Abstract
A new stream ciphering technique based on multiplicative polynomial inverses over Galois Field GF(73) is proposed, where a set of randomly generated key-bytes, between 1 and 15, is dynamically permuted and XORed with the identical number of message bytes. The output cipher is tested using NIST Statistical Test Suite and results are compared with that obtained by the well-known RC4 stream cipher. The new cipher is statistically random and observed to be better than RC4.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Zaman, J.K.M.S., Ghosh, R.: Multiplicative polynomial inverse over GF(73): crisis of EEA and its solution. Appl. Comput. Sec. Syst. 2, 87–107 (2014). (Springer)
Stallings, W.: Finite fields. In: Cryptography and Network Security Principles and Practices, 4th ed., pp. 95–133. Pearson Education, Delhi (2008)
Forouzan, B.A., Mukhopadhyay, D.: Mathematics of cryptography. In: Cryptography and Network Security, 2nd edn., pp. 15–43. TMH, New Delhi (2011)
Roos, A.: A Class of Weak Keys in the RC4 Stream Cipher (Sept. 1995)
Fluhrer, S., Mantin, I., Shamir, A.: Weakness in the key scheduling algorithm of RC4. In: Proceedings of International Workshop on Selected Areas in Cryptography, Berlin Heidelberg, LNCS 2259, pp. 1–24 (2001)
Paul, B., Preneel: A new weakness in the RC4 Keystream. Generator and an approach to improve the security of the cipher. In: Proceedings of Fast Software Encryption, Berlin, LNCS 3017, pp. 245–259 (2004)
Maitra, S., Paul, G.: Analysis of RC4 and proposal of additional layers for better security margin. In: Proceedings of Indocrypt, IIT Kharagpur, LNCS 5365, pp. 27–39 (2008)
Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants. Chapman & Hall/CRC, Boca Raton (2012)
Stinson, D.R.: The RSA cryptosystem and factoring integers. In: Cryptography Theory and Practice, 3rd edn., pp. 161–232 Chapman & Hall/CRC, Boca Raton (2006)
Knuth, D.E.: The Art of Computer Programming Seminumerical Algorithms, 3rd edn., Vol. 2. Pearson Education, Upper Saddle River (2011)
Church, R.: Tables of irreducible polynomials for the first four prime moduli. Ann. Math. 36(1), 198–209 (1935)
Lidl, R., Niederreiter, H.: Finite Fields, Encyclopedia of Mathematics and Its Applications, Vol. 20. Addison-Wesley Publishing Company (1983)
Arguello, F.: Lehmer-based algorithm for computing inverses in Galois fields GF(2m). Electron. Lett. IET J. Mag. 42(5), 270–271 (2006)
Yan, Z., Starwate, D.V.: New systolic architectures for inversion and division in GF(2 m). IEEE Trans. Comput. 52(11), 1514–1519 (2003)
Hasan, M.A.: Double-basis multiplicative inversion over GF(2 m). IEEE Trans. Comput. 47(9), 960–970 (1998)
Guo, J.H., Wang, C.L.: Systolic array implementation of euclid’s algorithm for inversion and division in GF(2m). IEEE Trans. Comput. 47(10), 1161–1167 (1998)
Brunner, H., Curiger, A., Hofstetter, M.: On computing multiplicative inverses in GF(2m). IEEE Trans. Comput. 42(8), 1010–1015 (1993)
Wang, C.C., Truong, T.K., Shao, H.M., Deutsch, L.J., Omura, J.K., Reed, I.S.: VLSI architecture for computing multiplications and inverses in GF(2m). IEEE Trans. Comput. C-34(8), 709–717 (1985)
Rukhin, A., Soto, J., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST, US, Technology Administration, U.S. Department of Commerce (2010)
http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf
Rukhin, A., Soto, J., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST, Technology Administration, U.S. Department of Commerce (2008)
http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html
Zaman, J.K.M.S., Ghosh, R.: Review on fifteen statistical tests proposed by NIST. Int. J. Theor. Phys. Crypt. 1, 18–31 (2012)
Acknowledgments
We express our gratitude toward the DST, New Delhi and the TEQIP (Phase-II), University of Calcutta for providing financial support, respectively, to the first author and the second author. We are also indeed thankful to the Head of the Department of Radio Physics and Electronics, University of Calcutta for providing necessary infrastructural facilities to undertake the research activities.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer India
About this chapter
Cite this chapter
Zaman, J.K.M.S.U., Dey, S., Ghosh, R. (2016). Dynamic Ciphering-15 Based on Multiplicative Polynomial Inverses Over Galois Field GF(73). In: Chaki, R., Cortesi, A., Saeed, K., Chaki, N. (eds) Advanced Computing and Systems for Security. Advances in Intelligent Systems and Computing, vol 395. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2650-5_3
Download citation
DOI: https://doi.org/10.1007/978-81-322-2650-5_3
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2648-2
Online ISBN: 978-81-322-2650-5
eBook Packages: EngineeringEngineering (R0)