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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- 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.
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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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