Deterministic Random Number Generator Algorithm for Cryptosystem Keys

Authors: Adi A. Maaita, Hamza A. A. Al_Sewadi

Abstract:

One of the crucial parameters of digital cryptographic systems is the selection of the keys used and their distribution. The randomness of the keys has a strong impact on the system’s security strength being difficult to be predicted, guessed, reproduced, or discovered by a cryptanalyst. Therefore, adequate key randomness generation is still sought for the benefit of stronger cryptosystems. This paper suggests an algorithm designed to generate and test pseudo random number sequences intended for cryptographic applications. This algorithm is based on mathematically manipulating a publically agreed upon information between sender and receiver over a public channel. This information is used as a seed for performing some mathematical functions in order to generate a sequence of pseudorandom numbers that will be used for encryption/decryption purposes. This manipulation involves permutations and substitutions that fulfill Shannon’s principle of “confusion and diffusion”. ASCII code characters were utilized in the generation process instead of using bit strings initially, which adds more flexibility in testing different seed values. Finally, the obtained results would indicate sound difficulty of guessing keys by attackers.

Keywords: Cryptosystems, Information Security agreement, Key distribution, Random numbers.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100935

References:

[1] B. Schneier, “Applied cryptography: protocols, algorithms, and source code in C,” Second Edition, John Wiley & Sons, 1996.
[2] D. Dilli, Madhu S., “Design of a New Cryptography Algorithm using Reseeding -Mixing Pseudo Random Number Generator,” IJITEE, vol. 52, No. 5, 2013
[3] K. Marton, A. Suciu, C. Sacarea, and Octavian Cret, “Generation and Testing of Random Numbers for Cryptographic Applications,” Proceedings of the Ramanian Academy, Series A, Vol. 13, No. 4, 2012, PP 368–377.
[4] S. Martain, “Testing of True Random Number Generator Used in Cryptography,”International Journal of Computer Applications IJCA, Vol.2, No. 4, 2012.
[5] Wikipedia, “Pseudorandom number generator”, Last visited December 2014.
[6] D. Dilli, and S. Madhu, “Design of a New Cryptography Algorithm using Reseeding -Mixing Pseudo Random Number Generator,” IJITEE, vol. 52, no. 5, 2013.
[7] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A Statistical Test Suite for Random and Pseudorandom Generators for Cryptographic Application,” NIST Special Publication 800-22, 2001.
[8] P. Burns, “Lagged, Fibonacci Random Number Generators”, GS 510, fall 2004, http://lamar.colostate.edu/~grad511/lfg.pdf.
[9] A. B. Orue, F. Montoya, and L. H. Encinas, “Trifork, a New Pseudorandom Number Generator Based on Lagged Fibonacci Maps,” Journal of Computer Science and Engineering, vol. 1, no. 10, 2010.
[10] Random.org (Randomness and Integrity Service LTD),
[11] https://www.random.org/integers/, Last visited 3/1/2015.
[12] F. W. Burton, and R. L. Page, “Distributed random number generation”, Journal of Functional Program, vol. 2, no. 2, 1992, PP 203–212.
[13] K. Claessen, and M. Palka, "Splittable Pseudorandom Number Generators using Cryptographic Hashing," Proceedings of Haskell Symposium, 2013, PP 47-58.
[14] J. M. Bahi, and C. Guyeux, “Topological chaos and chaotic iterations, application to hash functions,” IEEE World Congress on Computational Intelligence WCCI’, Barcelona, Spain, July 2010. Best paper award, PP 1–7,
[15] J. Bahi, C. Guyeux, and Q. Wang, “A novel pseudo-random generator based on discrete chaotic iterations,” INTERNET’09, 1-st International conference on Evolving Internet, Cannes, France, August 2009, PP 71– 76.
[16] J. Bahi, C. Guyeux, and Qianxue Wang, ”A pseudo random numbers generator based on chaotic iterations; Application to watermarking,” International conference on Web Information Systems and Mining, WISM 2010, vol. 6318 of LNCS, Sanya, China, October 2010, PP 202– 211.
[17] Y. Hu, X. Liao, K. W. Wong, and Qing Zhou, “A true random number generator based on mouse movement and chaotic cryptography,” Chaos, Solitons & Fractals, vol.40, no. 5, 2009, PP 2286–2293.
[18] L. De Micco, C. M. Gonzaez, H.A. Larrondo, M.T. Martin, A. Plastino, and O.A. Rosso, “Randomizing nonlinear maps via symbolic dynamics,” Physica A: Statistical Mechanics and its Applications, vol. 387, no. 14, 2008, PP 3373–3383.
[19] L. Larger, and J. M. Dudley, “Nonlinear dynamics Optoelectronic chaos,” Nature, vol. 465, no. 7294, 2010, PP 41–42.
[20] Q. Wang, J. Bahi, C. Guyeux, and X. Fang, “Randomness quality of CI chaotic generators; application to internet security,” INTERNET’2010. The 2nd International Conference on Evolving Internet, Valencia, Spain, September 2010. IEEE Computer Society Press. Best Paper award, PP 125–130.
[21] H. B. Neumann, S. Scholze, and M. Voegeler, “Method of generating pseudo-random numbers,” US 20090150467 A1 , Jun 11, 2009.
[22] M. N. Elsherbeny, and M. Raha, “Pseudo –Random Number Generator Using Deterministic Chaotic System,” International Journal of Scientific and Technology Research,” vol. 1, no. 9, Oct. 2012.
[23] S. Behnia, A. Akhavan, A. Akhshani, and A.Samsudin, “A novel dynamic model of pseudo random number generator,” Journal of Computational and Applied Mathematics –J COMPUT APPL MATH, vol. 235, no. 12, 2011, PP 3455-3463.
[24] W. Bhaya and W. Mahdi, “ Fingerprint Security Approach for Information Exchange on Networks,” European Journal of Scientific Research, vol. 123, no 2, 2014, PP 169-181.