Abstract
Random number generator (RNG) is a fundamental and important cryptographic element, which has made an outstanding contribution to guaranteeing the network and communication security of cryptographic applications in the Internet age. In reality, if the random number used cannot provide sufficient randomness (unpredictability) as expected, these cryptographic applications are vulnerable to security threats and cause system crashes. Min-entropy is one of the approaches that are usually employed to quantify the unpredictability. The NIST Special Publication 800-90B adopts the concept of min-entropy in the design of its statistical entropy estimation methods, and the predictive model-based estimators added in the second draft of this standard effectively improve the overall capability of the test suite. However, these predictors have problems on limited application scope and high computational complexity, e.g., they have shortfalls in evaluating random numbers with long dependence and multivariate due to the huge time complexity (i.e., high-order polynomial time complexity). Fortunately, there has been increasing attention to using neural networks to model and forecast time series, and random numbers are also a type of time series. In our work, we propose several new and efficient approaches for min-entropy estimation by using neural network technologies and design a novel execution strategy for the proposed entropy estimation to make it applicable to the validation of both stationary and nonstationary sources. Compared with the 90B’s predictors officially published in 2018, the experimental results on various simulated and real-world data sources demonstrate that our predictors have a better performance on the accuracy, scope of applicability, and execution efficiency. The average execution efficiency of our predictors can be up to 10 times higher than that of the 90B’s for 10 6 sample size with different sample spaces. Furthermore, when the sample space is over 2 2 and the sample size is over 10 8 , the 90B’s predictors cannot give estimated results. Instead, our predictors can still provide accurate results. Copyright© 2019 John Wiley & Sons, Ltd.
Highlights
Random number generator (RNG) is a fundamental and important element in modern cryptography, which especially provides a basic guarantee for the security of the network and communication system, as in [1,2,3,4].e output of RNGs, called random number, is widely used in a large number of security and cryptographic applications. ese applications include the generation of cryptographic keys, initialization vectors in cryptographic algorithm, digital signature generation, and nonces and padding values
In order to guide the designers, users, and assessors to analyze the security of RNGs, many research organizations or individuals have provided a number of approaches for testing and evaluating the RNGs. ese approaches can be roughly divided into two classes: statistical property test and entropy estimation
We train our predictive models Feedforward neural networks (FNNs) and recurrent neural networks (RNNs) on a number of representative simulated data sources, of which the theoretical entropy can be obtained from the known probability distribution of the outputs
Summary
Random number generator (RNG) is a fundamental and important element in modern cryptography, which especially provides a basic guarantee for the security of the network and communication system, as in [1,2,3,4].e output of RNGs, called random number, is widely used in a large number of security and cryptographic applications. ese applications include the generation of cryptographic keys, initialization vectors in cryptographic algorithm, digital signature generation, and nonces and padding values. The statistical property test is proposed at first, such as the NIST Special Publication 800-22 [8], AIS 31 [9], Diehard battery [10], and TestU01 [11], which detects whether the output sequence has obvious statistical defects. Because it only focuses on the statistical properties of outputs rather than the internal structure and generation principle of RNGs, the statistical property test is a universal (black-box) testing method for various types of generators, and it is easy to operate. Min-entropy is a very conservative measure, which means the difficulty of guessing the most-likely output of entropy sources [13]
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