Uniform Random Quantity Generator using Complete Vortex Array Technology

Uniformly distributed random quantity generators are widely used in various applications ranging from mathematics, radio-electronic and technical designing to medical and biological research. This paper proposes a novel approach to generating random quantities by combining the initial congruent array with a global circular vortex for complete stochastic sequences. We experimentally confirmed that for the complete sequences generation of this type provides random quantity uniform distribution. The proposed software includes the generation technique tuning methods where random quantities may take any bit length. Moreover, we examined the automatic switching of such generator parameters as initial values and congruent constants, which allowed us to increase the amount of the options of the generated sequences. Findings of the research confirm the absolute uniformity of distribution without any repeated or skipped elements in generated sequences of random quantities.

References

[1] Tusnoo Y., Saito T., Suzaki T., Shigeri M., Miyauchi H. Cryptanalysis of DES implemented on computers with cache. Proc. Cryptographic Hardware and Embedded Systems - CHES 2003. 5th Int. Workshop, 2003, pp. 62-76. DOI: 10.1007/978-3-540-45238-6_6 Available at: http://link.springer.com/chapter/10.1007%2F978-3-540-45238-6_6

[2] Ozturk E., Sunar V., Savas E. Low-power elliptic curve cryptography using scaled modular arithmetic. Proc. Cryptographic Hardware and Embedded Systems - CHES 2004. 6th Int. Workshop, 2004, pp. 92-106. DOI: 10.1007/978-3-540-28632-5_7 Available at: http://link.springer.com/chapter/10.1007%2F978-3-540-28632-5_7

[3] Panneton F., L’Ecuyer R., Matsumoto M. Improved long-period generators based on linear recurrences modulo 2. ACM TOMS, 2006, vol. 32, no. 1, pp. 1-16. DOI: 10.1145/1132973.1132974 Available at: http://dl.acm.org/citation.cfm?doid=1132973.1132974

[4] Deon A.F., Menyaev Yu.A. The complete set simulation of stochastic sequences without repeated and skipped elements. Journal of Universal Computer Science, 2016, vol. 22, no. 8, pp. 1023-1047. DOI: 10.3217/jucs-022-08-1023 Available at: http://www.jucs.org/jucs_22_8/the_complete_set_simulation

[5] Entacher K. Bad subsequences of well-known linear congruential pseudorandom number generators. ACM TOMACS, 1998, vol. 8, no. 1, pp. 61-70. DOI: 10.1145/272991.273009 Available at: http://dl.acm.org/citation.cfm?doid=272991.273009

[6] Leeb H., Wegenkittl S. Inversive and linear congruential pseudorandom number generators in empirical tests. ACM TOMACS, 1997, vol. 7, pp. 272-286. DOI: 10.1145/249204.249208 Available at: http://dl.acm.org/citation.cfm?doid=249204.249208

[7] Park S.K., Miller K.W. Random number generators: good ones are hard to find. Communication of the ACM, 1988, vol. 31, no. 10, pp. 1192-1201. DOI: 10.1145/63039.63042 Available at: http://dl.acm.org/citation.cfm?doid=63039.63042

[8] Menyaev Yu.A., Nedosekin D.A., Sarimollaoglu M., Juratli M.A., Galanzha E.I., Tuchin V.V., Zharov V.P. Optical clearing in photoacoustic flow cytometry. Biomed. Opt. Express., 2013, vol. 4, no. 12, pp. 3030-3041. DOI: 10.1364/BOE.4.003030 Available at: https://www.osapublishing.org/boe/abstract.cfm?uri=boe-4-12-3030

[9] Wiese K.C., Hendriks A., Deschenes A., Youssef V.V. The impact of pseudorandom number quality on P-RnaPredict, a parallel genetic algorithm for RNA secondary structure prediction. GECCO ’05. Proc. 7th Annual Conf. on Genetic and Evolutionary Computation, 2005, pp. 479-480. DOI: 10.1145/1068009.1068089 Available at: http://dl.acm.org/citation.cfm?doid=1068009.1068089

[10] Leonard P., Jackson D. Efficient evolution of high entropy RNGs using single node genetic programming. GECCO ’15. Proc. of the 2015 Annual Conf. on Genetic and Evolutionary Computation, 2015, pp. 1071-1078. DOI: 10.1145/2739480.2754820 Available at: http://dl.acm.org/citation.cfm?doid=2739480.2754820

