Abstract
Random Number Generators (RNGs) are essential for cryptographic systems and communication security. A cryptographic application is prone to have a serious security risk if the entropy source that generates the random number cannot provide sufficient randomness (unpredictability) as expected. The min-entropy is usually employed to evaluate the unpredictability, which measures the difficulty of guessing the most likely output of RNGs. Recently, predictors for min-entropy estimation are proposed in the NIST 800-90B (90B), which attempt to predict the next sample in a sequence based on all previous samples. However, these predictors have shortfalls in evaluating random number with long dependence and multivariate due to huge time complexity (i.e., high-order polynomial time complexity). From the concept of predictors, we provide several suitable and efficient predictors based on neural networks for min-entropy estimation. The neural networks apply to approximating the Probability Distribution Function (PDF) and have a linear complexity of the sample space. Compared to the 90B’s predictors, the experimental results on various simulated source demonstrate that our proposed predictors have a comparable accuracy, and the execution efficiency has a significant improvement. Furthermore, when the sample space is over \(2^2\) and sample size is over \(10^8\), the 90B’s predictors cannot give the estimated result. Instead, our proposed predictors still can provide an accurate result.
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References
Amaki, T., Hashimoto, M., Mitsuyama, Y., Onoye, T.: A worst-case-aware design methodology for noise-tolerant oscillator-based true random number generator with stochastic behavior modeling. IEEE Trans. Inf. Forensics Secur. 8(8), 1331–1342 (2013)
Aras, S., Kocakoç, I.D.: A new model selection strategy in time series forecasting with artificial neural networks: IHTS. Neurocomputing 174, 974–987 (2016). https://doi.org/10.1016/j.neucom.2015.10.036
Baudet, M., Lubicz, D., Micolod, J., Tassiaux, A.: On the security of oscillator-based random number generators. J. Cryptol. 24(2), 398–425 (2011)
Cai, X., Zhang, N., Venayagamoorthy, G.K., Wunsch II, D.C.: Time series prediction with recurrent neural networks trained by a hybrid PSO-EA algorithm. Neurocomputing 70(13–15), 2342–2353 (2007). https://doi.org/10.1016/j.neucom.2005.12.138
Donate, J.P., Li, X., Sánchez, G.G., de Miguel, A.S.: Time series forecasting by evolving artificial neural networks with genetic algorithms, differential evolution and estimation of distribution algorithm. Neural Comput. Appl. 22(1), 11–20 (2013). https://doi.org/10.1007/s00521-011-0741-0
Dorrendorf, L., Gutterman, Z., Pinkas, B.: Cryptanalysis of the random number generator of the windows operating system. ACM Trans. Inf. Syst. Secur. 13(1), 10:1–10:32 (2009)
Golic, J.D.: New methods for digital generation and postprocessing of random data. IEEE Trans. Comput. 55(10), 1217–1229 (2006)
Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016). http://www.deeplearningbook.org
de Groot, C., Würtz, D.: Analysis of univariate time series with connectionist nets: a case study of two classical examples. Neurocomputing 3(4), 177–192 (1991). https://doi.org/10.1016/0925-2312(91)90040-I
Gutterman, Z., Pinkas, B., Reinman, T.: Analysis of the linux random number generator. In: 2006 IEEE Symposium on Security and Privacy (S&P 2006), 21–24 May 2006, Berkeley, California, USA, pp. 371–385 (2006)
Hagerty, P., Draper, T.: Entropy bounds and statistical tests. https://csrc.nist.gov/csrc/media/events/random-bit-generation-workshop-2012/documents/hagerty_entropy_paper.pdf
ISO/IEC JTC 1/SC 27, Berlin, Germany: ISO/IEC 18031: Information technology - Security techniques - Random bit generation (2011)
