Rhotrix-Modules and the Multi-Cipher Hill ciphers

S. M. Tudunkaya, S. Usaini

Abstract


Now a days, Hill cipher is almost relegated. It is mostly referred to as a reference or rather history material. This is due to its weaknesses in terms of security, difficulty in both the multiplication and inverse computation of matrices. This
paper presented a variant of the Hill Cipher that can be used to encrypt several ciphertexts together via the concept of rhotrices. In the proposed scheme, computation of products and inverses is easier and faster since computing products and inverses of rhotrices using heart based multiplication method is known to be easier than that of matrices. Also each plaintext rhotrix is indirectly encrypted by using its own key since it is presented in a row or column major similar to a plaintext block. Therefore, the presented scheme

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References


Ajibade, A.O., The Concept of Rhotrix in Mathematical Enrichment, Int. J. Math. Educ. Sci. Technol., vol 34: 175-179 (2003)

Hill, L.S., Cryptography in an Algebraic Alphabet. Am. Math. Mon., 36: 306-312 (1929).

Hill, L.S., Concerning Certain Linear Transformation Apparatus of Cryptography. Am. Math. Mon., 38: 135-154 (1931).

Ismail, I. A., Amin, M. and Diab, H., How to Repair the Hill Cipher, J. Zhejiang Uni., SCIENCE A, vol 7(12): 2022-2030 (2006).

Keliher, L., Cryptanalysis of a Modified Hill Cipher, Int. J. Comp. Network Sec., vol 2(7): 122-126 (2010).

Krishna, A. V. N. and Madhuravani, K., A Modified Hill Cipher using Randomized Approach, Int. J. Comp. Netw. Inform. Sec., vol 5: 56-62 (2012).

Lang, S., Algebra : Graduate Texts in Mathematics (fourth edition), New York, Springer-Verlag.

Li, C., Zhang, D. and Chen, G., Cryptanalysis of an Image Encryption Scheme based on the Hill Cipher, J. Zhejiang Uni., SCIENCE A, vol 9(08): 1118-1123 (2008).

Lin, C. H. and Lee, C. Y.,. Comments on Saeednias improved scheme for the Hill cipher, J. Chinese Inst. Eng., vol 27: 743-746 (2004).

Menezes, A. J., Oorschot, P. C. and Vanstone, S. A., Handbook of Applied Cryptography; Boca Raton, CRC Press (1997).

Mohammed, A., A Note on Rhotrix Exponent Rule and it's Application to Special Series and Polynomial Equations Defined over Rhotrices, Notes Num. Theo. Discrete Math., 13: 1-15 (2007).

Mohammed, A., Theoretical Development and Application of Rhotrices, PhD Dissertation. Amazon.com (2011).

Ning H., An Enhanced Hill Cipher and Its Application in Software Copy Protection, J. Networks, vol 9(10): (2014).

Overbey J., Traves W., and Wojdylo J., On the Key space of the Hill Cipher. Cryptologia., 29(1): 59-72 (2005).

Tudunkaya, S.M. and Makanjuola, S.O., Certain Construction of Finite Fields, J. Nig. Mathl Phy., vol 22: 95-104 (2012).

Tudunkaya, S.M. and Makanjuola, S.O., On the Structure of Rhotrix Rhotrices, J. Nig. Mathl Phy., vol 23: 41-50 (2013).

Tudunkaya, S.M., On the Hill Ciphers of Rhotrices, Afr. J. Comp. ICT, vol 8 (2)2: 109-114 (2015).

Saeedinia S., How to make the Hill Cipher Secure, Cryptologia, vol. 24 (4): 353-360 (2000).

Sani, B., An Alternative Method for Multiplication of Rhotrices, Int. J. Math. Educ. Sci. Tech., vol. 35: 777-781 (2004).

Stallings, W., Cryptography and Network Security : Principles and Practice (fifth edition), Boston, Practice Hall (2011).

Stinson, D. R., Cryptography : Theory and Practice (fourth edition), Boca Raton, Chapman and Hall/CRC Press (2006).

Toorani, M. and Falahati, A., A Secure Variant of the Hill Cipher, Proc.IEEE Symp. Comp. Comm., Susse, Tunisia. 313-316 (2009).


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