Skip to main content

Dynamic Ciphering-15 Based on Multiplicative Polynomial Inverses Over Galois Field GF(73)

  • Chapter
  • First Online:
Advanced Computing and Systems for Security

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 395))

  • 1628 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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)

    Google Scholar 

  2. Stallings, W.: Finite fields. In: Cryptography and Network Security Principles and Practices, 4th ed., pp. 95–133. Pearson Education, Delhi (2008)

    Google Scholar 

  3. Forouzan, B.A., Mukhopadhyay, D.: Mathematics of cryptography. In: Cryptography and Network Security, 2nd edn., pp. 15–43. TMH, New Delhi (2011)

    Google Scholar 

  4. Roos, A.: A Class of Weak Keys in the RC4 Stream Cipher (Sept. 1995)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    Google Scholar 

  8. Paul, G., Maitra, S.: RC4 Stream Cipher and Its Variants. Chapman & Hall/CRC, Boca Raton (2012)

    MATH  Google Scholar 

  9. 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)

    Google Scholar 

  10. Knuth, D.E.: The Art of Computer Programming Seminumerical Algorithms, 3rd edn., Vol. 2. Pearson Education, Upper Saddle River (2011)

    Google Scholar 

  11. Church, R.: Tables of irreducible polynomials for the first four prime moduli. Ann. Math. 36(1), 198–209 (1935)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lidl, R., Niederreiter, H.: Finite Fields, Encyclopedia of Mathematics and Its Applications, Vol. 20. Addison-Wesley Publishing Company (1983)

    Google Scholar 

  13. Arguello, F.: Lehmer-based algorithm for computing inverses in Galois fields GF(2m). Electron. Lett. IET J. Mag. 42(5), 270–271 (2006)

    Article  Google Scholar 

  14. Yan, Z., Starwate, D.V.: New systolic architectures for inversion and division in GF(2 m). IEEE Trans. Comput. 52(11), 1514–1519 (2003)

    Google Scholar 

  15. Hasan, M.A.: Double-basis multiplicative inversion over GF(2 m). IEEE Trans. Comput. 47(9), 960–970 (1998)

    Article  MathSciNet  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Brunner, H., Curiger, A., Hofstetter, M.: On computing multiplicative inverses in GF(2m). IEEE Trans. Comput. 42(8), 1010–1015 (1993)

    Article  MathSciNet  Google Scholar 

  18. 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)

    Google Scholar 

  19. 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)

    Google Scholar 

  20. http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

  21. 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)

    Google Scholar 

  22. http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html

  23. Zaman, J.K.M.S., Ghosh, R.: Review on fifteen statistical tests proposed by NIST. Int. J. Theor. Phys. Crypt. 1, 18–31 (2012)

    Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to J K M Sadique Uz Zaman .

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics