Advertisement

Cryptographically Secure Diffusion Sequences—An Attempt to Prove Sequences Are Random

  • M. Y. Mohamed ParveesEmail author
  • J. Abdul Samath
  • B. Parameswaran Bose
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 750)

Abstract

The use of random numbers in day-to-day digital life is increasing drastically to make the digital data more secure in various disciplines, particularly in cryptography, cloud data storage, and big data applications. Generally, all the random numbers or sequences are not truly random enough to be used in various applications of randomness, predominantly in cryptographic applications. Therefore, the sequences generated by pseudorandom number generator (PRNGs) are not cryptographically secure. Hence, this study proposes a concept that the diffusion sequences which are used during cryptographic operations need to be validated for randomness, though the random number generator produces the random sequences. This study discusses the NIST, Diehard and ENT test suite results of random diffusion sequences generated by two improved random number generators namely, Enhanced Chaotic Economic Map (ECEM), and Improved Linear Congruential Generator (ILCG).

Keywords

Random number generator Chaotic map Diffusion Confusion Sequences Encryption Security 

References

  1. 1.
    Chen, J., Miyaji, A., Su, C.: Distributed pseudo-random number generation and its application to cloud database. In: Huang, X., Zhou, J. (eds.) Information Security Practice and Experience. ISPEC 2014. Lecture Notes in Computer Science, vol. 8434. Springer, Cham (2014)Google Scholar
  2. 2.
    Deng, L.Y., Bowman, D.: Developments in pseudo-random number generators: Pseudo-random number generators. Wiley Interdisc. Rev. Comput. Stat. 9(5), e1404 (2017).  https://doi.org/10.1002/wics.1404
  3. 3.
    Stoyanov, B.P., Kordov, K.: A Novel pseudorandom bit generator based on Chirikov standard map filtered with shrinking rule. Math. Prob. Eng. 2014, (2014) Article ID 986174, p. 4.  https://doi.org/10.1155/2014/986174
  4. 4.
    Patidar, V., Sud K.K., Pareek K.: A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica 33, 441–452 (2009)Google Scholar
  5. 5.
    Stoyanov, B.P., Szczypiorski, K., Kordov, K.: Yet another pseudorandom number generator. Int. J. Electron. Telecommun. 63(2), 195–199 (2017).  https://doi.org/10.1515/eletel-2017-0026CrossRefGoogle Scholar
  6. 6.
    Kordov, K., Stoyanov B.:, Least significant bit steganography using Hitzl-Zele Chaotic Map. Int. J. Electron. Telecommun. 63(4) (2017)Google Scholar
  7. 7.
    Rahimov, H., Babaie, M., Hassanabadi, H.: Improving middle square method RNG using chaotic map. Appl. Math. 2, 482–486 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sridevi, R., Philominat, P., Padmapriya, P., Rayappan, J.B.B., Amirtharajan, R.: Logistic and standard coupled mapping on pre and post shuffled images: a method of image encryption. Asian J. Sci. Res. 10(1), 10–23. (2016).  https://doi.org/10.3923/ajsr.2017.10.23
  9. 9.
    Patidar, V.R., Sud, K.K.: A novel pseudo random bit generator based on chaotic standard map and its testing. Electron. J. Theoret. Phys. 6(20), 327–344 (2009)Google Scholar
  10. 10.
    Rukhin, A., Soto, J., Nechvatal, J., et al.: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Application. NIST Special Publication 800-22, Revision 1a (Revised: April 2010), Lawrence E. Bassham III, (2010). http://csrc.nist.gov/groups/ST/toolkit/rng/index.html
  11. 11.
    Marsaglia, G. Diehard: a battery of tests of randomness (1996) http://www.fsu.edu/pub diehard
  12. 12.
    Walker, J.: ENT: a pseudorandom number sequence test program (2008) http://www.fourmilab.ch/random/
  13. 13.
    Soto, J.: Randomness testing of the advanced encryption standard candidate algorithms. NIST Internal Reports 6390 (1999), http://csrc.nist.gov/publications/nistir/ir6390.pdf
  14. 14.
    Parvees, M.Y.M., Samath, J.A.: Bose BP secured medical images—a chaotic pixel scrambling approach. J. Med. Syst. 40, 232 (2016).  https://doi.org/10.1007/s10916-016-0611-5CrossRefGoogle Scholar
  15. 15.
    Parvees, M.Y.M., Samath, J.A., Bose, B.P.: Medical images are safe—an enhanced chaotic scrambling approach. J. Med. Syst. 41, 167 (2017).  https://doi.org/10.1007/s10916-017-0809-1CrossRefGoogle Scholar
  16. 16.
    Stępień, R., Walczak, J.: Statistical analysis of the LFSR generators in the NIST STS test suite. Comput. Appl. Electr. Eng. 11, 356–362 (2013)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • M. Y. Mohamed Parvees
    • 1
    • 2
    Email author
  • J. Abdul Samath
    • 3
  • B. Parameswaran Bose
    • 4
    • 5
  1. 1.Division of Computer & Information ScienceAnnamalai UniversityChidambaramIndia
  2. 2.Research & Development CentreBharathiar UniversityCoimbatoreIndia
  3. 3.Department of Computer ScienceGovernment Arts CollegeUdumalpetIndia
  4. 4.Fat Pipe Network Pvt. Ltd.ChennaiIndia
  5. 5.BengaluruIndia

Personalised recommendations