Jain, A., Kumar, A.M.: Hybrid neural network models for hydrologic time series forecasting. Appl. Soft Comput. 7(2), 585–592 (2007). https://doi.org/10.1016/j.asoc.2006.03.002
Menezes Jr., J.M.P., Barreto, G.A.: Long-term time series prediction with the NARX network: an empirical evaluation. Neurocomputing 71(16–18), 3335–3343 (2008). https://doi.org/10.1016/j.neucom.2008.01.030
Kelsey, J., McKay, K.A., Sönmez Turan, M.: Predictive models for min-entropy estimation. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 373–392. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48324-4_19
Killmann, W., Schindler, W.: AIS 31: Functionality Classes and Evaluation Methodology for True (Physical) Random Number Generators. Version 3.1. T-Systems GEI GmbH and Bundesamt fr Sicherheit in der Informationstechnik (BSI), Bonn, Germany (2001)
Killmann, W., Schindler, W.: A design for a physical RNG with robust entropy estimators. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 146–163. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85053-3_10
Luna-Sanchez, J.C., Gómez-Ramírez, E., Najim, K., Ikonen, E.: Forecasting time series with a logarithmic model for the polynomial artificial neural networks. In: The 2011 International Joint Conference on Neural Networks, IJCNN 2011, San Jose, California, USA, 31 July–5 August 2011, pp. 2725–2732 (2011). https://doi.org/10.1109/IJCNN.2011.6033576
Ma, Y., Lin, J., Chen, T., Xu, C., Liu, Z., Jing, J.: Entropy evaluation for oscillator-based true random number generators. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 544–561. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44709-3_30
Menezes, A., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
NIST: The NIST Statistical Test Suite (2010). http://csrc.nist.gov/groups/ST/toolkit/rng/documents/sts-2.1.2.zip
Turan, M.S., Barker, E., Kelsey, J., McKay, K., Baish, M., Boyle, M.: (Second Draft) NIST special publication 800-90B: recommendation for the entropy sources used for random bit generation, January 2016. https://csrc.nist.gov/CSRC/media/Publications/sp/800-90b/draft/documents/sp800-90b_second_draft.pdf
Vanhoef, M., Piessens, F.: Predicting, decrypting, and abusing WPA2/802.11 group keys. In: 25th USENIX Security Symposium, USENIX Security 16, Austin, TX, USA, 10–12 August 2016, pp. 673–688 (2016)
Wieczorek, P.Z., Golofit, K.: Dual-metastability time-competitive true random number generator. IEEE Trans. Circuits Syst. 61–I(1), 134–145 (2014). https://doi.org/10.1109/TCSI.2013.2265952
Yang, J., Ma, Y., Chen, T., Lin, J., Jing, J.: Extracting more entropy for TRNGs based on coherent sampling. In: Deng, R., Weng, J., Ren, K., Yegneswaran, V. (eds.) SecureComm 2016. LNICSSITE, vol. 198, pp. 694–709. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59608-2_38
Zhu, S., Ma, Y., Chen, T., Lin, J., Jing, J.: Analysis and improvement of entropy estimators in NIST SP 800-90B for Non-IID entropy sources. IACR Trans. Symmetric Cryptol. 2017(3), 151–168 (2017)
Zhu, S., Ma, Y., Lin, J., Zhuang, J., Jing, J.: More powerful and reliable second-level statistical randomness tests for NIST SP 800-22. In: Proceedings Advances in Cryptology - ASIACRYPT 2016 - 22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, 4–8 December 2016, Part I, pp. 307–329 (2016)
Acknowledgments
This work was partially supported by National Natural Science Foundation of China (No. 61602476 and No. 61772518), and Cryptography Development Foundation of China (No. MMJJ20170205).
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Yang, J., Zhu, S., Chen, T., Ma, Y., Lv, N., Lin, J. (2018). Neural Network Based Min-entropy Estimation for Random Number Generators. In: Beyah, R., Chang, B., Li, Y., Zhu, S. (eds) Security and Privacy in Communication Networks. SecureComm 2018. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 255. Springer, Cham. https://doi.org/10.1007/978-3-030-01704-0_13
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