MaD0: An Ultrafast Nonlinear Pseudorandom Number Generator
Article No.: 13, Pages 1 - 19
Abstract
In this article, we present MaD0, an ultrafast nonlinear pseudorandom number generator (PRNG) for noncryptographic applications. MaD0 uses byte-oriented operations for state initialization and fast integer-oriented operations for state transition and pseudorandom number generation. Its state transition follows a pseudorandom mapping. MaD0 generates high-quality pseudorandom numbers and reaches a generation speed of half cycle per byte on an Intel Core i3 processor. It has a state space of 2,240 bits and an expected period length around 21120. It also shows other good properties, such as fast recovery from biased states and ease of use.
References
[1]
Richard W. Hamming. 1950. Error detecting and error correcting codes. Bell System Technical Journal 29, 2, 147--160.
[2]
Donald E. Knuth. 1998. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms (3rd ed.). Addison Wesley Longman, New York, NY.
[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.
[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.
[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.
[11]
George Marsaglia and Wai Wan Tsang. 2002. Some difficult-to-pass tests of randomness. Journal of Statistical Software 7, 3, 1--9.
[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.
[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.
[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.
[18]
Brouce Schneier. 1996. Applied Cryptography. Protocols, Algorithms, and Source Code in C. John Wiley & Sons.
[19]
Paul C. Van Oorschot and Michael J. Wiener. 1999. Parallel collision search with cryptanalytic applications. Journal of Cryptology 12, 1, 1--28.
[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.
[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.
Index Terms
- MaD0: An Ultrafast Nonlinear Pseudorandom Number Generator
Recommendations
Bit-Wise Behavior of Random Number Generators
In 1985, G. Marsaglia proposed the m-tuple test, a runs test on bits, as a test of nonrandomness of a sequence of pseudorandom integers. We try this test on the outputs from a large set of pseudorandom number generators and discuss the behavior of the ...
Recycling random bits in parallel
HICSS '95: Proceedings of the 28th Hawaii International Conference on System SciencesShows that r pseudo-random bits can be obtained by concatenating t blocks of r/t pseudo-random bits, where the blocks are generated in parallel. This can be considered as a parallel version of R. Impagliazzo and D. Zuckerman's (1989) method of recycling ...
A Comparative Statistical Analysis of Pseudorandom Bit Sequences
IAS '09: Proceedings of the 2009 Fifth International Conference on Information Assurance and Security - Volume 02Many users applied built-in random generator for their cryptography applications which is simple and fast. However, the randomness of generated pseudorandom numbers (PRNs) is under questioned whether it can support the reliable security in secure ...
Comments
Information & Contributors
Information
Published In
January 2016
152 pages
ISSN:1049-3301
EISSN:1558-1195
DOI:10.1145/2875131
- Editor:
- Adelinde M. Uhrmacher
Copyright © 2016 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 06 January 2016
Accepted: 01 September 2015
Revised: 01 August 2015
Received: 01 January 2015
Published in TOMACS Volume 26, Issue 2
Check for updates
Author Tags
Qualifiers
- Research-article
- Research
- Refereed
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 216Total Downloads
- Downloads (Last 12 months)1
- Downloads (Last 6 weeks)0
Reflects downloads up to 24 Jan 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in