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MaD0: an ultrafast nonlinear pseudorandom number generator. (English) Zbl 1369.65008
MSC:
65C10 Random number generation in numerical analysis
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[1] Richard W. Hamming. 1950. Error detecting and error correcting codes. Bell System Technical Journal 29, 2, 147–160. · doi:10.1002/j.1538-7305.1950.tb00463.x
[2] Donald E. Knuth. 1998. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms (3rd ed.). Addison Wesley Longman, New York, NY. · Zbl 0895.65001
[3] Valentin Fedorovich Kolchin. 1986. Random Mappings. Springer.
[4] Pierre L’Ecuyer and Richard Simard. 2007. TestU01: A C library for empirical testing of random number generators. ACM Transactions on Mathematical Software 33, 4, 22. · Zbl 1365.65008
[5] Pierre L’Ecuyer, Richard Simard, E. Jack Chen, and W. David Kelton. 2002. An object-oriented random-number package with many long streams and substreams. Operations Research 50, 6, 1073–1075. · doi:10.1287/opre.50.6.1073.358
[6] Felix V. Leitner. 2009. Source Code Optimization. Retrieved December 22, 2015, from http://www.linux-kongress.org/2009/slides/compiler_survey_felix_von_leitner.pdf.
[7] Jie Li. 2013. Ultrafast Pseudorandom Number Generation Using Pseudorandom Permutations and Mappings. P.h.D. Dissertation. Publication No. 3601931. City University of New York, ProQuest/UMI.
[8] Chris Lomont. 2008. Random number generation. In Games Programming Gems 7, Course Technology. Retrieved December 22, 2015, from http://www.lomont.org/Math/Papers/2008/Lomont_PRNG_2008.pdf.
[9] George Marsaglia. 1995. The Marsaglia Random Number CDROM Including the Diehard Battery of Tests of Randomness. New version available at http://www.csis.hku.hk/diehard/.
[10] George Marsaglia. 2003. Xorshift RNGs. Journal of Statistical Software 8, 14, 1–6. · doi:10.18637/jss.v008.i14
[11] George Marsaglia and Wai Wan Tsang. 2002. Some difficult-to-pass tests of randomness. Journal of Statistical Software 7, 3, 1–9. · doi:10.18637/jss.v007.i03
[12] Makoto Matsumoto and Takuji Nishimura. 1998. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation 8, 1, 3–30. · Zbl 0917.65005 · doi:10.1145/272991.272995
[13] Bruce D. McCullough. 1998. Assessing the reliability of statistical software: Part I. American Statistician 52, 4, 358–366.
[14] National Institute of Standards and Technology. 2008. Secure Hash Standard (SHS). National Institute of Standards and Technology. Federal Information Processing Standards Publication 180-3.
[15] François Panneton, Pierre L’Ecuyer, and Makoto Matsumoto. 2006. Improved long-period generators based on linear recurrences modulo 2. ACM Transactions on Mathematical Software 32, 1, 1–16. · Zbl 1346.94089 · doi:10.1145/1132973.1132974
[16] Andrew Rukhin, Juan Soto, James Nechvatal, Miles Smid, Elaine Barker, Stefan Leigh, Mark Levenson, Mark Vangel, David Banks, Alan Heckert, James Dray, and San Vo. 2001. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST Special Publication 800-22. National Institute of Standards and Technology, Gaithersburg, MD.
[17] Mutsuo Saito and Makoto Matsumoto. 2008. SIMD-oriented fast Mersenne Twister: A 128-bit pseudorandom number generator. In Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, 607–622. · Zbl 1141.65319 · doi:10.1007/978-3-540-74496-2_36
[18] Brouce Schneier. 1996. Applied Cryptography. Protocols, Algorithms, and Source Code in C. John Wiley & Sons. · Zbl 0853.94001
[19] Paul C. Van Oorschot and Michael J. Wiener. 1999. Parallel collision search with cryptanalytic applications. Journal of Cryptology 12, 1, 1–28. · Zbl 0992.94028 · doi:10.1007/PL00003816
[20] A. F. Webster and S. E. Tavares. 1986. On the design of S-boxes. In Advances in Cryptology—CRYPTO ’85 Proceedings. Lecture Notes in Computer Science, Vol. 218. Springer, 523–534. · doi:10.1007/3-540-39799-X_41
[21] Jianliang Zheng and Jie Li. 2013. MARC: Modified ARC4. In Foundations and Practice of Security. Lecture Notes in Computer Science, Vol. 7743. Springer, 33–44. · Zbl 1317.94138 · doi:10.1007/978-3-642-37119-6_3
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