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Języki publikacji
Abstrakty
A class of Xorshift Random Number Generators (RNGs) are introduced by Marsaglia. We have proposed an algorithm which constructs a primitive Xorshift RNG from a given prim- itive polynomial. We also have shown a weakness present in those RNGs and suggested its solution. A separate algorithm also proposed which returns a full periodic Xorshift generator with desired number of Xorshift operations.
Czasopismo
Rocznik
Tom
Strony
1--13
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Center for Artificial Intelligence and Robotics, Defence Research and Development Organisation, CV Raman Nagar, Bengaluru 560093, India
- Faculty of Informatics, Masaryk Univerzity, Czechia
autor
- Indian Institute of Technology, Ropar, Punjab 140001, India
Bibliografia
- [1] S. W. Golomb. Shift Register Sequences. Cambridge University Press, 1967.
- [2] R. Lidl and H. Niederreiter. Finite fields. Cambridge University Press, 1996. DOI: 10.1017/cbo9780511525926.
- [3] S. R. Ghorpade, S. U. Hasan, and M. Kumari. Primitive polynomials, singer cycles and word-oriented linear feedback shift registers. Designs, Codes and Cryptography, 58(2):123-134, 2011. DOI: 10.1007/s10623-010-9387-7.
- [4] H. Niederreiter. The Multiple-Recursive Matrix Method for Pseudorandom Number Generation. Finite Fields and Their Applications, 1(1):3-30, 1995. DOI: 10.1006/ta.1995.1002.
- [5] H. Niederreiter. Pseudorandom vector generation by the multiple-recursive matrix method.Mathematics of Computation, 64(209):279-294, 1995. DOI: 10.1090/s0025-5718-1995-1265018-4.
- [6] H. Niederreiter. Improved Bounds in the Multiple-Recursive Matrix Method for Pseudorandom Number and Vector Generation. Finite Fields and Their Applications, 2(3):225-240,1996. DOI: 10.1006/ta.1996.0015.
- [7] G. Zeng, W. Han, and K. He. Word-oriented feedback shift register: σ-LFSR. Cryptology ePrint Archive: Report 2007/114, 2007.
- [8] R. P. Brent. On the periods of generalized Fibonacci recurrences. Mathematics of Computation, 63(207):389-389, 1994. DOI: 10.1090/s0025-5718-1994-1216256-7.
- [9] F. Panneton and P. L'ecuyer. On the xorshift random number generators. ACM Transactions on Modeling and Computer Simulation, 15(4):346-361, 2005. DOI: 10.1145/1113316.1113319.
- [10] A. J Menezes, P. C. Van Oorschot, and S. A. Vanstone. Handbook of applied cryptography. CRC press, 1996.
- [11] D. R. Stinson. Cryptography: theory and practice. CRC press, 2006.
- [12] S. K. Bishoi, H. K. Haran, and S. U. Hasan. A note on the multiple-recursive matrix method for generating pseudorandom vectors. Discrete Applied Mathematics, 222:67-75, 2017. DOI: 10.1016/j.dam.2017.01.033.
- [13] S. K. Bishoi and V. Matyas. Investigating results and performance of search and construction algorithms for word-based LFSRs, -LFSRs. Discrete Applied Mathematics, 2018. Accepted for publication.
- [14] G. Marsaglia. Xorshift RNGs. Journal of Statistical Software, 8(14), 2003. DOI:10.18637/jss.v008.i14.
- [15] D. Knuth et al. The Art of Computer Programming, Volume 2: Semi numerical Algorithms. Addison-Wesley Longman, Inc, 1998.
- [16] V. Chepyzhov and B. Smeets. On A Fast Correlation Attack on Certain Stream Ciphers. In Advances in Cryptology | EUROCRYPT '91, pages 176-185. Springer Berlin Heidelberg. DOI: 10.1007/3-540-46416-6 16.
- [17] V. V. Chepyzhov, T. J., and B. Smeets. A Simple Algorithm for Fast Correlation Attacks on Stream Ciphers. In Fast Software Encryption, pages 181-195. Springer Berlin Heidelberg, 2001. DOI: 10.1007/3-540-44706-7 13.
- [18] P. R. Mishra, I. Gupta, and N. Gaba. Distribution of Primitive Polynomials Over GF(2) with Respect to Their Weights. In Mathematics and Computing, pages 441-449. Springer India, 2015. DOI: 10.1007/978-81-322-2452-5 30.
- [19] A. Compagner. The hierarchy of correlations in random binary sequences. Journal of Statistical Physics, 63(5-6):883-896, 1991. DOI: 10.1007/bf01029989.
Uwagi
PL
Opracowanie w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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