21, December 2011.

[8]John Lorch, "Linear Magic Rectangles", Linear and Multilinear Algebra, January 2012.

[9]Feng Shun Chai, "Construction of magic rectangles of odd order", Australasian Journal of Combinatorics, Vol.55, 2013.

[10]Israa N. Alkallak, "Using Magic Square of Order 3 To Solve Sudoku Grid Problem",Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26, January 2013.

[11]RinoviaSimanjuntak, Mona Elviyenti, Mohammad NafieJauhari, AlfanSukmanaPraja, and Ira ApniPurwasih, "Magic labelings of distance at most 2",, December 2013.

[12]Prashant Vasant Divase, SurajkumarRajeshwarThakare, MandarArunPingale, VivekJagnnathPatsawane and Mr. C. B. Pednekar, "User Side Authentication using Session Passwords and Colors Box", International Journal of Advance Research in Science and Engineering, IJARSE, Vol.4, Issue. 02, February 2015.

[13]Kunal Jain, Jitender Singh, RushikeshKapadnis and Bharti Dhote, "Effective Cryptposystem using MRGA with Steganography", International Journal of Advanced Research in Computer and Communication Engineering, Vol. 4, Issue 3, March 2015.

[14]DaliborFroncek, "Magic rectangle sets of odd order", December 2015.

[15]Omar A. Dawood,Abdul Monem S. Rahma and Abdul Mohssen J. Abdul Hossen, "Generalized Method for Constructing Magic Cube by Folded Magic Squares", I.J. Intelligent Systems and Applications, January 2016.

[16]NithiyaDevi.G, Sharmila.S, Saranya.N, Rajkumar.K and Gomathi.K, "Novel Architecture for Data – Shuffling Using Enhanced Fisher Yates Shuffle Algorithm", International Journal of Engineering Science and Computing, May 2016.

[17]ShikhaMathur and Deepika Gupta, "A Modified RSA Approach for Encrypting Video using Multi- Power, Multi Public Keys, Multi Prime Numbers and K-Nearest Neighbor Algorithm", International Journal on Recent and Innovation Trends in Computing and Communication, Vol. 4, Issue. 7, July 2016.