ABSTRACT
Chaotic Pseudo Random Number Generators have been seen as a promising candidate for secure random number generation. Using the logistic map as state transition function, we perform number generation experiments that illustrate the challenges when trying to do a replication study. Those challenges range from uncertainties about the rounding mode in arithmetic hardware over chosen number representations for variables to compiler or programmer decisions on evaluation order for arithmetic expressions. We find that different decisions lead to different streams with different security properties, where we focus on period length, but descriptions in articles often are not detailed enough to deduce all decisions unambiguously. Similar problems might, to some extent, appear in other types of replication studies for security applications. Therefore we propose recommendations for descriptions of numerical experiments on security applications to avoid the above challenges.
- Marcel Ausloos and Michel Dirickx (Eds.). 2006. The Logistic Map and the Route to Chaos. Springer, Berlin Heidelberg. https://doi.org/10.1007/3-540-32023-7Google Scholar
- Oded Goldreich. 2001. Foundations of cryptography I: Basic Tools. Cambridge University Press, Cambridge, UK.Google Scholar
- IEEE754 2019. IEEE Standard for Floating-Point Arithmetic. https://doi.org/10.1109/IEEESTD.2019.8766229 IEEE Standard 754-2019 (Revision of IEEE 754-2008).Google Scholar
- Jörg Keller and Hanno Wiese. 2007. Period Lengths of Chaotic Pseudo-Random Number Generators. In Proc. IASTED International Conference on Communication, Network, and Information Security (CNIS 2007). Acta Press, Calgary, Canada, 7 pages.Google Scholar
- Wolfgang Killmann and Werner Schindler. 2011. A proposal for: Functionality classes for random number generators. Report AIS 20/31 V2.0. Federal Office for Information Security / Bundesamt für Sicherheit in der Informationstechnik (BSI), Bonn, Germany.Google Scholar
- Ronald T. Kneusel. 2018. Random Numbers and Computers. Springer, Cham (CH).Google Scholar
- Israel Koren. 2001. Computer Arithmetic Algorithms(2nd ed.). Taylor & Francis, Milton Park, UK.Google ScholarDigital Library
- Ping Li, Zhong Li, Wolfgang A. Halang, and Guanrong Chen. 2007. A stream cipher based on a spatiotemporal chaotic system. Chaos, Solitons & Fractals 32, 5 (2007), 1867–1876. https://doi.org/10.1016/j.chaos.2005.12.021Google ScholarCross Ref
- Gerald Luber. 2014. Statistical Analysis of Outputs from Chaotic Pseudo Random Number Generators with Fixpoint Representation (in German: Statistische Analyse der Ausgaben von chaotischen Pseudozufallszahlengeneratoren mit Festkommadarstellung). Master thesis, FernUniversität in Hagen, Germany.Google Scholar
- George Marsaglia. 1995. The Marsaglia Random Number CDROM including the Diehard Battery of Tests of Randomness. Technical Report. Florida State University, Tallahassee, FL.Google Scholar
- Lena Oden and Jörg Keller. 2021. Improving Cryptanalytic Applications with Stochastic Runtimes on GPUs. In Proc. 11th International Workshop on Accelerators and Hybrid Emerging Systems (AsHES@IPDPS 2021). IEEE, New York, NY, 6 pages.Google ScholarCross Ref
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 ...
Resolution-stationary random number generators
Besides speed and period length, the quality of uniform random number generators (RNGs) is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F"2-...
Attacks on Pseudo Random Number Generators Hiding a Linear Structure
Topics in Cryptology – CT-RSA 2022AbstractWe introduce lattice-based practical seed-recovery attacks against two efficient number-theoretic pseudo-random number generators: the fast knapsack generator and a family of combined multiple recursive generators. The fast knapsack generator was ...
Comments