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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 626408, 14 pages
http://dx.doi.org/10.1155/2015/626408
Research Article

New Statistical Randomness Tests Based on Length of Runs

1Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey
2Mathematics Department, Atılım University, 06836 Ankara, Turkey

Received 27 September 2014; Accepted 17 March 2015

Academic Editor: Anna Vila

Copyright © 2015 Ali Doğanaksoy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. J. Menezes, S. A. Vanstone, and P. C. V. Oorschot, Handbook of Applied Cryptography, CRC Press, Boca Raton, Fla, USA, 1st edition, 1996.
  2. D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison-Wesley, Longman Publishing, Boston, Mass, USA, 3rd edition, 1997.
  3. A. L. Rukhin, “Testing randomness: a suite of statistical procedures,” Theory of Probability & Its Applications, vol. 45, no. 1, pp. 111–132, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Marsaglia, “The marsaglia random number CDROM including the diehard battery of tests of randomness,” 1995, http://www.stat.fsu.edu/pub/diehard/.
  5. W. Caelli, “Crypt x package documentation,” Tech. Rep., Information Security Research, 1992. View at Google Scholar
  6. P. L'ecuyer and R. Simard, “TestU01: a C library for empirical testing of random number generators,” ACM Transactions on Mathematical Software, vol. 33, no. 4, article 22, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. L. E. Bassham III, A. L. Rukhin, J. Soto et al., “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Tech. Rep. Sp 800-22 rev.1a, NIST, Gaithersburg, Md, USA, 2010. View at Google Scholar
  8. U. M. Maurer, “A universal statistical test for random bit generators,” Journal of Cryptology, vol. 5, no. 2, pp. 89–105, 1992. View at Publisher · View at Google Scholar · View at Scopus
  9. V. Katos, “A randomness test for block ciphers,” Applied Mathematics and Computation, vol. 162, no. 1, pp. 29–35, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. P. M. Alcover, A. Guillamón, and M. D. C. Ruiz, “A new randomness test for bit sequences,” Informatica, vol. 24, no. 3, pp. 339–356, 2013. View at Google Scholar · View at Scopus
  11. S. W. Golomb, Shift Register Sequences, Aegean Park Press, Laguna Hills, Calif, USA, 1982.
  12. S.-J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the nist statistical test suite for randomness,” International Association for Cryptologic Research, p. 18, 2004. View at Google Scholar
  13. K. Hamano and H. Yamamoto, “A randomness test based on T-codes,” in Proceedings of the International Symposium on Information Theory and its Applications (ISITA '08), pp. 1–6, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. K. Hamano and T. Kaneko, “Correction of overlapping template matching test included in NIST randomness test suite,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 90, no. 9, pp. 1788–1792, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Soto and L. Bassham, “Randomness testing of the advanced encryption standard finalist candidates,” NIST IR 6483, National Institute of Standards and Technology, 1999. View at Google Scholar
  16. F. Sulak, A. Doğanaksoy, B. Ege, and O. Koçak, “Evaluation of randomness test results for short sequences,” in Sequences and Their Applications—SETA 2010, vol. 6338 of Lecture Notes in Computer Science, pp. 309–319, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar
  17. S. Ross, A First Course in Probability, Prentice Hall, New York, NY, USA, 6th edition, 2002.
  18. C. Burwick, D. Coppersmith, E. D'Avignon et al., Mars—a candidate cipher for AES, NIST AES Proposal, 1999.
  19. R. L. Rivest, M. J. B. Robshaw, Y. Yin, and R. Sidney, The RC6 Block Cipher, 1998.
  20. J. Daemen and V. Rijmen, The Design of Rijndael, Springer, New York, NY, USA, 2002.
  21. E. Biham, R. J. Anderson, and L. R. Knudsen, “Serpent: a new block cipher proposal,” in Fast Software Encryption: 5th International Workshop, FSE' 98 Paris, France, March 23–25, 1998 Proceedings, vol. 1372 of Lecture Notes in Computer Science, pp. 222–238, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar
  22. B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall, and N. Ferguson, “Twofish: a 128-bit block cipher,” in Proceedings of the 1st Advanced Encryption Standard (AES) Conference, Ventura, Calif, USA, August 1998.
  23. H. M. Heys, “A tutorial on linear and differential cryptanalysis,” Cryptologia, vol. 26, no. 3, pp. 189–221, 2002. View at Publisher · View at Google Scholar