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An Improved Divisibility Test Algorithm for Primality Testing

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 214)

Abstract

Security of information is a major concern now a days in the world. Cryptography plays a major role in ensuring the safety of the information that is being transferred over the internet or any unsecure medium. Prime Numbers are very important aspect of any Cryptographic System and play a major role in ensuring the safety of the concerned Cryptographic System. Currently there are various algorithms used for checking that a particular number is a prime or not. Few of the commonly used algorithms are Divisibility Test, Fermat Test, and Chinese Primality Test etc. This paper proposes an enhancement in the Divisibility Primality Testing algorithm that reduces the number of comparisons to be made and thus enhancing the performance of the algorithm. In addition to this the pseudo code and implementation code of the improved algorithm are provided in detail. An analysis and comparison of the existing algorithm and the enhanced algorithm is also presented in the given paper.

Keywords

Primality testing Prime numbers Divisibility primality testing algorithm 

Notes

Acknowledgments

We thank Anu Kumari, Anshul Verma and Rajeev Pratap Singh for their contribution and sharing their insight on improved divisibility test algorithm development.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2011-0023076) and 2011 ADD project.

References

  1. 1.
    Schneier, B.: Applied Cryptography: Protocols, Algorithms, and Source Code In C. Wiley, New York (1996)MATHGoogle Scholar
  2. 2.
    Van Der Lubbe, J.C.A.: Basic Methods of Cryptography. Cambridge University Press, New York (1998)MATHGoogle Scholar
  3. 3.
    Kejariwal, A.: Cryptic primes. IEEE Potential 23, 43–45 (2004)CrossRefGoogle Scholar
  4. 4.
    Kumar, R.S., Pradeep,E., Naveen, K., Gunasekaran, R.: Enhanced cost effective symmetric key algorithm for small amount of data. In: 2nd IEEE International Conference on Signal Acquisition and Processing, pp. 354–357. IEEE Press, Bangalore (2010)Google Scholar
  5. 5.
    Singh, S.: Analysis and implementation of public-key cryptosystem based on the boolean satisfiability problem. In: 7th Malasia International Conference on Communication, pp. 704–709. IEEE Press, Kuala Lumpur (2005)Google Scholar
  6. 6.
    Bresson, P D.C., Pointcheval, D.: A simple public key cryptosystem with a double trapdoor decryption mechanism and its applications. In: Aciacrypt 2003. LNCS, vol. 2894, pp. 37–54. Springer, Berlin (2003)Google Scholar
  7. 7.
    Adleman, L.M.: On distinguishing prime numbers from composite numbers. In: 21st IEEE Annual Symposium on Foundations of Computer Science, pp. 387–406. IEEE Press, New York (1980)Google Scholar
  8. 8.
    Fellows, M.R., Koblitz, N.: Self-witnessing polynomial-time complexity and prime factorization. In: Proceedings of the Seventh Annual Structure in Complexity Theory Conference, pp. 107–110.I EEE Press, Canada (1992)Google Scholar
  9. 9.
    Forouzan, B.A., Mukhopadhyay, D.: Cryptography and Network Security. Mc Graw Hill, India (2011)Google Scholar
  10. 10.
    Agrawal, M., Kayal, N., Saxena, N.: PRIMES is in P. Ann. Math. 2, 781–793 (2002)MathSciNetGoogle Scholar
  11. 11.
    Rabin, M.O.: Probabilistic algorithm for testing primality. J. Num. Theory 12, 128–138 (1980)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Agrawal, M., Biswas, S.: Primality and identity testing via Chinese remaindering. In: 40th IEEE Annual Symposium on Foundations of Computer Science, pp. 202–208. IEEE Press, Kanpur (1999)Google Scholar
  13. 13.
    Zhu, W.T.: Analyzing euler-fermat theorem based multicast key distribution schemes with chinese remainder theorem. In: IFIP International Conference on Network and Parallel Computing, pp. 11–17. IEEE Press, Shanghai (2008)Google Scholar
  14. 14.
    Penzhorn, W.T.: Fast algorithms for the generation of large primes for the RSA cryptosytem. In: Proceedings of the 1992 South African Symposium on Communication and Signal Processing, pp. 169–172. IEEE Press, South Africa (1992)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Ubiquitous-ITDongseo UniversityBusanKorea
  2. 2.Department of Communication and Information EngineeringDongseo UniversityBusanKorea

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