[11] Niederreiter H. Some linear and nonlinear methods for pseudorandom number generation. WSC ’95. Proc. of the 27th Conf. on Winter Simulation, 1995, pp. 250-254. DOI: 10.1145/224401.224611 Available at: http://dl.acm.org/citation.cfm?doid=224401.224611

[12] Entacher K. Parallel streams of linear random numbers in the spectral test. ACM TOMACS, 1999, vol. 9, no. 1, pp. 31-44. DOI: 10.1145/301677.301682 Available at: http://dl.acm.org/citation.cfm?doid=301677.301682

[13] Matsumoto M., Nishimura T. Mersenne twister: a 623-dimensionnally equidistributed uniform pseudorandom number generator. ACM TOMACS, 1998, vol. 8, no. 1, pp. 3-30. DOI: 10.1145/272991.272995 Available at: http://dl.acm.org/citation.cfm?doid=272991.272995

[14] Nishimura T. Tables of 64-bit Mersenne twisters. ACM TOMACS, 2000, vol. 10, no. 4, pp. 348-357. DOI: 10.1145/369534.369540 Available at: http://dl.acm.org/citation.cfm?doid=369534.369540

[15] Makino J. Lagged-Fibonacci random number generators on parallel computers. Parallel Comput., 1994, vol. 20, no. 9, pp. 1357-1367. DOI: 10.1016/0167-8191(94)90042-6 Available at: http://www.sciencedirect.com/science/article/pii/0167819194900426?via%3Dihub

[16] Aluru S. Lagged Fibonacci random number generators for distributed memory parallel computers. J. Parallel Distr. Com., 1997, vol. 45, no. 1, pp. 1-12. DOI: 10.1006/jpdc.1997.1363 Available at: http://www.sciencedirect.com/science/article/pii/S0743731597913630?via%3Dihub

[17] Blum L., Blum M., Shub M. A Simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 1986, vol. 15, no. 2, pp. 364-383. DOI: 10.1137/0215025 Available at: http://epubs.siam.org/doi/10.1137/0215025

[18] Schildt H. C# 4.0: the complete reference. New York, The McGraw-Hill Companies, 2010, 949 p.

[19] Saito M., Matsumoto M. SIMD-oriented fast Mersenne twister: a 128-bit pseudorandom number generator. In: Monte Carlo and quasi-Monte Carlo methods 2006. Heidelberg, Berlin, Springer, 2008, pp. 607-622. DOI: 10.1007/978-3-540-74496-2_36 Available at: http://link.springer.com/chapter/10.1007%2F978-3-540-74496-2_36

[20] Lewis T.G., Payne W.H. Generalized feedback shift register pseudorandom number algorithm. J. ACM., 1973, vol. 20, no. 3, pp. 456-486. DOI: 10.1145/321765.321777 Available at: http://dl.acm.org/citation.cfm?doid=321765.321777

[21] Chandrasekaran S., Amira A. High performance FPGA implementation of the Mersenne twister. DELTA. IEEE Int. Workshop on Electronic Design, Test and Applications, 2008, pp. 482-485. DOI: 10.1109/DELTA.2008.113 Available at: http://ieeexplore.ieee.org/document/4459598

[22] Pellicer-Lostao C., Lopez-Ruiz R. Pseudo-random bit generation based on 2D chaotic maps of logistic type and its applications in chaotic cryptography. Proc. Computational Science and its Applications - ICCSA 2008 Int. Conf. Part. II. 2008, vol. 5073, pp. 784-796. DOI: 10.1007/978-3-540-69848-7_62 Available at: http://link.springer.com/chapter/10.1007%2F978-3-540-69848-7_62

[23] Bos J.W., Kleinjung T., Lenstra A.K., Montgomery P.L. Efficient SIMD arithmetic modulo a Mersenne number. ARITH ’11. Proc. IEEE 20th Symp. on Computer Arithmetic, 2011, pp. 213-221. DOI: 10.1109/ARITH.2011.37 Available at: http://ieeexplore.ieee.org/document/5992129

[24] Rahimov H., Babaie M., Hassanabadi N. Improving middle square method RNG using chaotic map. Appl. Math., 2011, vol. 2, pp. 482-486. DOI: 10.4236/am.2011.24062 Available at: http://file.scirp.org/pdf/AM20110400016_12226152.pdf

[25] Deon A.F., Menyaev Yu.A. Parametrical tuning of twisting generator. Journal of Computer Science, 2016, vol. 12, no. 8, pp. 363-378. DOI: 10.3844/jcssp.2016.363.378 Available at: http://thescipub.com/abstract/10.3844/jcssp.2016.363.378