Abstract
Ring oscillator-based true random number generators (RO-based TRNGs) are widely used to provide unpredictable random numbers for cryptographic systems. The unpredictability of the output numbers, which can be measured by entropy, is extracted from the jitter of the oscillatory signal. To quantitatively evaluate the entropy, several stochastic models have been proposed, all of which take the jitter as a key input parameter. So it is crucial to accurately estimate the jitter in the process of entropy evaluation. However, several previous methods have estimated the jitter with non-negligible error, which would cause the overestimation of the entropy. In this paper, we propose a jitter estimation method with high accuracy. Our method aims at eliminating the quantization error in previous counter-based jitter estimation methods and finally can estimate the jitter with the error smaller than \(1\%\). Furthermore, for the first time, we give a theoretical error bound for our jitter estimation. The error bound confirms the \(1\%\) error level of our method. As a consequence, our method will significantly help to evaluate the entropy of RO-based TRNGs accurately. Finally, we present the application of our jitter estimation method on a practical FPGA device and provide a circuit module diagram for on-chip implementation.
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Notes
- 1.
\((\sigma _s^{th})^2/4\) is equivalent to the quality factor Q defined in [1].
- 2.
Different \(f_{\mu _m}\)s are indicated by different colors as well as in following figures.
References
Baudet, M., Lubicz, D., Micolod, J., Tassiaux, A.: On the security of oscillator-based random number generators. J. Cryptol. 24(2), 398–425 (2011)
Fischer, V., Lubicz, D.: Embedded evaluation of randomness in oscillator based elementary TRNG. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 527–543. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44709-3_29
Haddad, P., Teglia, Y., Bernard, F., Fischer, V.: On the assumption of mutual independence of jitter realizations in P-TRNG stochastic models. In: Design, Automation & Test in Europe Conference & Exhibition, DATE 2014, Dresden, Germany, March 24–28, 2014, pp. 1–6 (2014)
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
Kollar, I.: Bias of mean value and mean square value measurements based on quantized data. IEEE Trans. Instrum. Meas. 43(5), 733–739 (1994)
Lundberg, K.H.: Noise sources in bulk CMOS (2002). http://www.mit.edu/people/klund/papers/UNP_noise.pdf
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
Ma, Y., Lin, J., Jing, J.: On the entropy of oscillator-based true random number generators. In: Handschuh, H. (ed.) CT-RSA 2017. LNCS, vol. 10159, pp. 165–180. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52153-4_10
Marsaglia, G.: The Marsaglia random number CDROM including the DIEHARD battery of tests of randomness. Diehard Tests (1995)
Rukhin, A., et al.: NIST SP800-22: a statistical test suite for random and pseudorandom number generators for cryptographic applications. http://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf
Sheppard, W.F.: On the calculation of the most probable values of frequency-constants for data arranged according to equidistant division of a scale. Proc. London Math. Soc. 29(1), 353–380 (1897)
Sripad, A.B., Snyder, D.L.: A necessary and sufficient condition for quantization errors to be uniform and white. IEEE Trans. Acoust. Speech Signal Process. 25(5), 442–448 (1977)
Sunar, B., Martin, W.J., Stinson, D.R.: A provably secure true random number generator with built-in tolerance to active attacks. IEEE Trans. Comput. 56(1), 109–119 (2007)
Valtchanov, B., Aubert, A., Bernard, F., Fischer, V.: Modeling and observing the jitter in ring oscillators implemented in FPGAs. In: Proceedings of the 11th IEEE Workshop on Design & Diagnostics of Electronic Circuits & Systems (DDECS 2008), Bratislava, Slovakia, April 16–18, 2008, pp. 158–163 (2008)
Acknowledgments
This work is supported by the Nation Key R&D Program of China (2018YFB0904900, 2018YFB0904901) and China’s National Cryptography Development Fund (No. MMJJ20170214, No. MMJJ20170211).
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Zhu, S., Chen, H., Fan, L., Chen, M., Xi, W., Feng, D. (2019). Jitter Estimation with High Accuracy for Oscillator-Based TRNGs. In: Bilgin, B., Fischer, JB. (eds) Smart Card Research and Advanced Applications. CARDIS 2018. Lecture Notes in Computer Science(), vol 11389. Springer, Cham. https://doi.org/10.1007/978-3-030-15462-2_9
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